© QUALITY COUNCIL OF INDIANA CQE 2006
INTRO-1 (1)
THE QUALITY ENGINEER PRIMER
Eighth Edition - September 1, 2006 © by Quality Council of Indiana - All Rights Reserved Bill Wortman Quality Council of Indiana 602 West Paris Avenue West Terre Haute, IN 47885 TEL: (812) 533-4215 FAX: (812) 533-4216
[email protected] http://www.qualitycouncil.com
003
© QUALITY COUNCIL OF INDIANA CQE 2006
INTRO-5 (2)
CQE PRIMER CONTENTS I. CERTIFICATION OVERVIEW . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . I-1 CQE BOK . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . I-6 II. MANAGEMENT &LEADERSHIP . . . . . . . . . . . . . . . . . . . . . . . . . . . II-1 QUALITY FOUNDATIONS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . II-2 QUALITY MANAGEMENT SYSTEMS . . . . . . . . . . . . . . . . . . . . II-22 STRATEGIC PLANNING . . . . . . . . . . . . . . . . . . . . . . . . . . . . II-22 STAKEHOLDERS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . II-33 BENCHMARKING . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . II-37 PROJECT MANAGEMENT . . . . . . . . . . . . . . . . . . . . . . . . . . II-40 QUALITY INFORMATION SYSTEMS . . . . . . . . . . . . . . . . . . II-51 ASQ CODE OF ETHICS. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . II-55 LEADERSHIP PRINCIPLES . . . . . . . . . . . . . . . . . . . . . . . . . . . . II-57 FACILITATION TECHNIQUES . . . . . . . . . . . . . . . . . . . . . . . . . . II-78 COMMUNICATION SKILLS . . . . . . . . . . . . . . . . . . . . . . . . . . . II-88 CUSTOMER RELATIONS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . II-95 SUPPLIER MANAGEMENT . . . . . . . . . . . . . . . . . . . . . . . . . . . II-103 BARRIERS TO QUALITY IMPROVEMENT . . . . . . . . . . . . . . . II-111 REFERENCES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . II-113 III.
QUALITY SYSTEMS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . III-1 QUALITY SYSTEM ELEMENTS . . . . . . . . . . . . . . . . . . . . . . . . III-2 QUALITY SYSTEM DOCUMENTATION . . . . . . . . . . . . . . . . . . III-8 QUALITY STANDARDS & GUIDELINES . . . . . . . . . . . . . . . . . III-19 ISO 9001:2000 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . III-22 MBNQA/BNQP . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . III-31 QUALITY AUDITS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . III-35 AUDIT TYPES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . III-37 AUDIT COMPONENTS . . . . . . . . . . . . . . . . . . . . . . . . . . . . III-44 COST OF QUALITY . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . III-52 QUALITY COST CATEGORIES . . . . . . . . . . . . . . . . . . . . . III-54 QUALITY COST BASES . . . . . . . . . . . . . . . . . . . . . . . . . . . III-60 QUALITY TRAINING . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . III-66 TRAINING NEEDS ASSESSMENT III-68 TRAINING EFFECTIVENESS . . . . . . . . . . . . . . . . . . . . . . . III-71 REFERENCES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . III-73
© QUALITY COUNCIL OF INDIANA CQE 2006
IV.
INTRO-5 (3)
PRODUCT & PROCESS DESIGN . . . . . . . . . . . . . . . . . . . . . . . IV-1 QUALITY CHARACTERISTICS . . . . . . . . . . . . . . . . . . . . . . . . . IV-2 DESIGN REVIEW . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . IV-6 DFSS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . IV-11 QFD . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . IV-17 ROBUST DESIGN . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . IV-20 DFX . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . IV-28 TECHNICAL DRAWINGS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . IV-32 GD&T DEFINITIONS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . IV-55 DESIGN VERIFICATION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . IV-61 RELIABILITY AND MAINTAINABILITY . . . . . . . . . . . . . . . . . . IV-64 PREVENTIVE MAINTENANCE . . . . . . . . . . . . . . . . . . . . . . IV-65 R&M INDICES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . IV-69 BATHTUB CURVE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . IV-79 HAZARD ASSESSMENT TOOLS . . . . . . . . . . . . . . . . . . . . IV-81 REFERENCES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . IV-96
V. PRODUCT & PROCESS CONTROL . . . . . . . . . . . . . . . . . . . . . . . . V-1 TOOLS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . V-4 CONTROL PLANS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . V-7 MATERIAL CONTROL . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . V-12 MATERIAL IDENTIFICATION . . . . . . . . . . . . . . . . . . . . . . . . V-12 MATERIAL SEGREGATION . . . . . . . . . . . . . . . . . . . . . . . . . V-14 CLASSIFICATION OF DEFECTS . . . . . . . . . . . . . . . . . . . . . V-20 MRB . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . V-21 ACCEPTANCE SAMPLING . . . . . . . . . . . . . . . . . . . . . . . . . . . . V-24 SAMPLING CONCEPTS . . . . . . . . . . . . . . . . . . . . . . . . . . . . V-24 SAMPLING STANDARDS . . . . . . . . . . . . . . . . . . . . . . . . . . . V-43 SAMPLING INTEGRITY . . . . . . . . . . . . . . . . . . . . . . . . . . . . . V-61 REFERENCES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . V-63 VI.
TESTING & MEASUREMENT . . . . . . . . . . . . . . . . . . . . . . . . . . VI-1 MEASUREMENT TOOLS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . VI-2 DEFINITIONS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . VI-38 DESTRUCTIVE TESTS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . VI-42 NONDESTRUCTIVE TESTS . . . . . . . . . . . . . . . . . . . . . . . . . . . VI-46 METROLOGY . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . VI-64 MEASUREMENT SYSTEM ANALYSIS . . . . . . . . . . . . . . . . . . VI-78 REFERENCES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . VI-89
© QUALITY COUNCIL OF INDIANA CQE 2006
VII.
INTRO-5 (4)
CONTROL & MANAGEMENT TOOLS . . . . . . . . . . . . . . . . . . . . VII-1 QUALITY CONTROL TOOLS . . . . . . . . . . . . . . . . . . . . . . . . . . . VII-2 FLOW CHARTS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . VII-6 HISTOGRAMS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . VII-11 PARETO DIAGRAMS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . VII-17 MANAGEMENT & PLANNING TOOLS . . . . . . . . . . . . . . . . . . VII-23 AFFINITY DIAGRAMS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . VII-24 MATRIX DIAGRAMS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . VII-30 PRIORITIZATION MATRICES . . . . . . . . . . . . . . . . . . . . . . . VII-34 ACTIVITY NETWORK DIAGRAMS . . . . . . . . . . . . . . . . . . . VII-36 REFERENCES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . VII-38
VIII. IMPROVEMENT TECHNIQUES . . . . . . . . . . . . . . . . . . . . . . . . VIII-1 IMPROVEMENT MODELS . . . . . . . . . . . . . . . . . . . . . . . . . . . . VIII-2 PDCA . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . VIII-3 SIX SIGMA . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . VIII-6 KAIZEN . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . VIII-11 LEAN TECHNIQUES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . VIII-12 TQM . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . VIII-29 CORRECTIVE & PREVENTIVE ACTIONS . . . . . . . . . . . . . . VIII-33 ROOT CAUSE ANALYSIS . . . . . . . . . . . . . . . . . . . . . . . . . VIII-42 MISTAKE PROOFING . . . . . . . . . . . . . . . . . . . . . . . . . . . . VIII-44 REFERENCES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . VIII-46 IX.
BASIC STATISTICS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . IX-1 COLLECTING DATA . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . IX-2 TYPES OF DATA . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . IX-2 MEASUREMENT SCALES . . . . . . . . . . . . . . . . . . . . . . . . . . IX-7 DATA COLLECTION METHODS . . . . . . . . . . . . . . . . . . . . . . IX-9 DATA ACCURACY . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . IX-12 DESCRIPTIVE STATISTICS . . . . . . . . . . . . . . . . . . . . . . . . IX-13 GRAPHICAL RELATIONSHIPS . . . . . . . . . . . . . . . . . . . . . IX-24 QUANTITATIVE CONCEPTS . . . . . . . . . . . . . . . . . . . . . . . . . . IX-33 STATISTICAL CONCLUSIONS . . . . . . . . . . . . . . . . . . . . . . IX-35 PROBABILITY TERMS . . . . . . . . . . . . . . . . . . . . . . . . . . . . IX-37 PROBABILITY DISTRIBUTIONS . . . . . . . . . . . . . . . . . . . . . . . IX-46 CONTINUOUS DISTRIBUTIONS . . . . . . . . . . . . . . . . . . . . . IX-46 DISCRETE DISTRIBUTIONS . . . . . . . . . . . . . . . . . . . . . . . . IX-61 REFERENCES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . IX-68
© QUALITY COUNCIL OF INDIANA CQE 2006
INTRO-5 (5)
X. STATISTICAL APPLICATIONS . . . . . . . . . . . . . . . . . . . . . . . . . . . . X-1 STATISTICAL PROCESS CONTROL . . . . . . . . . . . . . . . . . . . . . X-2 OBJECTIVES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . X-2 COMMON VS. SPECIAL CAUSES . . . . . . . . . . . . . . . . . . . . . X-4 RATIONAL SUBGROUPING . . . . . . . . . . . . . . . . . . . . . . . . . . X-8 CONTROL CHARTS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . X-11 CONTROL CHART ANALYSIS . . . . . . . . . . . . . . . . . . . . . . . X-37 PRE-CONTROL CHARTS . . . . . . . . . . . . . . . . . . . . . . . . . . . X-46 SHORT-RUN SPC . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . X-48 CAPABILITY . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . X-53 CAPABILITY STUDIES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . X-53 PERFORMANCE VS. SPECIFICATIONS . . . . . . . . . . . . . . . X-56 CAPABILITY INDICIES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . X-64 PERFORMANCE INDICIES . . . . . . . . . . . . . . . . . . . . . . . . . . X-67 REFERENCES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . X-68 XI.
ADVANCED STATISTICS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . XI-1 STATISTICAL DECISION MAKING . . . . . . . . . . . . . . . . . . . . . . XI-2 POINT ESTIMATES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . XI-3 CONFIDENCE INTERVALS . . . . . . . . . . . . . . . . . . . . . . . . . . XI-4 HYPOTHESIS TESTING . . . . . . . . . . . . . . . . . . . . . . . . . . . . XI-7 PAIRED-COMPARISON TESTS . . . . . . . . . . . . . . . . . . . . . XI-32 GOODNESS-OF-FIT TESTS . . . . . . . . . . . . . . . . . . . . . . . . XI-39 CONTINGENCY TABLES . . . . . . . . . . . . . . . . . . . . . . . . . . XI-46 ANALYSIS OF VARIANCE . . . . . . . . . . . . . . . . . . . . . . . . . . . . XI-50 RELATIONSHIPS BETWEEN VARIABLES . . . . . . . . . . . . . . . XI-60 LINEAR REGRESSION . . . . . . . . . . . . . . . . . . . . . . . . . . . . XI-60 SIMPLE LINEAR CORRELATION . . . . . . . . . . . . . . . . . . . . XI-70 TIME-SERIES ANALYSIS . . . . . . . . . . . . . . . . . . . . . . . . . . XI-73 DESIGN OF EXPERIMENTS . . . . . . . . . . . . . . . . . . . . . . . . . . XI-74 TERMINOLOGY . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . XI-76 PLANNING EXPERIMENTS . . . . . . . . . . . . . . . . . . . . . . . . XI-86 BLOCK EXPERIMENTS . . . . . . . . . . . . . . . . . . . . . . . . . . . XI-94 FULL-FACTORIAL EXPERIMENTS . . . . . . . . . . . . . . . . . . XI-97 FRACTIONAL FACTORIALS . . . . . . . . . . . . . . . . . . . . . . XI-101 OTHER EXPERIMENTS . . . . . . . . . . . . . . . . . . . . . . . . . . XI-108 REFERENCES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . XI-116
XII.
APPENDIX/INDEX. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . XII-1 ANSWERS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . XII-31
© QUALITY COUNCIL OF INDIANA CQE 2006
INTRO-6 (6)
CQE Primer Question Contents Questions Primer Section
%
Exam
Primer
CD
II. Management & Leadership
9.5%
15
38
95
III. Quality Systems
9.5%
15
38
95
IV. Product Design
15.5%
25
62
155
V. Product Control
10%
16
40
100
VI. Testing & Measurement
10%
16
40
100
VII. Control & Mgmt Tools
9%
14
36
90
9.5%
15
38
95
IX. Basic Statistics
9%
14
36
90
X. Stat Applications
8%
13
32
80
XI. Advanced Statistics
10%
16
40
100
100%
160
400
1000
VIII. Improvement Techniques
Total
Comparison B/T CQE Primer & ASQ BOK Primer ASQ BOK
II
III
IV
V
VI
VII
VIII
IX
X
I II III IV IV V V VI VI AºI AºF AºE AºC DºF A&B CºE AºC F&G
XI VI D, E, H
© QUALITY COUNCIL OF INDIANA CQE 2006
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I-1 (7)
CERTIFICATION OVERVIEW
Professionalizing Quality Education
I KNOW OF NO MORE ENCOURAGING FACT THAN THE UNQUESTIONABLE ABILITY OF MAN TO ELEVATE HIS LIFE BY A CONSCIOUS ENDEAVOR. HENRY DAVID THOREAU
© QUALITY COUNCIL OF INDIANA CQE 2006
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I-2 (8)
CERTIFICATION OVERVIEW
Preface This text is designed to be a Primer for those interested in taking the certification examination offered twice a year by the American Society for Quality. Test questions are provided at the end of each Section. These test questions and answers must be removed if this text is to be used as a reference during a certification examination. They are printed on blue paper for easy distinction.
2006 CQE Primer Notable Changes Overall: Primer expanded from 830 pages to 878 pages. There was a 12% replacement of questions. Added the new BOK and Bloom’s taxonomy. Section by section changes are noted in the Primer.
© QUALITY COUNCIL OF INDIANA CQE 2006
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CERTIFICATION OVERVIEW
Certified Quality Engineer Exam Objective To provide recognized quality engineer fundamental training and to prepare persons interested in taking the CQE examination. Certification Certification is the independently verified prescribed level of knowledge as defined through a combination of experience, education and examination. The Certified Quality Engineer Is a professional who can carry out in a responsible manner proven techniques which make up the body of knowledge recognized by those who are experts in quality technology.
© QUALITY COUNCIL OF INDIANA CQE 2006
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CERTIFICATION OVERVIEW
CQE Exam (Continued) Eligibility CQE participants must register with ASQ headquarters. Eligibility entails a combination of eight years work experience and/or higher education. Three years of this requirement must be in a decision making position. Cost The national test fee is determined by ASQ and is detailed in the CQE brochure. Location Proctors are provided by ASQ sections in your area. Duration The test lasts 5 hours and will begin at an advised time (typically 8 A.M.).
© QUALITY COUNCIL OF INDIANA CQE 2006
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CERTIFICATION OVERVIEW
CQE Exam (Continued) Other Details Can be obtained by calling ASQ headquarters at (800) 248-1946 or (414) 272-8575. They will send a CQE brochure free of charge. Bibliography Sources The reference sources recommended in the ASQ brochure are excellent. Four favorites are: (1) Juran's Quality Handbook (2) Western Electric's Statistical Quality Control Handbook (3) Gryna's Quality Planning and Analysis (4) Grant & Leavenworth's Statistical Quality Control ANSI/ASQ Z1.4 should be reviewed and taken into the exam. Other options are listed in the Primer.
© QUALITY COUNCIL OF INDIANA CQE 2006
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CERTIFICATION OVERVIEW
CQE Exam (Continued) Study The author recommends that this Primer be taught by a qualified CQE using classroom lecture, study assignments and a review of test questions. Training may vary from 27 hours to 48 hours. Additionally, the student should spend about 90 hours of individual study on the Primer, test questions, and other bibliography sources. If the student studies unaided, a minimum of 130 hours of preparation is suggested.
Exam Hints The CQE applicant should take into the exam:
C Several #2 pencils C A calculator (capable of determining standard deviation and natural log) C The CQE Primer (without test questions) C A recommended quality reference C ANSI/ASQ Z1.4-2003 C A good statistical reference (one the student knows) C Scratch paper
© QUALITY COUNCIL OF INDIANA CQE 2006
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CERTIFICATION OVERVIEW
Exam Hints (Continued) Arrive early, get a good seat, organize your materials. Answer all questions. There's no penalty for wrong answers. Save difficult questions until the end. Use good time management. If there are 160 questions on the 5 hour exam, one must average 1.88 minutes/question. Some tests begin with difficult questions, avoid panic. Keep test question numbers and the answer sheet aligned. Bring any exam errata to your proctor's attention. Mentally note weakness categories in case you have to take the exam again. ASQ will report only flagrant areas.
© QUALITY COUNCIL OF INDIANA CQE 2006
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CERTIFICATION OVERVIEW
ASQ CQE Body of Knowledge I. Management and Leadership (15 Questions) A. Quality Philosophies and Foundations Explain how modern quality has evolved from quality control through statistical process control (SPC) to total quality management and leadership principles (including Deming’s 14 points), and how quality has helped form various continuous improvement tools including lean, six sigma, theory of constraints, etc. (Remember) B. The Quality Management System (QMS) 1.
Strategic planning (Apply) Identify and define top management’s responsibility for the QMS, including establishing policies and objectives, setting organization-wide goals, supporting quality initiatives, etc.
© QUALITY COUNCIL OF INDIANA CQE 2006
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CERTIFICATION OVERVIEW
ASQ CQE BOK (Continued) 2.
Deployment techniques (Apply) Define, describe, and use various deployment tools in support of the QMS: benchmarking, stakeholder identification and analysis, performance measurement tools, and project management tools such as PERT charts, Gantt charts, critical path method (CPM), resource allocation, etc.
3.
Quality information system (QIS) (Remember) Identify and define the basic elements of a QIS, including who will contribute data, the kind of data to be managed, who will have access to the data, the level of flexibility for future information needs, data analysis, etc.
C. ASQ Code of Ethics for Professional Conduct Determine appropriate behavior in situations requiring ethical decisions. (Evaluate)
© QUALITY COUNCIL OF INDIANA CQE 2006
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CERTIFICATION OVERVIEW
ASQ CQE BOK (Continued) D. Leadership Principles and Techniques (Analyze) Describe and apply various principles and techniques for developing and organizing teams and leading quality initiatives. E.
Facilitation Principles and Techniques (Analyze) Define and describe the facilitator’s role and responsibilities on a team. Define and apply various tools used with teams, including brainstorming, nominal group technique, conflict resolution, force-field analysis, etc.
F.
Communication Skills
(Analyze)
Describe and distinguish between various communication methods for delivering information and messages in a variety of situations across all levels of the organization.
© QUALITY COUNCIL OF INDIANA CQE 2006
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CERTIFICATION OVERVIEW
ASQ CQE BOK (Continued) G. Customer Relations
(Analyze)
Define, apply, and analyze the results of customer relation measures such as quality function deployment (QFD), customer satisfaction surveys, etc. H. Supplier Management
(Analyze)
Define, select, and apply various techniques including supplier qualification, certification, evaluation, ratings, performance improvement, etc. I.
Barriers to Quality Improvement
(Analyze)
Identify barriers to quality improvement, their causes and impact, and describe methods for overcoming them.
© QUALITY COUNCIL OF INDIANA CQE 2006
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CERTIFICATION OVERVIEW
ASQ CQE BOK (Continued) II.
The Quality System( 15 Questions) A. Elements of the Quality System
(Evaluate)
Define, describe, and interpret the basic elements of a quality system, including planning, control, and improvement, from product and process design through quality cost systems, audit programs, etc. B. Documentation of the Quality System
(Apply)
Identify and apply quality system documentation components, including quality policies, procedures to support the system, configuration management and document control to manage work instructions, quality records, etc. C. Quality Standards and Other Guidelines (Apply) Define and distinguish between national and international standards and other requirements and guidelines, including the Malcolm Baldrige National Quality Award (MBNQA), and describe key points of the ISO 9000 series of standards and how they are used. [Note: Industry-specific standards will not be tested.]
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CERTIFICATION OVERVIEW
ASQ CQE BOK (Continued) D. Quality Audits 1.
Types of audits (Apply) Describe and distinguish between various types of quality audits such as product, process, management (system), registration (certification), compliance (regulatory), first, second, and third party, etc.
2.
Roles and responsibilities in audits Identify and define roles and responsibilities for audit participants such as audit team (leader and members), client, auditee, etc. (Understand)
3.
Audit planning and implementation (Apply) Describe and apply the steps of a quality audit, from the audit planning stage through conducting the audit, from the perspective of an audit team member.
4.
Audit reporting and follow up (Apply) Identify, describe, and apply the steps of audit reporting and follow up, including the need to verify corrective action.
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CERTIFICATION OVERVIEW
ASQ CQE BOK (Continued) E.
Cost of Quality (COQ)
(Analyze)
Identify and apply COQ concepts, including cost categories, data collection methods and classification, and reporting and interpreting results. F.
Quality Training
(Apply)
Identify and define key elements of a training program, including conducting a needs analysis, developing curricula and materials, and determining the program’s effectiveness. III. Product and Process Design (25 Questions) A. Classification of Quality Characteristics (Evaluate) Define, interpret, and classify quality characteristics for new products and processes. [Note: The classification of product defects is covered in IV.B.3.]
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CERTIFICATION OVERVIEW
ASQ CQE BOK (Continued) B. Design Inputs and Review
(Analyze)
Identify sources of design inputs such as customer needs, regulatory requirements, etc. and how they translate into design concepts such as robust design, QFD, and Design for X (DFX, where X can mean six sigma (DFSS), manufacturability (DFM), cost (DFC), etc.). Identify and apply common elements of the design review process, including roles and responsibilities of participants. C. Technical Drawings and Specifications (Evaluate) Interpret technical drawings including characteristics such as views, title blocks, dimensioning, tolerancing, GD&T symbols, etc. Interpret specification requirements in relation to product and process characteristics. D. Design Verification
(Evaluate)
Identify and apply various evaluations and tests to qualify and validate the design of new products and processes to ensure their fitness for use.
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ASQ CQE BOK (Continued) E.
Reliability and Maintainability
(Analyze)
1.
Predictive and preventive maintenance tools Describe and apply these tools and techniques to maintain and improve process and product reliability.
2.
Reliability and maintainability indices Review and analyze indices such as, MTTF, MTBF, MTTR, availability, failure rate, etc. (Analyze)
3.
Bathtub curve (Analyze) Identify, define, and distinguish between the basic elements of the bathtub curve.
4.
Reliability / Safety / Hazard Assessment Tools Define, construct, and interpret the results of failure mode and effects analysis (FMEA), failure mode, effects, and criticality analysis (FMECA), and fault tree analysis (FTA). (Analyze)
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CERTIFICATION OVERVIEW
ASQ CQE BOK (Continued) IV. Product and Process Control (32 Questions) A. Tools
(Analyze)
Define, identify, and apply product and process control methods such as developing control plans, identifying critical control points, developing and validating work instructions, etc. B. Material Control 1.
Material identification, status, and traceability Define and distinguish these concepts, and describe methods for applying them in various situations. [Note: Product recall procedures will not be tested.] (Analyze)
2.
Material segregation (Evaluate) Describe material segregation and its importance, and evaluate appropriate methods for applying it in various situations.
3.
Classification of defects (Evaluate) Define, describe, and classify the seriousness of product and process defects.
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ASQ CQE BOK (Continued) 4.
Material review board (MRB) (Analyze) Identify the purpose and function of an MRB, and make appropriate disposition decisions in various situations.
C. Acceptance Sampling 1.
Sampling concepts (Analyze) Define, describe, and apply the concepts of producer and consumer risk and related terms, including operating characteristic (OC) curves, acceptable quality limit (AQL), lot tolerance percent defective (LTPD), average outgoing quality (AOQ), average outgoing quality limit (AOQL), etc.
2.
Sampling standards and plans (Analyze) Interpret and apply ANSI/ASQ Z1.4 and Z1.9 standards for attributes and variables sampling. Identify and distinguish between single, double, multiple, sequential, and continuous sampling methods. Identify the characteristics of Dodge-Romig sampling tables and when they should be used.
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CERTIFICATION OVERVIEW
ASQ CQE BOK (Continued) 3.
Sample integrity (Analyze) Identify the techniques for establishing and maintaining sample integrity.
D. Measurement and Test
E.
1.
Measurement tools (Analyze) Select and describe appropriate uses of inspection tools such as gage blocks, calipers, micrometers, optical comparators, etc.
2.
Destructive and nondestructive tests Distinguish between destructive and nondestructive measurement test methods and apply them appropriately. (Analyze) Metrology
(Analyze)
Identify, describe, and apply metrology techniques such as calibration systems, traceability to calibration standards, measurement error and its sources, and control and maintenance of measurement standards and devices.
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ASQ CQE BOK (Continued) F.
Measurement System Analysis (MSA) (Evaluate) Calculate, analyze, and interpret repeatability and reproducibility (Gage R&R) studies, measurement correlation, capability, bias, linearity, etc., including both conventional and control chart methods.
V.
Continuous Improvement (30 Questions) A. Quality Control Tools
(Analyze)
Select, construct, apply, and interpret tools such as 1) flowcharts, 2) Pareto charts, 3) cause and effect diagrams, 4) control charts, 5) check sheets, 6) scatter diagrams, and 7) histograms. B. Quality Management and Planning Tools Select, construct, apply, and interpret tools such as 1) affinity diagrams, 2) tree diagrams, 3) process decision program charts (PDPC), 4) matrix diagrams, 5) interrelationship digraphs, 6) prioritization matrices, and 7) activity network diagrams. (Analyze)
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ASQ CQE BOK (Continued) C. Continuous Improvement Techniques (Analyze) Define, describe, and distinguish between various continuous improvement models: total quality management (TQM), kaizen, plan-do-check-act (PDCA), six sigma, theory of constraints (TOC), lean, etc. D. Corrective Action
(Evaluate)
Identify, describe, and apply elements of the corrective action process including problem identification, failure analysis, root cause analysis, problem correction, recurrence control, verification of effectiveness, etc. E.
Preventive Action
(Evaluate)
Identify, describe, and apply various preventive action tools such as errorproofing/poka-yoke, robust design, etc., and analyze their effectiveness.
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CERTIFICATION OVERVIEW
ASQ CQE BOK (Continued) VI. Quantitative Methods and Tools (43 Questions) A. Collecting and Summarizing Data 1.
Types of data (Apply) Define, classify, and compare discrete (attributes) and continuous (variables) data.
2.
Measurement scales (Apply) Define, describe, and use nominal, ordinal, interval, and ratio scales.
3.
Data collection methods (Apply) Describe various methods for collecting data, including tally or check sheets, data coding, automatic gaging, etc., and identify their strengths and weaknesses.
4.
Data accuracy (Apply) Describe the characteristics or properties of data (e.g., source/resource issues, flexibility, versatility, etc.) and various types of data errors or poor quality such as low accuracy, inconsistency, interpretation of data values, and redundancy. Identify factors that can influence data accuracy, and apply techniques for error detection and correction.
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CERTIFICATION OVERVIEW
ASQ CQE BOK (Continued) 5.
Descriptive statistics (Evaluate) Describe, calculate, and interpret measures of central tendency and dispersion (central limit theorem), and construct and interpret frequency distributions including simple, categorical, grouped, ungrouped, and cumulative.
6.
Graphical methods for depicting relationships Construct, apply, and interpret diagrams and charts such as stem-and-leaf plots, box-and-whisker plots, etc. [Note: Run charts and scatter diagrams are covered in V.A.] (Analyze)
7.
Graphical methods for depicting distributions Construct, apply, and interpret diagrams such as normal probability plots, Weibull plots, etc. [Note: Histograms are covered in V.A.] (Analyze)
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CERTIFICATION OVERVIEW
ASQ CQE BOK (Continued) B. Quantitative Concepts 1.
Terminology (Analyze) Define and apply quantitative terms, including population, parameter, sample, statistic, random sampling, expected value, etc.
2.
Drawing statistical conclusions (Evaluate) Distinguish between numeric and analytical studies. Assess the validity of statistical conclusions by analyzing the assumptions used and the robustness of the technique used.
3.
Probability terms and concepts (Apply) Describe and apply concepts such as independence, mutually exclusive, multiplication rules, complementary probability, joint occurrence of events, etc.
C. Probability Distributions 1.
Continuous distributions (Analyze) Define and distinguish between these distributions: normal, uniform, bivariate normal, exponential, lognormal, Weibull, chi square, Student’s t, F, etc.
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CERTIFICATION OVERVIEW
ASQ CQE BOK (Continued) 2.
Discrete distributions (Analyze) Define and distinguish between these distributions: binomial, Poisson, hypergeometric, multinomial, etc.
D. Statistical Decision-Making 1.
Point estimates and confidence intervals Define, describe, and assess the efficiency and bias of estimators. Calculate and interpret standard error, tolerance intervals, and confidence intervals. (Evaluate)
2.
Hypothesis testing (Evaluate) Define, interpret, and apply hypothesis tests for means, variances, and proportions. Apply and interpret the concepts of significance level, power, type I and type II errors. Define and distinguish between statistical and practical significance.
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ASQ CQE BOK (Continued) 3.
Paired-comparison tests (Apply) Define and use paired-comparison (parametric) hypothesis tests, and interpret the results.
4.
Goodness-of-fit tests (Apply) Define and use chi square and other goodness-of-fit tests, and interpret the results.
5.
Analysis of variance (ANOVA) (Analyze) Define and use ANOVAs and interpret the results.
6.
Contingency tables (Analyze) Define, construct, and use contingency tables to evaluate statistical significance.
E.
Relationships Between Variables 1.
Linear regression (Analyze) Calculate the regression equation for simple regressions and least squares estimates. Construct and interpret hypothesis tests for regression statistics. Use regression models for estimation and prediction, and analyze the uncertainty in the estimate. [Note: Non-linear models and parameters will not be tested.]
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CERTIFICATION OVERVIEW
ASQ CQE BOK (Continued) 2.
Simple linear correlation (Analyze) Calculate the correlation coefficient and its confidence interval, and construct and interpret a hypothesis test for correlation statistics. [Note: Serial correlation will not be tested.]
3.
Time-series analysis (Analyze) Define, describe, and use time-series analysis including moving average, and interpret time-series graphs to identify trends and seasonal or cyclical variation.
F.
Statistical Process Control (SPC) 1.
Objectives and benefits (Understand) Identify and explain objectives and benefits of SPC such as assessing process performance.
2.
Common and special causes (Analyze) Describe, identify, and distinguish between these types of causes.
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CERTIFICATION OVERVIEW
ASQ CQE BOK (Continued) 3.
Selection of variable (Analyze) Identify and select characteristics for monitoring by control chart.
4.
Rational subgrouping (Apply) Define and apply the principles of rational subgrouping.
5.
Control charts (Analyze) Identify, select, construct, and use various control charts, including X 6 - R, X 6 - s, individuals and moving range (ImR or XmR), moving average and moving range (MamR), p, np, c, u, and CUSUM charts.
6.
Control chart analysis (Evaluate) Read and interpret control charts, use rules for determining statistical control.
7.
PRE-control charts (Apply) Define and describe how these charts differ from other control charts and how they should be used.
8.
Short-run SPC (Apply) Identify, define, and use short-run SPC rules.
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CERTIFICATION OVERVIEW
ASQ CQE BOK (Continued) G. Process and Performance Capability 1.
Process capability studies (Analyze) Define, describe, calculate, and use process capability studies, including identifying characteristics, specifications, and tolerances, developing sampling plans for such studies, establishing statistical control, etc.
2.
Process performance vs. specifications Distinguish between natural process limits and specification limits, and calculate percent defective. (Analyze)
3.
Process capability indices (Evaluate) Define, select, and calculate Cp, Cpk, Cpm, and Cr, and evaluate process capability.
4.
Process performance indices (Evaluate) Define, select, and calculate Pp and Ppk and evaluate process performance.
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CERTIFICATION OVERVIEW
ASQ CQE BOK (Continued) H. Design and Analysis of Experiments 1.
Terminology (Understand) Define terms such as dependent and independent variables, factors, levels, response, treatment, error, and replication.
2.
Planning and organizing experiments Define, describe, and apply the basic elements of designed experiments, including determining the experiment objective, selecting factors, responses, and measurement methods, choosing the appropriate design, etc. (Analyze)
3.
Design principles (Apply) Define and apply the principles of power and sample size, balance, replication, order, efficiency, randomization, blocking, interaction, and confounding.
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CERTIFICATION OVERVIEW
ASQ CQE BOK (Continued) 4.
One-factor experiments (Analyze) Construct one-factor experiments such as completely randomized, randomized block, and Latin square designs, and use computational and graphical methods to analyze the significance of results.
5.
Full-factorial experiments (Analyze) Construct full-factorial designs and use computational and graphical methods to analyze the significance of results.
6.
Two-level fractional factorial experiments Construct two-level fractional factorial designs (including Taguchi designs) and apply computational and graphical methods to analyze the significance of results. (Analyze)
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CERTIFICATION OVERVIEW
Levels of Cognition ( 2001) Based on Bloom’s Taxonomy In addition to content specifics, the subtext for each topic in this BOK also indicates the intended complexity level of the test questions for that topic. These levels are based on “Levels of Cognition” (from Bloom’s Taxonomy – Revised, 2001) and are presented below in rank order, from least complex to most complex. Remember Recall or recognize terms, definitions, facts, ideas, materials, patterns, sequences, methods, principles, etc. Understand Read and understand descriptions, communications, reports, tables, diagrams, directions, regulations, etc. Apply Know when and how to use ideas, procedures, methods, formulas, principles, theories, etc.
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CERTIFICATION OVERVIEW
Levels of Cognition (Continued) Analyze Break down information into its constituent parts and recognize their relationship to one another and how they are organized; identify sublevel factors or salient data from a complex scenario. Evaluate Make judgments about the value of proposed ideas, solutions, etc., by comparing the proposal to specific criteria or standards. Create Put parts or elements together in such a way as to reveal a pattern or structure not clearly there before; identify which data or information from a complex set is appropriate to examine further or from which supported conclusions can be drawn.
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MANAGEMENT & LEADERSHIP
IF YOU DON'T KNOW WHERE YOU ARE GOING, YOU WILL PROBABLY END UP SOMEWHERE ELSE. LAURENCE J. PETER
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MANAGEMENT & LEADERSHIP QUALITY FOUNDATIONS
Management and Leadership Management and Leadership is presented in the following topic areas:
C C C C C C C C C
Quality foundations Quality management systems ASQ code of ethics Leadership principles Facilitation techniques Communication skills Customer relations Supplier management Barriers to quality improvement
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MANAGEMENT & LEADERSHIP QUALITY FOUNDATIONS
Quality Evolution There have been a number of hot quality topic areas that arrive, build, maintain, wane, and fade. In some cases, the topic disappears because of new technology or improved techniques. In many cases, the latest “craze” merely builds and expands on the best ideas that came before it. Some examples follow: Craftsmanship: A historic approach lasting from the middle ages until today (in certain applications). Standardization of parts: Beginning with Eli Whitney (1798 in the USA) and still continuing because of the need for the interchangeability of parts. Definition of a system: The scientific management technique is attributed to Fredrick Taylor (1911). There are some on-going applications today. Quality control: (1950s - 1960s). Originally associated with the proliferation of sampling plans, but continuing with modern applications such as control plans.
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MANAGEMENT & LEADERSHIP QUALITY FOUNDATIONS
Quality Evolution (Continued) Quality assurance: (1970s - 1980s). Included many preventative techniques, like SPC and quality cost measurement. Still in wide usage and still necessary. Total quality management: (1980s - 1990s). Built on the very best of prior concepts and added the key ingredient of management direction. Continuous quality improvement: (1980s - 2000s). Expanded the total quality management base, but recognized the advantages of project improvement teams and an on-going, organized, improvement structure. Six sigma: (lean six sigma). Emphasizes the reduction of variation, consideration of internal processes, concentration on the bottom line, utilization of advanced technical tools, use of a formalized problem solving approach (DMAIC), the elimination of internal wastes, and the need for key management leadership and support.
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MANAGEMENT & LEADERSHIP QUALITY FOUNDATIONS
Quality Evolution (Continued) There has been a vast array of other concepts:
C C C C C C C C C C C C C C C C C C C C C
Automated inspection Endorsement of international standards Competitive benchmarking Taguchi and other DOE approaches The use of statistical software Quality audits The recognition of the value of human resources Design techniques (DFSS, DFM, FEMA, DFP, etc.) The establishment of solid supplier relationships Attention to internal and external customers Quality function deployment (QFD) Rapid prototype development Award achievement (Deming prize, MBNQA) Theory of constraints (TOC) Kaizen techniques The use of color coded inventory control (kanban) Mistake proofing devices Awareness of measurement uncertainty Formalized documentation systems Quality circles/quality teams Manufacturing cells and flexible manufacturing
The above list is far from inclusive.
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MANAGEMENT & LEADERSHIP QUALITY FOUNDATIONS
Quality Philosophies and Approaches Guru
Contribution
Philip B. Crosby
Senior manager involvement 4 absolutes of quality management Quality cost measurements
W. Edwards Deming
Plan-do-study-act (wide American usage) Top management involvement Concentration on system improvement Constancy of purpose
Armand V. Feigenbaum
Total quality control/management Top management involvement
Kaoru Ishikawa
4M (5M) or cause-and-effect diagram Companywide quality control Next operation as customer
Joseph M. Juran
Top management involvement Quality Trilogy (project improvement) Quality cost measurement Pareto Analysis
Walter A. Shewhart
Assignable cause vs. chance cause Control charts Plan-do-check-act (in product design) Use of statistics for improvement
Genichi Taguchi
Loss function concepts Signal to noise ratio Experimental design methods Concept of design robustness
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MANAGEMENT & LEADERSHIP QUALITY FOUNDATIONS
Philip B. Crosby (1928 - 2001) Philip B. Crosby was the corporate vice president of ITT for 14 years. Mr. Crosby consulted, spoke, and wrote about strategic quality issues throughout his professional life. Awards: Fellow, ASQ Past president of ASQ Books: Quality Is Free (1979)12 The Art of Getting Your Own Sweet Way (1981) Quality Without Tears (1984)13 The Eternally Successful Organization (1988) Leading, the Art of Becoming an Executive (1990) Completeness Quality for the 21st Century (1992) Running Things (1992) Quality and Me: Lessons from an Evolving Life (1999) Statement on quality: Quality is conformance to requirements.
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MANAGEMENT & LEADERSHIP QUALITY FOUNDATIONS
Philip B. Crosby (Continued) Other quality deep thinkers could be viewed as academicians, but Crosby was considered a businessman. This explained the numbers of top management that flocked to his quality college. Crosby believed that quality was a significant part of the company and senior managers must take charge of it. He believed the quality professionals must become more knowledgeable and communicative about the business. Crosby stated that corporate management must make the cost of quality a part of the financial system of their company.
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MANAGEMENT & LEADERSHIP QUALITY FOUNDATIONS
Philip B. Crosby (Continued) Philip Crosby preached four absolutes of quality management: 1. Quality means conformance to requirements The requirements are what the customer says they are and “do it right the first time.” 2. Quality comes from prevention Correct problems in the system. 3. The quality performance standard is zero defects You must insist on zero defects. Otherwise, it is acceptable to send out nonconforming goods. 4. Quality measurement nonconformance
is
the
price
A measurement of quality is needed to get management’s attention.
of
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MANAGEMENT & LEADERSHIP QUALITY FOUNDATIONS
Philip B. Crosby (Continued) The four absolutes of quality management are basic requirements for understanding the purpose of a quality system. Philip Crosby also developed a 14 step approach to quality improvement: 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14.
Management commitment Quality improvement teams Measurement Cost of quality Quality awareness Corrective action Zero defects planning Employee education Zero defects day Goal setting Error cause removal Recognition Quality councils Do it all over again
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MANAGEMENT & LEADERSHIP QUALITY FOUNDATIONS
Dr. W. Edwards Deming (1900 - 1993) Education: B.S., University of Wyoming; M.S., University of Colorado; Ph.D., Physics, Yale. Awards: Shewhart Medal, ASQ, 1955 Second Order Medal of the Sacred Treasure, 1960 Honorary Member, ASQ, 1970, and numerous others. Books: Over 200 published papers, articles, and books. Quality, Productivity, and Competitive Position (1982) Out of the Crisis (1986) Statement on quality: He was the founder of the third wave of the industrial revolution.
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MANAGEMENT & LEADERSHIP QUALITY FOUNDATIONS
Dr. W. Edwards Deming (Continued) W. Edwards Deming was the one individual who stood for quality and for what it means. He is a national folk hero in Japan and was perhaps the leading speaker for the quality revolution in the world. He visited Japan between 1946 and 1948, for the purpose of census taking. He developed a fondness for the Japanese people during that time. JUSE (Japanese Union of Scientists and Engineers) invited Deming back in 1950 for executive courses in statistical methods. He refused royalties on his seminar materials and insisted that the proceeds be used to help the Japanese people. JUSE named their ultimate quality prize after him. Deming would return to Japan on many other occasions to teach and consult. He was well known in Japan, but not so in America. Only when NBC published its white paper, “If Japan can, why can’t we?” did America discover him. His message to America is listed in his famous 14 points and 7 deadly diseases.
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MANAGEMENT & LEADERSHIP QUALITY FOUNDATIONS
Dr. W. Edwards Deming (Continued) The Fourteen Obligations of Top Management: 1. Create constancy of purpose for improvement of products and service 2. Adopt a new philosophy; we are in a new economic age 3. Cease dependence upon inspection as a way to achieve quality 4. End the practice of awarding business based on price tag 5. Constantly improve the process of planning, production, and service - this system includes people 6. Institute training on-the-job 7. Institute improved supervision (leadership)
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MANAGEMENT & LEADERSHIP QUALITY FOUNDATIONS
Dr. W. Edwards Deming (Continued) The Fourteen Obligations of Top Management: 8. Drive out fear 9. Break down barriers between departments 10. Eliminate slogans/targets asking for increased productivity without providing methods 11. Eliminate numerical quotas 12. Remove barriers that stand between workers and their pride of workmanship; the same for all salaried people 13. Institute programs for education and retraining 14. Put a total emphasis in the company to accomplish the transformation
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MANAGEMENT & LEADERSHIP QUALITY FOUNDATIONS
Dr. Deming’s Profound Knowledge Dr. Deming’s profound following elements:
C C C C
knowledge
includes
the
Appreciation for a system Theory of variation Theory of knowledge Understanding psychology
The system of profound knowledge is a framework for applying management’s best efforts to the right tasks. It applies statistical principles to processes and systems. The theory of knowledge is needed for prediction. A knowledge of psychology is needed to deal with people.
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MANAGEMENT & LEADERSHIP QUALITY FOUNDATIONS
Seven Deadly Diseases That Management Must Cure: 1. Lack of constancy of purpose to plan a marketable product and service 2. Emphasis on short-term profits 3. Personal evaluation appraisal, by whatever name, the effects of which are devastating 4. Mobility of management; job hopping 5. Use of visible figures, with little or no consideration of figures that are unknown or unknowable 6. Excessive medical costs 7. Excessive costs of warranty, fueled by lawyers
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MANAGEMENT & LEADERSHIP QUALITY FOUNDATIONS
Other Deming Concepts Among other educational techniques, Deming promoted the parable of the red beads, the PDSA cycle, and the concept of 94% system variation (management controllable) versus 6% special variation (some of which may be operator controllable).
Deming’s Chain Reaction Deming shared the following chain reaction with Japan in the summer of 1950: Improve quality º decrease costs (less rework, fewer delays) º productivity Improves º capture the market with better quality and price º stay in business º provide jobs.
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MANAGEMENT & LEADERSHIP QUALITY FOUNDATIONS
Dr. Armand V. Feigenbaum (1920 -
)
Currently president of General Systems Company, Pittsfield, MA., Dr. Feigenbaum was associated with General Electric for 26 years. Education: B.S., Union College; M.S./Ph.D., MIT Awards: (A few shown) Honorary Member, ASQ, 1986 E. Jack Lancaster Award, ASQ, 1981 Edwards Medal, ASQ, 1965 Fellow, AAAS Life Member, IEEE and ASME 2-time president of ASQ 1961/63 Founding chairman, International Academy for Quality Books: Quality Control: Principles, Practice (1951) Total Quality Control (1961) Total Quality Control, 3rd ed. (1983) Total Quality Control, 40th Anniversary Edition (1991)18
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MANAGEMENT & LEADERSHIP QUALITY FOUNDATIONS
Dr. Armand V. Feigenbaum (Continued) Statement on total quality control: An effective system for integrating the quality development, quality maintenance, and quality improvements of the various groups in an organization so as to enable production and service at the most economical levels allowing for full customer satisfaction. Feigenbaum is generally given credit for establishing the concept of “total quality control” in the late 1940s at General Electric. His TQC statement was first published in 1961, but, at that time, the concept was so new, that no one listened. Feigenbaum states that the American industry must strive to become as strong as it can be in its own marketplace. This has become valuable as global competitiveness has spread into the U.S. Proper design, production, selling, and servicing will provide the potential for supremacy in the marketplace.
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MANAGEMENT & LEADERSHIP QUALITY FOUNDATIONS
Dr. Armand V. Feigenbaum (Continued) The TQC philosophy maintains that all areas of the company must be involved in the quality effort. The success of TQC includes these principles:
C C C C C C C C C C C
TQC is a companywide process Quality is what the customer says it is Quality and production costs are in partnership Higher quality will equate with lower costs Both individual and team zeal are required Quality is a way of managing, using leadership Quality and innovation can work together All of management must be involved in quality Continuous improvement is required Quality is an inexpensive route to productivity Both customers and suppliers must be considered
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Dr. Armand V. Feigenbaum (Continued) Listed below are selected quality phrases of A.V. Feigenbaum: “Quality does not travel under an exclusive foreign passport.” “Quality and costs are partners, not adversaries.” Failure driven companies... “If it breaks we’ll fix it.” versus the quality excellence approach... “No defects, no problems, we are essentially moving toward perfect work processes.” “Quality is everybody’s job, but because it is everybody’s job, it can become nobody’s job without the proper leadership and organization.”
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Dr. Kaoru Ishikawa (1915 - 1989) Education: B.S. in chemistry and Doctorate of Engineering University of Tokyo Awards: (A few are noted) Deming Prize (1952) Nihon Keizai Press Prize Industrial Standardization Prize Grant Award (ASQ) Shewhart Medal (ASQ), first Japanese to be awarded Honorary Member, ASQ (1986) Ishikawa Award (ASQ) (established in his honor) Books: Authored the first Japanese book to define TQC Guide to Quality Control (1982) What is Total Quality Control? The Japanese Way (1985)
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Dr. Kaoru Ishikawa (Continued) Statement on total quality control: To practice quality control is to develop, design, produce, and service a quality product that is most economical, most useful, and always satisfactory to the consumer. Abstract: Kaoru Ishikawa was involved with the quality movement in its earliest beginnings and remained so until his death in 1989. Ishikawa’s training tapes, produced in 1981, contain many of the statements of quality that are in vogue today. Subjects such as total quality control, next operation as customer, training of workers, empowerment, customer satisfaction, elimination of sectionalism and humanistic management of workers, are examples. To reduce confusion between Japanese style total quality control and western style total quality control, he called the Japanese method the companywide quality control (CWQC).
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Dr. Kaoru Ishikawa (Continued) There are 6 main characteristics that make CWQC different: 1. More education and training in quality control 2. Quality circles are really only 20% of the activities for CWQC 3. Participation by all members of the company 4. Having QC audits 5. Using the seven tools and advanced statistical methods 6. Nationwide quality control promotion activities CWQC involves the participation of workers from top to bottom of the organization and from the start to the finish of the product life cycle. CWQC requires a management philosophy that has respect for humanity. Kaoru Ishikawa was known for his lifelong efforts as the father of Japanese quality control efforts. The fishbone diagram is also called the Ishikawa diagram in his honor.
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Dr. Joseph M. Juran (1904 -
)
Founder and Chairman Emeritus of The Juran Institute. Education: B.S., University of Minnesota; J.D., Loyola University; and numerous honorary doctorates. Awards: Edwards Medal, ASQ Brumbaugh Awards, ASQ Grant Awards, ASQ Honorary Member, ASQ Plus 30 other medals and fellowships Books: 15 books, 40 videotapes Juran on Planning for Quality (1988) Juran on Leadership for Quality (1989) Juran on Quality by Design (1992) Quality Planning & Analysis (1993) Juran’s Control Handbook, 5th ed. (1999)
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Dr. Joseph M. Juran (Continued) Statement on quality: Adopt a revolutionary rate of improvement in quality, making quality improvements by the thousands, year after year. Dr. Juran also defined quality as fitness for use. Abstract: J.M. Juran started in quality after his graduation from engineering school with an inspection position at Western Electric’s Hawthorne plant in Chicago in 1924. He left Western Electric to begin a career in research, lecturing, consulting, and writing that has lasted over 50 years. The publication of his book...Quality Control Handbook, and his work in quality management, led to an invitation from JUSE in 1954. Juran’s first lectures in Japan were to the 140 largest company CEOs, and later to 150 senior managers. The right audience was there at the start.
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Dr. Joseph M. Juran (Continued) J.M. Juran has a basic belief that quality in America is improving, but it must be improved at a revolutionary rate. Quality improvements need to be made by the thousands, year after year. Only then does a company become a quality leader. Juran’s basics for success can be described as follows:
C Top management must commit the time and resources for success C CEOs must serve on the quality council (steering committee) C Specific quality improvement goals must be in the business plan and include: C The means to measure results against goals C A review of results against goals C A reward for superior quality performance C The responsibility for improvements must be assigned to individuals C People must be trained for improvement C The workforce must be empowered to participate
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Juran Trilogy Juran has felt that managing for quality requires the same attention that other functions obtain. Thus, he developed the Juran trilogy or quality trilogy which involves:
C Quality planning C Quality control C Quality improvement Juran sees these items as the keys to success. Top management can follow this sequence just as they would use one for financial budgeting, cost control, and profit improvement.
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Contrast of Big Q and Little Q Dr. Juran developed a mechanism for contrasting quality in the smaller tactical sense (little Q) with quality in the larger strategic sense (big Q). It provides an individual with an instant recognition of what is being defined. For instance:
C Having a team solve a specific process problem is a little Q item C Having teams throughout the company solve problems is a big Q item This methodology is often associated with quality cost analysis.
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Dr. Walter A. Shewhart (1891 - 1967) Education: B.S. and M.S., University of Illinois; Ph.D. in Physics, University of California Awards: Holley Medal, ASME Honorary Fellowship of the Royal Statistical Society First Honorary Member of ASQ Honorary Professor Rutgers University The Shewhart Medal is named in his honor Books: Articles in Bell System Technical Journal Economic Control of Quality of Manufactured Product (1931) Statistical Method from the Viewpoint of Quality Control (1939)
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Dr. Walter A. Shewhart (Continued) Quote: “Both pure and applied science have gradually pushed further and further the requirements for accuracy and precision. However, applied science, particularly in the mass production of interchangeable parts, is even more exacting than pure science in certain matters of accuracy and precision.” Abstract: Shewhart worked for the Western Electric Company. In 1924, Shewhart framed the problem in terms of “assignable cause” and “chance cause” variation and introduced the control chart as a tool for distinguishing between the two. Bringing a production process into a state of statistical control, where the only variation is chance cause, is necessary to manage a process economically.
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Dr. Walter A. Shewhart (Continued) Walter Shewhart’s statistical process control charts have become a quality legacy that continues today. Control charts are widely used to monitor processes and to determine when a process changes. Process changes are only made when points on the control chart are outside acceptable ranges. Dr. Deming stated that Shewhart’s genius was in recognizing when to act, and when to leave a process alone.
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The Shewhart Cycle The Shewhart cycle (PDCA) and the Deming cycle (PDSA) are very helpful procedures for improvement. This problem solving methodology can be used with or without a special cause being indicated by use of any statistical tool. What Shewhart actually contributed to this technique was a four stage product design cycle (with iterations) which Deming presented to the Japanese in 1951. This design cycle was adapted as a general problem solving technique by the Japanese. Deming in turn, modified the Japanese approach to a continual improvement spiral called PDSA. Deming gave credit for the technique to Shewhart, although there were one or more intermediate Japanese contributors.
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Dr. Genichi Taguchi ( 1924 -
)
Dr. Taguchi was the past director of the American Supplier Institute, Inc. He is called the “father of quality engineering.” Awards: Deming Prize, 1960 Rockwell Award, 1986 MITI Purple Ribbon Award, 1989 Indigo Award, Japan, 1989 ASME Medal, 1992 Books: System of Experimental Design, 2 volumes Introduction to Quality Engineering (1986) Off-line Quality Control (1979) Statement on quality: Quality is related to the financial loss to society caused by a product during its life cycle.
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Dr. Genichi Taguchi (Continued) Abstract: Quality engineering techniques were developed by Genichi Taguchi in the 1950s. The techniques enabled engineers to develop products and processes in a fraction of the time as required by conventional engineering practices. He made his first visit to the U.S. in the summer of 1980 to assist American industry in the pursuit of quality. In 1983, Ford and Xerox began to promote Taguchi’s system, both internally and among suppliers. Taguchi’s system was appealing because it was a complete system that started with the product concept and continued into design and then into manufacturing operations. It optimizes the design of products and processes in a cost-effective manner.
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Dr. Genichi Taguchi (Continued) Taguchi’s plan takes a different view of product quality: 1. The evaluation of quality Use the loss function and signal-to-noise ratio as ways to evaluate the cost of not meeting the target value. Taguchi feels the quality loss increases parabolically as the product strays from a single target value. 2. Improvement of quality and cost factors Use statistical methods for system design, parameter design, and tolerance design of the product. The methods could include QFD, signal to noise characteristics, and DOE (using orthogonal arrays). 3. Monitoring and maintaining quality Reduce the variability of the production line. Insist on consistency from the floor. Take measurements of quality characteristics from the floor and use the feedback.
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Dr. Genichi Taguchi (Continued) Taguchi methods and other design of experiment techniques have been described as tools that tell us how to make something happen, whereas most statistical methods tell us what has happened. The concept of robust products is now being explored in the design phase to reduce quality losses. Robustness derives from consistency. Robust products and processes demonstrate more insensitivity to those variables that are either difficult to control or noncontrollable. Building parts to target (nominal) is the key to success. One should work relentlessly to achieve designs that can be produced consistently and demand consistency from the factory.
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Strategic Planning A strategic plan should evolve from good sound strategic thinking. Strategic thinking is the process of considering the same key issues and concerns that the CEO and upper management use to help shape and direct the organization's future. The CEO and top management must decide what they want their company to look like at some point in the future. Some of the variables, that comprise strategic thinking include:
C C C C C
Current products Employee abilities Markets Competitors Suppliers
C C C C
Market segments R&D Facilities The environment
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Strategic Planning (Continued) Some of the critical issues that would arise from the strategic thinking process are:
C C C C C C C
Time frames Market share growth Product catalogs Investment needs Customer concerns Counters to external threats Quality
Planning includes an analysis and organization of key items, plus a logical implementation plan.
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Strategic Planning (Continued) A short outline of the strategic planning process should include the following:
C C C C C C C C
Develop a vision for the company Gather data on the environment in which it operates Assess corporate strengths and weakness Make assumptions about outside factors Establish appropriate goals Develop implementation steps Evaluate performance to goals Reevaluate the above steps for perpetual use
Strategic planning and decision making should enhance the health of the business.
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Organizational Performance Goals The organization performs many useful functions for its stakeholders. Stakeholders are parties or groups that have an interest in the welfare and operation of the company. These stakeholders include: stockholders, customers, suppliers, company management, employees and their families, the community and society. Organizational performance and the related strategic goals may be determined for:
C C C C C
Short-term or long-term emphasis Profit Cycle times Marketplace response Resources
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Performance Goals (Continued) The profit margin required to operate a business should be optimized for all stakeholder requirements. An optimal level of stockholder dividends, investments, personnel costs, and such, must be maintained. For maintaining competitiveness, a reduced product cycle time must be emphasized. This applies to both new product development and existing product lines. Reduced cycle times will affect such things as the company's inventory, WIP, waste, and efficiency. The marketplace response is an organizational performance measure. The ability to respond quickly to competitor quality, technology, product designs, safety features, or field service are collectively very important.
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Mission Statements A company mission statement will address how the company will realize its vision and strategic goals. A vision statement describes a future state, perhaps 5 to 10 years into the future. The company mission statement will also have concise statements of objectives to be achieved. A departmental mission statement concisely states how the strategic quality goals (and needs) of the organization will be implemented. Specific quantitative goals must be included in the mission statement. The quality professional must be able to supply or gather information to answer such questions as:
C What does the organization need? C What tasks can the department do? C How can the department help the organization? The end result is a departmental mission statement for use as an operating guide.
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Quality Principles The term “principles” means a basic foundation of beliefs, truths... upon which others are based. One method for the leaders (the quality manager and others) of the organization to gain “the truth.” A collective philosophy will be developed and shared with the organization. A common vision for the company will be developed and shared. In general, the total quality effort will stress some of the following points:
C C C C C C C C C
Customer satisfaction is a key Defects must be prevented Manufacturing assumes responsibility for quality The process must be controlled Every one participates in quality Quality is designed into the product TQ is a group activity Respect for humanity Adopt a revolutionary rate of quality improvement
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Quality Policies Quality policies are often developed by top management in order to link together policies among all departments. A document explaining the quality policy, responsibilities, rationale, and expected benefits should be explained to the company personnel. Some sample quality policies follow:
C C C C C C
The only acceptable level of defects is zero We will meet or exceed customer expectations Defective products will not be shipped We will not ship anything before its time We will build relationships with our customers We will ensure that quality is never compromised
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Strategic and Tactical Quality Goals Strategic quality goals should be of such an important nature that they will fit into the strategic business plan. All departments will have quality goals or sub-goals that come from the strategic business plan (which they then need resources to attack). For instance, the basic information could be divided into two groups:
C Those of a strategic nature: items that cut across many departments and/or are issues that are applicable companywide. C Secondly, tactical ones: the many detailed subgoals that are derived from strategic quality goals.
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Strategic Goals C C C C C C C
Company vision, mission statement, quality policy Shared total quality philosophy Effects of quality systems...ISO 9001, MBNQA, etc. Emergence of new competitors Highlights of new quality techniques and tools Uncontrollable environmental factors Field intelligence on the competition
Tactical Goals C C C C C
Status of customer complaints, returns Results of customer surveys, mailings In-house scrap, rework, defective rates Supplier ratings, deliveries Others that are important to an organization
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The Quality Department Role The quality department has a basic function in the organization: to coordinate the quality efforts. Historically, the organization needed the quality function to fill a narrow inspection-oriented role. While the needs of the company for a quality effort are met, the ultimate needs of the customer, are still often overlooked. The customer has become more sophisticated and demanding. The quality assurance department needs to develop its abilities to study process capabilities and make sure that key quality characteristics are under control. Purchasing, production, engineering, manufacturing, marketing, vendors, suppliers, and related staffs must work together to meet the quality requirements.
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Quality Department Role (Cont’d) Often a quality council or management steering team provides guidance and direction for the organization, the quality department will have responsibilities that support the improvement activities of the other departments in the organization. These activities may involve data collection, data analysis, product research, team building, feedback analysis from customers, market research, training, cross-functional planning, manufacturing engineering, purchasing, packaging, etc.
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Quality Department Role (Cont’d) Companywide problems could include:
C C C C C C C C
Process operations quality requirements Customer specifications from marketing Purchasing and supplier quality requirements R & D product designs Team building issues Quality cost data Quality information systems Quality planning
The other 20% of the quality problems may be internal to the quality department itself. These problems include:
C C C C C
Variation in lab tests Calibration of instruments and gages Sampling procedures Auditing procedures Inspection results
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The Quality Plan The overall strategic business planning follows a structured process. The process will define the purpose and goals for the company, and then add the follow through necessary to reach those goals. Quality planning, at the highest level of the organization, will provide more recognition and commitment to the quality effort. Quality planning, at the strategic level, can be described as strategic quality planning. For total quality to succeed, a structured process should be used. According to Juran, the process should include:
C C C C C C C
A quality council (steering committee) Quality policies Strategic quality goals Deployment of quality goals Resources for control Measurement of performance Quality audits
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Establish a Quality Council The quality council is a steering committee for the quality movement. The quality council has the responsibility for the growth, control, and effectiveness of total quality (TQ), as well as the incorporation of TQ into the strategic business plan. Some of the specific tasks of the quality council may include:
C C C C C
Develop an educational module Define quality objectives Refine the improvement strategy Determine and report cost of quality data Develop and maintain an awareness program
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Quality Policies Quality policies are guidelines that the organization's employees and management can follow. This is defined in ISO 9001:2000 (Element 5.3), which requires that top management not only develop an appropriate quality policy, but that it be communicated and understood throughout the organization. In general, quality policies should be concise and meaningful. A quality policy usually has statements that indicate a company will meet or exceed customer expectations, delight the customer, etc.
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Strategic Quality Goals Strategic quality goals may gain priority and emphasis from the quality council, as well as feedback from customers, top management or other organizational levels. The goals, determined to be of a strategic nature, become a part of the strategic business plan. The quality goals are specific, quantified, and scheduled. “We will achieve 95% ratings from all of our designated customers by August, 2007” would fit a quality goal definition. Quality goals may be linked to product performance, service performance, customer satisfaction, quality improvement, or cost of quality. Having quality goals placed in the strategic business plan, indicates to all employees that quality goals have special importance.
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Deployment of Quality Goals The word “deployment” means to spread out, to station, or to move in accordance with a plan. The quality council has the initial task of deploying (spreading out) the main strategic quality goals into bit-size pieces for the lower levels of the organization. As each level of the organization (function or team) receives its goals, it is expected that they should review their mission, capabilities, and resources. If the function or team requires additional resources or training, those things must be resolved to accomplish the required objective.
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Resources for Control For each goal, resources must be secured. The TQ structure must have a basic process for goal setting, goal deployment, training of personnel, goal tracking, goal evaluation and recognition of effort. Through tie-in to the strategic business plan, this may indicate that resources, in the form of additional staff help, equipment, or external staff, are required for a total quality effort to succeed. However, the quality manager has a vital role to play in this structure. The resources, to aid in the total quality effort, may be coordinated directly by the quality manager. Thus, he/she can provide assistance and guidance.
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Measurement of Performance A system is in place when the quality goals contained inside the strategic business plan are agreed upon, assigned to various sections (or teams) in the organization, and funded. The measurement of performance must then be addressed. Each level of the organization will regularly review their progress against the goals. This means that the senior executives with quality goals are measured, just as they are measured against earnings per share. At different levels of the organization, reviews are held to measure quality progress. These quality reviews should be held in conjunction with the reviews of other strategic goals.
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Quality Audits The quality audit is a necessary step in the process to provide independent and unbiased information to all of those who have a need to know. Top management, operating departments, and related staffs must know where the system stands in relation to a performance measure. The scope of an audit will be determined by the guidelines set forth by the quality council. Quality audits can be conducted through internal teams, outside auditors, upper managers, or by the president.
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Stakeholder Identification Businesses have many stakeholders including stockholders, customers, suppliers, management, employees (and their families), the community, and society. Each stakeholder has unique relationships with the business. some typical business – stakeholder relationships are shown below: SOCIETY
INTERNAL COMPANY PROCESSES
MANAGEMENT AND EMPLOYEES
CUSTOMERS
SUPPLIERS
STOCKHOLDERS OR OWNERS
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Stakeholder Analysis A project with high impact will bring about major changes to a system or to the entire company. The change can affect various people inside and outside of the system. Major resistance to the change can develop. As part of the define process, attempts to remove or reduce the resistance must be made. Stakeholders can be identified as:
C C C C C C C
Managers of the process People in the process Upstream people in the process Downstream people in the process Customers Suppliers Financial areas
A communication plan should involve the stakeholders and identify, on a scale, the level of commitment or resistance that the stakeholder is perceived to have.
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Performance Measurement Performance goals and corresponding measurements are often established in the areas of:
C C C C
Profit Cycle times Marketplace response Resources
Measurement methods and reporting units must be defined for each goal.
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Profit C C C C C C
Stockholder value Community comparison Capital investment Return on investment Personnel costs Sales dollars
Profit may be short-term (6 months or less) or long-term (2 years or more).
Cycle Times C C C C
Existing cycle times External benchmarks Internal benchmarks Reduction in cycle times
Ten fold reductions in cycle times are possible.
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Marketplace Response C C C C C C
Analysis of returns Customer losses Product development times Courtesy ratings Customer retention ratings Customer survey results
Resources C C C C C C
Number of improvement projects Reduction in variation Return on capital invested Cost of quality goals Process capability studies Percent defects
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Benchmarking Benchmarking is the process of comparing the current project, methods, or processes with the best practices and using this information to drive improvement of overall company performance. The standard for comparison may be a competitor within the industry but, quite often, is found in unrelated business segments.
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Process Benchmarking Process benchmarking focuses on discrete work processes and operating systems, such as the customer complaint process, the billing process, or the strategic planning process. This form of benchmarking seeks to identify the most effective operating practices from many companies that perform similar work functions.
Performance Benchmarking Performance benchmarking enables managers to assess their competitive positions through product and service comparisons. This form of benchmarking usually focuses on elements of price, technical quality, ancillary product or service features, speed, reliability, and other performance characteristics.
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Project Benchmarking Benchmarking of project management is easier than many business processes, because of the opportunities for selection outside of the group of direct competitors. Areas such as new product introduction, construction, or new services are activities common to many types of organizations. The projects will share the same constraint factors of time, costs, resources, and performance. Project management benchmarking is useful in selecting new techniques for planning, scheduling, and controlling the project.
Strategic Benchmarking In general terms, strategic benchmarking examines how companies compete. Strategic benchmarking is seldom industry-focused. It moves across industries seeking to identify the winning strategies that have enabled highperforming companies to be successful in their marketplaces.
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Benchmarking (Continued) Benchmarking as a continuous improvement process in which a company. Compares its own performance against:
C C C C C C C C
Best in class company performance Companies recognized as industry leaders The company’s toughest competitors Any known superior process
Determines how that performance was achieved Uses that information to improve Achieves the benchmarked performance Continually repeats the process
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Benchmarking (Continued) Shown below is a comparison between a typical and a breakthrough benchmark approach. Typical Benchmark
Time
Breakthrough Benchmark
Time
It should be noted that organizations often choose benchmarking partners who are not best-in-class, because they have identified the wrong partner or simply picked someone who is handy.
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Benchmarking Sequences Benchmarking activities often follow the following sequence:
C Determine current practices C C C C C
Select the problem area Identify key performance factors Understand your own processes Understand the processes of others Select criteria based on needs and priorities
C Identify best practices C Measure the performance within the organization C Determine the leader(s) in the criteria areas C Find an internal or external benchmark C Analyze best practices C C C C
Visit the organization as a benchmark partner Collect benchmark information and data Compare current practices with the benchmark Note potential improvement areas
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Benchmarking Sequences (Continued) C Model best practices C C C C C
Drive changes to advance performance Extend performance breakthroughs Use the new information in decision making Share results with the benchmark partner Seek other benchmarks for further improvement
C Repeat the cycle Juran presents the following examples of benchmarks (slightly modified) in an advancing order of attainment:
C C C C C
The customer specification The actual customer desire The current competition The best in related industries The best in the world
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Project Management A project is a series of activities and tasks with a specified objective, starting and ending dates and resources. Resources consumed by the project include time, money, people, and equipment. The elements of project management are:
C Planning C Scheduling C Controlling
- deciding what to do - deciding when to do it - ensuring the desired results
Project management includes project planning and implementation to achieve:
C C C C
Specified goals and objectives At the desired performance or technology level Within the time and cost constraints While utilizing the allocated resources
Well executed project plans meet all of the above criteria. Crashing programs to return a project to the specified time frame is done at the expense of higher costs and resource usage. Performance is measured on results, not effort.
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Time Lines The project time line is the most visible yardstick for measurement of project performance. The unit of measurement is time in minutes, hours, days, weeks, months, or years, and is readily understood by all participants on a project. The overall project has definite starting and ending dates, both planned and attained. Tasks within the project are assigned starting and ending times. As a performance tool, the project time line is updated with actual completion dates and adjustments made to compensate for early or late performance. From a quality viewpoint, both early and late projects have the opportunity for poor quality compared to the project completed on schedule.
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Resources Allocation of resources is part of the planning process. As each project activity is broken into smaller tasks, the resources are assigned to complete those tasks. Resource conflicts are resolved according to the circumstances in which they occur. Conflicts between two different projects for resources can be settled on the basis of priority of the project. Resource conflicts within tasks of a project are decided by the impact on the project completion date. If one task has available slack time, the timing of the need for the resource can often be adjusted. Resource leveling is used to smooth peaks and valleys in the demand for resources and spread the use more evenly over time. While monitoring both time and resource use during the project is important, the more significant performance measures of the project are the project completion date and the total costs. This is the “bottom line” for the project performance.
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Methodology Methods for planning, monitoring, and controlling projects range from manual techniques to computer programs. Advantages of manual project management methods include:
C C C C C
Ease of use and low cost Best for monitoring schedules and timing of events A hands-on feel for the project status Can be customized to the specific project needs Training requirements are minimal
Disadvantages of manual project management methods include:
C C C C C C
May not be transportable Project status is only available at one site Complex projects may be difficult to display Activities and resource conflicts may be missed Requires manual summarizing of the information It is harder to analyze final project results
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Methodology (Continued) Advantages of computer/automated management methods include:
C C C C C C
Able to model alternate options Presents the information in a variety of formats Various levels of detail can be displayed Critical path, slack times, etc. are automatic Project status reports are easier to generate Some data collection activities can be automated
Disadvantages of computer/automated management methods include:
C C C C C C
project
project
High learning curve for the user Higher initial costs Data entry and updating can be time consuming Poor data will be accepted by the computer The manager may lose touch with the project The environment may be computer friendly
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Network Planning Rules C Before an activity may begin, all activities preceding it must be completed. C Arrows imply logical precedence only. The length and compass direction of the arrows have no meaning. C Any two events may be directly connected by only one activity. C Event numbers must be unique. C The network must start at a single event, and end at a single event. Common applications of network planning include the Program Evaluation and Review Technique (PERT), the Critical Path Method (CPM), and Gantt charts.
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PERT The program evaluation and review technique (PERT) requirements are:
C All individual project tasks must be included. C Activities must be sequenced to determine the critical path. C Time estimates must be made for each activity in the network, and stated as three values: optimistic, most likely, and pessimistic elapsed times. C The critical path and slack times for the project are calculated. The critical path is the sequence of tasks which require the greatest expected time. The slack time, S, for an event is the latest date an event can occur without extending the project (TL) minus the earliest date an event can occur (TE). S = TL - TE For events on the critical path, TL = TE, and S = 0.
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PERT (Continued) Advantages of using PERT include:
C The planning required to identify the task information for the network and the critical path analysis can identify interrelationships between tasks and problem areas. C The probability of achieving the project deadlines can be determined, and by development of alternative plans, the likelihood of meeting the completion date is improved. C Changes in the project can be evaluated to determine their effects. C A large amount of project data can be organized and presented in a diagram for use in decision making. C PERT can be used on unique, non-repetitive projects.
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PERT (Continued) Disadvantages of using PERT include:
C The complexity of PERT increases implementation problems. C More data is required as network inputs. Each starting or ending point for activities on a PERT chart is an event, and is denoted as a circle with an event number inside. Events are connected by arrows with a number indicating the time duration required to go between events. An event at the start of an arrow must be completed before the event at the end of the arrow may begin. The expected time between events, te is given by:
te =
t o + 4t m + tp 6
Where: to is optimistic time, tm is most likely time, tp is pessimistic time.
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PERT (Continued) An example of a PERT chart for a company seeking ISO 9001 certification is shown in the Primer. Circles represent the start and end of each task. The numbers within the circles identify the events. The arrows represent tasks and the numbers along the arrows are the task durations in weeks.
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Critical Path Method (CPM) The critical path method (CPM) is activity oriented. Unique features of CPM include:
C The emphasis is on activities C The time and cost factors for each activity are determined C Only activities on the critical path are considered C Activities with the lowest crash cost are selected first C As an activity is crashed, it is possible for a new critical path to develop To complete the project in a shorter period, the activity with the lowest incremental cost per time saved is crashed first. The critical path is recalculated.
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CPM Example B .4
J .4
E .6 H .1
A. 4
I .6
F .4
C .8
K .2
L .1
M .3
G .1 2
D .3
CPM Example The critical path is indicated by the thicker arrows, along path A-C-F-I-K-L-M. TASK
ACTIVITY
0 A B C D E F G H I J K L M 10
ISO 9001 Certification Planning Select Registrar Write Procedures Contact Consultant Schedule Audit Write Quality Manual Consultant Advising Send Manual to Auditor Perform Training Auditor Review Manual Internal Audits ISO Audit Corrective Action Certification
DURATION weeks normal crash 4 3 4 3 8 6 3 1 6 5 4 3 12 9 1 1 6 4 4 3 2 1 1 1 3 2 Milestone
COST $ normal crash 2000 3000 1000 1200 12000 15000 500 700 200 1000 800 1200 9600 14400 100 100 9000 12000 1000 1250 600 750 10000 10000 1600 2000
COST/ WEEK CRASH 1000 200 1500 100 800 400 1600 1500 250 150 400
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CPM Example (Continued) The Primer shows the priority arrangement of crashing CPM activities, and their costs. The CPM time-cost trade-off represented graphically:
CPM Time-Cost Trade-off Example Crashing activities beyond the activity I, increases cost without further reduction in time.
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Gantt Charts (Bar Charts) Gantt charts (bar charts) display activities or events as a function of time. Each activity is shown as a horizontal bar with ends positioned at the starting and ending dates for the activity. Advantages of Gantt Charts include:
C C C C C
The charts are easy to understand Each bar represents a single activity It is simple to change the chart The chart can be constructed with minimal data Program task progress versus date is shown
Disadvantages of Gantt Charts include:
C They do not show interdependencies of activities C The effects of early or late activities are not shown (Note to rotate the chart on the following page, press: <Shft>
+ in Adobe Reader 7) (To return the orientation to portrait, press: <Shft>- in Adobe Reader 7)
: :
//// Summary Task
==// Summary Progress
End 20-Sep 31-Mar 28-Apr 12-Jun 1-Aug 26-May 26-Jun 3-Jul 8-Aug 21-Apr 18-Jul 22-Aug 29-Aug 20-Sep 21-Sep
Detail Task
Slack - Milestone * Current Date <<<< Conflict Path: C indicates critical path Scale: Each character is 5 work days or 1 week
Key:
Start 6-Mar 6-Mar 3-Apr 1-May 5-Jul 3-Apr 30-May 27-Jun 27-Jun 3-Apr 24-Apr 9-Aug 23-Aug 30-Aug 21-Sep
As of Date : March 20, 200X File name : ISO9001.TLX
. . Delay
PP Task Progress
Mar Apr May Jun JulAug Sep Duration Path 1 3 1 1 3 1 1 28 wks C ==////////////////////////// 4 wks C PP. . . . . . * . . . . . 4 wks 6 wks * . . . * . . . . . 4 wks * . . . . 8 wks C 4 wks C * . . . . . 1 wk * . . . . . * . . . . 6 wks C 3 wks * . . . . . 12 wks * . . 2 wks C * . . . . . . * . . . . . . 1 wk C * . . . . . 3 wks C Milestone C * . . . . . . -
ISO 9001 Certification Project Quality Assurance Manager
Task ISO 9001 Certification Planning Select Registrar Schedule Audit Auditor Review Manual Write Procedures Write Quality Manual Send Manual Perform Training Contact Consultant Consultant Advising Internal Audits ISO Audit Corrective Action Certification
Schedule Project Manager
II.
Gantt Chart Example
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Quality Information Systems A quality information system (QIS) is an organized method of collecting, storing, analyzing and reporting information on quality to assist decision makers at all levels. The purpose of an effective QIS is to achieve timely corrective action. The following is a limited outline of QIS. I. Introduction and scope: In the quality field, the only product is information. II. Plan the quality information system:
C C C C C C C
Define and publish the scope and objectives Define outputs and their uses Identify data inputs Flow chart the system Determine processing/analysis requirements Document the system Plan the training required for system usage
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Quality Information Systems (Continued) III. How a quality information system works:
C Data can be obtained from: C C C C C C C
Market research Product design evaluation and test data Purchased parts and materials Process data Final inspection data Field performance information Audit results
C Internal process information: C Is often the principle source of QIS data C Collected by quality information equipment C Adjustments can be manual or automatic C Data storage can be: C C C C
On forms In files In a computer memory In computer external storage system
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Quality Information Systems (Continued) C Data can be analyzed or processed by: C Sorting C Calculations C Manipulation C Quality data is often displayed in the following ways: C Historical (where we've been) C Current (where we are) C By simulation (for predict) C The results of the quality analysis should be reported to management for decision making.
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Quality Information Systems (Continued) IV. Considerations when information system:
establishing
a
quality
C Determine the need for quality feedback: C What is inspected? C Did the process or product meet specifications? C What were the statistically significant variations? C Evaluate the need for an information system using good management rules: C Compare cost of data required with the value of the information obtainable C Determine the type of system required: C Manual C Computer (offering faster retrieval and analysis) C Combination
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Quality Information Systems (Continued) V.For computerized systems, consider the following:
C Software is the instruction to the computer to: C C C C
Store Retrieve Analyze Report information
C Software is QIS documentation including: C Procedures and forms C Design and data packages C Logistics and training packages C Computer system availability can be via: C C C C
Central systems located elsewhere Batch processed internal systems On-line internal systems Combinations
C Good form design provides: C Easier readability, usage, and filing C Error avoidance C Economy - faster input and sorting
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Quality Information Systems (Continued) VI. For continued use, a quality information system should:
C Have data inputs that are timely and accurate C Have systems that allow for security and retrieval C Provide data analysis that is valid and reliable C Be audited periodically C Provide reports and outputs that are: C C C C
Accurate (as to facts) Timely (for decision making) Valid (as to information portrayal) Reliable (must meet user needs)
C Generate report formats which will typically: C C C C C
Show trends (via charts or graphs) Compare performance (to a desired standard) Compare information (to other bases or indexes) Identify the vital few problems (Pareto) Highlight exceptions to the desired results
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MANAGEMENT & LEADERSHIP ASQ CODE OF ETHICS
ASQ Code of Ethics Fundamental Principles ASQ requires its members and certification holders to conduct themselves ethically by: I. Being honest and impartial in serving the public, their employers, customers and clients. II. Striving to increase the competence and prestige of the quality profession, and III. Using their knowledge and enhancement of human welfare.
skill
for
the
Relations with the Public Article 1 - Hold paramount the safety, health, and welfare of the public in the performance of their professional duties. Relations With Employers and Clients Article 2 - Perform services only in their areas of competence.
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ASQ Code of Ethics (Continued) Article 3 - Continue their professional development throughout their careers and provide opportunities for the professional and ethical development of others. Article 4 - Act in a professional manner in dealings with ASQ staff and each employer, customer, or client. Article 5 - Act as faithful agents or trustees and avoid conflict of interest and the appearance of conflicts of interest. Relations With Peers Article 6 - Build their professional reputation on the merit of their services and not compete unfairly with others. Article 7 - Assure that credit for the work of others is given to those to whom it is due.
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MANAGEMENT & LEADERSHIP ASQ CODE OF ETHICS
Professional Conduct and Ethics A professional code of ethics guides individuals toward actions that produce the greatest good for all. A quality professional must possess high standards of ethical conduct. ASQ’s Code of Ethics is a guide for achieving this objective. Professional ethics take into account:
C C C C
Relations between professionals and society Relations between professionals and their clients Relations among professionals Relations between an employer and employee
The ASQ certification programs are established to upgrade the technical knowledge and competence of professionals through an examination and recertification process. This is one way to address Article 3 of the ASQ Code.
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MANAGEMENT & LEADERSHIP ASQ CODE OF ETHICS
Professional Conduct and Ethics (Cont’d) Quality professionals should be aware of situations in which a conflict of interest could develop. Examples of potential conflicts of interest include:
C Providing recommendations on the purchase of products while owning stock in that company. C Presenting results of an ISO 9001 pre-assessment to a client with a recommendation to use consulting services provided by your company. C Participating in the awarding of a contract to a private company founded by a close family member. A professional cannot expect any code of ethics to be complete, consistent, and correct for all situations. A quality professional must also develop and use an internal sense of ethics to resolve the conflicts that are presented in their personal and professional lives.
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Leadership Skills and Conduct Traditionally, leadership pertains, in great part, to the vertical chain of command. However, quality managers and engineers may make their greatest contributions by establishing and maintaining good relations with personnel outside their direct chain of command. There are numerous attributes with which quality professionals should possess if they are to be truly successful. The following skills are essential:
C Motivating subordinates. The quality professional must inspire and encourage employees, reconciling their individual needs with the objectives of the organization. C Developing and maintaining peer relationships. The ability of the quality professional to maintain good peer relations usually determines their effectiveness.
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Leadership Skills and Conduct (Cont’d) C Establishing networks for the dissemination of information. Quality professionals spend a large portion of their time on activities devoted to the transmission of information. C Carrying out negotiations. Quality managers and engineers will also spend a great deal of time in negotiations; they work with customers in identifying and meeting their needs, negotiate quality problems, work with marketing, etc. C Resolving conflicts. Although most quality professionals are in a decision making capacity, they also must handle disputes. C Securing and allocating resources. To ensure an adequate operating budget, quality professionals must not only be negotiators, but they must also have good general knowledge of the operating expenses of their departments.
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Leadership Skills and Conduct (Cont’d) C Making decisions. The essential attribute that a successful quality professional must have is the ability to use good judgment to make decisions. C Making effective use of time. Time is one of the most precious commodities of a quality professional. Time thieves include: C C C C C C
Indecision Failure to delegate Lack of confidence in the organization Devoting time to trivial matters Permitting a desire to weaken a principal purpose Dwelling on the negative rather than the positive
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MANAGEMENT & LEADERSHIP LEADERSHIP PRINCIPLES
Leadership Skills and Conduct (Cont’d) The qualities that make a successful leader are often difficult to measure. There is no complete list of leadership attributes upon which authorities completely agree. Some good fundamental attributes are listed below:
C C C C C C C
Congeniality Creativity Patience Fairness Persistence Honesty Decisiveness
C C C C C C C
Communication skills Resourcefulness Strength of character Knowledge and wisdom Good health Compassion Enthusiasm
Quality professionals have discovered that in order to effectively motivate others, they must use a variety of leadership styles. Different styles must be used with employees at different times, depending on the conditions and circumstances.
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MANAGEMENT & LEADERSHIP LEADERSHIP PRINCIPLES
Leadership Principles The phrase best used to collectively describe how quality goals and efficiencies are best obtained is “through the processes of leadership.” Leadership is primarily a human relations activity. It may be defined as the art of motivating, guiding, and directing people.
Motivation Certainly the most challenging management responsibility is how to both sustain and increase internal motivation in the work group. The quality professional should recognize that people do have certain needs in common, which may often be met in basically the same way.
Communication Important factors present in motivating subordinates are verbal and written communication skills.
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Team Introduction A participative style of management is the best approach to ensure employee involvement in the improvement process. Many workers have higher educational backgrounds and are eager to participate in the decision making process that affects them. There is no better way of motivating employees than to provide them with challenging jobs which make use of their talents and abilities. Improvement teams:
C Can usually tackle larger issues than individuals working alone C Can build a fuller understanding of the process needing improvement C Can have immediate access to the skills and knowledge of all members C Can rely on the support and cooperation of team members
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Team Empowerment Team empowerment is derived from the organization’s management authority. A team is empowered by virtue of that power granted to it by management. A team charter is a very useful tool for helping a team and management understand just exactly what the team is empowered to do.
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Team Objectives The team process can be a highly effective, peoplebuilding, potential-releasing, goal-achieving social system that is characterized by:
C C C C C C
A climate of high support An open communication process Organizational goal achievement Creative problem-solving Individual achievement Commitment
The fundamental purpose of establishing teams is to improve the internal and external efficiencies of the company. If teams are properly functioning, they will:
C C C C C C C C C
Improve employee morale Remove areas of conflict Develop creative skills of members Improve communication skills of members Develop problem solving techniques Improve attitudes of all parties Indicate to members that management will listen Demonstrate that employees have good ideas Improve management/employee relationships
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Team Objectives (Continued) Listed below are some of the reasons that teams have been successful:
C If management has sanctioned teams in the company, this means that management will be more apt to listen to employees and believe they have ideas worthy of implementation. C The team procedure allows all team members to communicate and exercise creative expression. C The concept of teams is supported by modern motivational theories: C Maslow’s higher level of human needs C McGregor’s Theory Y, which recognizes the worth of an individual C Herzberg’s theory that true motivation is found in the work itself
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Company Team Benefits Usually team members have diverse skills and experience and may represent various departments and functions within the organization. What they share in common is their involvement in the problem to be addressed. The benefits of a team approach are numerous. The most significant gains are usually achieved by teams – groups of individuals pooling their talents and expertise.
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MANAGEMENT & LEADERSHIP LEADERSHIP PRINCIPLES
Team Member Benefits Teamwork offers some obvious benefits to team members, including:
C C C C C C
An opportunity for understanding of work issues A chance to be creative and share ideas The opportunity to forge stronger relationships The opportunity to learn new skills A chance to work on a project with full support The satisfaction of solving a problem
Team members must:
C Have a reason to work together C Accept an interdependent relationship C Commit to team values
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Team Building Activities Three key characteristics of effective team building are mutual trust, respect, and support. Team members need to be coached in the need to trust and support each other. Support involves actively keeping an eye on the other team members and demonstrating a willingness to help each other out when help is needed--even when it might not be requested. Team members encourage each other to stretch beyond their comfort zone by offering advice or assistance when asked or when it is obvious that the fellow team member needs it.
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Team Resources The development of productive teams will use considerable resources. Resources are time, talents, money, information, and materials. Management must optimize the resources available to teams. The team charter is the best place to establish the team’s expectations concerning available resources.
The Project Charter A team or project charter will help:
C C C C C
To eliminate any confusion To define the subject boundaries To identify areas which should not be addressed To identify the deliverable product To provide a basis for team goal setting
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Management Support Management must give more than passive team support. This means that management, and especially midmanagement, must be educated to the degree that they are enthusiastic about the team concept. In order for teams to be successful, management must recognize that there will be additional work created by their efforts. Leaders, facilitators, and team members should be thoroughly trained. Management supports the team process by:
C C C C C C
Ensuring a constancy of purpose Reinforcing positive results Sharing business results Giving people a sense of mission Developing a realistic and integrated plan Providing direction and support
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Types of Teams The following types of teams are used by industries throughout the world today:
Six Sigma Teams The structure and functional roles of six sigma teams closely follow the description of project and ad hoc teams, with the addition of black belt support. Problem solving techniques, ranging from basic to sophisticated, are required.
Improvement Teams A group belonging to any department chooses to solve a quality/productivity problem. It will continue until a reasonable solution is found and implemented. The problem may be management selected, but the solution is team directed. For a process improvement team, employees may be drawn from more than one department.
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Project Teams/Ad Hoc Teams Members are selected based on their experience and directed by management to look into specific areas such as the modernization of a piece of equipment or solution to a customer complaint. These teams are generally ad hoc and disband upon the completion of their assignments.
Cross Functional Teams Cross functional teams are made up of individuals who represent different departments or functional areas in the organization. Individuals who represent a department or functional area should be subject matter experts. That is, they should be very knowledgeable about the practices of their functional areas.
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Self Directed Teams This type of team operates with minimal day-to-day direction from management. Self directed teams are asked to accomplish objectives within time frames that are truly stretch objectives. Management must give the team the maximum latitude possible for achieving their objectives.
Quality Circles The concept of circles originated in Japan after WW II. They were so successful in Japan that many managers in the United States tried to duplicate them. The circle is a means of allowing and encouraging people on the production floor to participate in decisions that will improve quality and/or reduce manufacturing costs. Department members voluntarily participate to improve departmental performance. Since membership is voluntary, people are highly motivated to continue the improvement process.
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MANAGEMENT & LEADERSHIP LEADERSHIP PRINCIPLES
Quality Teams The quality circle approach has been on the decline in the U.S. for some time. The fundamental purpose of establishing quality teams is to improve the internal efficiencies of the company and both internal and external products and service quality. This is done through the efforts of the team members to improve quality, methods, and/or productivity.
Natural Work Teams Natural work team leadership is usually given to the area supervisor. Members of teams come from the supervisor’s work force. Outside members, from specialist organizations, can be included in the membership, either as active members or as contributing guests. Often, a facilitator is an important person in this team’s organizational structure. He or she is specifically trained to coordinate multiple team activities, oversee team progress, document results, and train team members.
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Synopsis of Team Applications Team Type
Structure
Best Applications
May be 8 to 10 members from a single department
Can work on quality or productivity issues. A process improvement team can consist of multi-department membership and focus on process flow and product issues.
Quality Teams May be 8 to 10 members from a single department
May initially work on quality topics or overall department performance. Can evolve into self directed teams.
Project Teams Can have broad or specific member selection and may consist of all or part management.
Works on specific projects such as the installation of a conveyor system. Can also focus on material related items like an improved inventory control system. Usually disbands upon the completion of a project.
Six Sigma Teams
Generally 8 to 12 members with black belt or master black belt support
Works on specific process or customer based projects of importance. Usually disbands upon project completion.
Cross Functional Teams
8 to 12 members from different areas, departments, or disciplines
Members are carefully selected. Knowledgeable people are required. Very similar to project teams. Tends to deal more with policies, practices and operations.
Self Directed Teams
6 to 15 members. Generally a natural work area team and may need staff support
Requires considerable training and exposure. Can be given objectives or develop their own. Some companies select people with co-operative skills to help with success.
Improvement Teams
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The Leader Role Some teams have both leaders and facilitators. This is common for manufacturing line teams. As a general rule, the team leader focuses on the team product (the results) and the facilitator is most concerned with the team process. The team leader will:
C C C C C C C C C C C C C C
Provide direction and suggest assignments Act as a communication hub and liaison Handle administrative details Ensure that individual needs are considered Recommends agendas and conducts meetings Assess group progress to plan and initiate action Take the steps necessary to ensure success Possess an ability to encourage participation Be genuinely concerned about people Be encouraging and supportive Be accepting and tolerant of mistakes Work with, not over participants Stick to the task at hand Be a good listener
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The Team Member Role Each team member is responsible for:
C C C C C C C
Participating in training to become effective Attending team meetings, as required Completing assignments between meetings Participating actively during meetings Encouraging participation by other team members Benefitting from the expertise of others Applying the steps of the improvement process
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The Recorder Role The recorder/secretary is normally a full-fledged team member. The recorder maintains the team’s minutes and agendas. The recorder also coordinates the preparation and distribution of letters, reports, and other documents. Often, this duty is rotated.
The Timekeeper Role The timekeeper’s role is an optional responsibility. This function sometimes becomes the responsibility of the facilitator. The timekeeper:
C Advises team of the remaining meeting time C Enforces any time “norms” of the team
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Initial Project Selection Many improvement and self directed teams have the latitude to select their own projects. The following factors should be considered when selecting an initial project:
C It should have appeal to members and management C It should be fairly simple - but not trivial C It should show some quick benefit (3/4 months) C It should be within the group’s control C It should consider time and resource constraints C The two major activities are project resolution and learning teamwork. Management may define the project.
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Selecting Team Members When selecting a team, upper management identifies those parts of the organization that are associated most closely with the problem. There are four places to look:
C C C C
Where the problem is observed Where causes of the problem might be found Among those with special knowledge In areas that can help develop the remedy
Often a cross functional team is assembled to accomplish significant results in a short period of time. The best and brightest people the organization has to offer should be chosen.
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Team Size A team can consist of members from only one area or can be made up of a group of representatives from different parts of the organization. It is usually impractical to include every person who could be involved. Conventional wisdom is that teams over 20 people become too unwieldy and lose the active participation of all team members. Teams of 4 people or less may not generate enough ideas.
Team Diversity To achieve optimum performance a team often needs diversity in the orientation of its individual team members. Some team members are needed who are primarily oriented towards task and target date accomplishment. Other team members will be needed who hold process, planning, organization, and methods in the highest regard. Teams also need members who nurture, encourage, and communicate well. Teams will certainly need some members who are creative and innovative.
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Typical Team Operating Guidelines Team agenda
Who sets? When published? Input invited?, etc. Recorder to publish?
Attendance
Excused absences only? How are late comers handled? What membership is required to conduct business?
Meetings
Time, frequency, place?
Decision process
Consensus, collaborative, majority? Can one person remove an item?
Minutes and reports
Select a recorder. How are minutes approved? Where posted? Who types? How distributed? Is the recorder a volunteer?
Leader role
How defined? Expectations?
Behavioral norms
Interruptions; beepers, radios, and cell phones off; no smoking; breaks called at members discretion; empathetic listening; constructive feedback.
How selected?
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Team Operating Guidelines (Continued) Confidentiality
What can be discussed outside the group?
Guests
How invited? How excused?
Audits
How frequent? Who is responsible?
Facilitator
How selected? Expectations? How will this role differ from the leader?
Conflict
Expected? How managed?
Recommendations
How initiated? How routed? Who is informed?
Commitments
Follow through on commitments, analysis, word processing, etc.
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Team Meeting Structure Any effective team meeting needs logical structure. Listed below is an example format. 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12.
Develop an agenda Distribute the agenda in advance Start on time Appoint a recorder to record minutes Use visual aids liberally Reinforce participation and consensus Summarize and repeat key points throughout Put unfinished items on next agenda Review assignments and completion dates Finish on time Distribute minutes promptly Critique meeting effectiveness periodically
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Sample Meeting Forms Some simplified team meeting forms are shown in the Primer.
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Team Stages Most teams go through four development stages before they become productive: forming, storming, norming, and performing.
Forming Forming is the beginning of team life. Expectations are unclear. Members test the water. Interactions are superficial. This is the honeymoon stage. When a team forms, its members typically start out by exploring the boundaries of acceptable group behavior. Members looks to the team leader (or facilitator) for guidance as to his or her role and responsibilities.
Storming The second phase consists of conflict and resistance to the group’s task and structure. There are healthy and unhealthy types of storming. Conflict often occurs in the following major areas: authority issues, vision and values dissonance, and personality and cultural differences. However, if dealt with appropriately, these stumbling blocks can be turned into performance later. This is the most difficult stage for any team to work through. Teams realize feel overwhelmed. They want the project to move forward but are not yet proficient at team improvement skills.
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Team Stages (Continued) Norming During the third phase, a sense of group cohesion develops. Team members use more energy on data collection and analysis as they begin to test theories and identify root causes. Members accept other team members and develop norms for resolving conflicts, making decisions, and completing assignments. Conflicts are no longer as frequent and no longer throw the team off course. Scheduled team meetings give a sense of predictability and orientation. Norming is cultivated through team-building events and activities. Norming is a necessary transition stage. A team can’t perform if it doesn’t norm.
Performing This is the payoff stage. The group has developed its relationships, structure, and purpose. The team begins to tackle the tasks at hand. The team begins to work effectively and cohesively. During this stage, the team may still have its ups and downs. Occasionally, feelings that surfaced during the storming stage may recur.
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Team Stages (Continued) Performing Members: show maturity focus on the process achieve goals operate smoothly Norming Members: cooperate talk things out focus on objectives have fewer conflicts Storming Members: have confrontation think individually are learning roles have divided loyalties Forming Members are: inexperienced excited anxious proud Time
Adjourning At the end of some projects the team disbands. This step is called adjourning to rhyme with the four other team stages. Adjourning is also a very common practice for project teams, and ad hoc teams.
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Team Life Cycle Characteristics Shown below is another representation of team development stages.
Build Phase (Forming/Storming)
C C C C
Group will be uncertain Group lacks cohesiveness Group will not easily develop consensus Leader exhibits a high task/ high relationship style
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Team Life Cycle Characteristics (Cont’d) Develop Phase (Norming)
C C C C
Task related work is assumed by the group The group must involve non-participating members Leader exhibits a low task/high relationship style Team focuses on tasks, and relationships
Optimize Phase (Performing)
C C C C C
Members prioritize and perform tasks Members work out decisions in a caring way Conflict is accepted, but cooperation is preferred Team leader is a delegator Team exhibits a high task/high relationship style
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Well Functioning Teams Environmental Factors C Team members meet regularly C Adequate skills and authority levels are present C The team has management and worker support
Goal Factors C Team members help set objectives C Objectives are understood by all members C Objectives are set and met realistically
Role Factors C There is strong leadership with clear responsibilities C Roles are understood and supported by all C Members work as a team
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Well Functioning Teams (Continued) Relationship Factors C C C C C
There is a team identity There is an emphasis on conflict resolution Conflict is open; there is growth and learning Team members support each other Members enjoy each other
Process Factors C C C C C C C
Decisions are made by consensus Meetings are efficient and task oriented All members participate in discussions and meetings Members are kept informed Minutes are kept There is feedback regarding performance Members listen well
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Team Opposition In spite of the potential benefits, some people are skeptical of the long-term success of teams. These people point out that the traditional style of management in the typical American industry carries with it such momentum that the team approach will have little appreciable long-term effect.
Additional Team Problem Areas The following team problem areas must be addressed by leaders, facilitators, sponsors, and management:
C C C C C C C C C C C C C C C
There is waning management support. There is inadequate meeting documentation There is inadequate time or training allotted Exposed problems may threaten mid-management Facilitators and leaders controversies can develop Good facilitation skills may be hard to find Suggestion programs may add complications Labor unions may be resistance to team involvement Teams may tackle problems outside their areas Crisis management creates team scheduling problems A company’s reward system may be inconsistent Unproductive competition and conflict may occur Idea evaluation occurs too soon Facts and opinions are not distinguished There is a failure to assign member responsibilities
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Team Facilitation Many companies find facilitators useful both for team start-ups and for a variety of other team arrangements. Facilitators are useful in assisting a group in the following ways:
C C C C C C C C C C C C C C C C C
Identifying members of the group that need training Avoiding team impasses Providing feedback on group effectiveness Summarizing points made by the group Balancing group member activity Helping to secure resources that the team needs Providing an outside neutral perspective Clarifying points of view on issues Keeping the team on track with the process Helping with interpersonal difficulties that may arise Focusing on progress Assessing the change process Assessing cultural barriers (attitudes, personalities) Assessing group accomplishments Asking for feelings on sensitive issues Helping the leader to do his/her job more easily Coaching the leader and participants
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Team Facilitation (Continued) If there is no facilitator, the team leader, or an assigned coach, must assume many facilitator duties. The facilitator must avoid:
C Being judgmental of team members or their ideas, comments, opinions C Taking sides or becoming caught up in the subject matter C Dominating the group discussions C Solving a problem or giving an answer C Making suggestions on the task instead of on the process
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Team Facilitation (Continued) Facilitation and leadership requirements often diminish as leadership capability is developed within the team. Refer to the diagram below:
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Common Team Problems Problem
Examples
How to Fix
Floundering
C C C
Team direction is unclear Members seem overwhelmed Decisions are postponed
C C C
Leader must provide clarity Review the team purpose Ask “How can we proceed?”
Dominant Participants
C C
Members interrupt others Members dominate the conversation
C C
Promote equal participation Structure the discussion
Overbearing Participants
C C C
A member has excessive influence A member has legitimate authority A member is an “expert”
C C C
Reinforce team concepts Ask the expert to lead the group Have a private discussion with “expert”
Negative Nellies
C C C
Members say “we tried that already” Members defend their turf Members are negative of suggestions
C C C
Reinforce the positive Ask for other points of view Separate idea generation from criticism
Opinions as Facts
C C C
Members present opinions as facts Members make unfounded assumptions Self assurance seen as unquestionable
C C C
Ask for support data Question opinions and assumptions See groupthink discussion
Shy Members
C C
Members are reluctant to speak Members afraid of making mistakes
C C
Structure group participation Direct conversation their way
Jump to Solutions
C C C
Members rush to accomplish something Members avoid data collection and analysis Members want immediate decisions
C C C
Reinforce the need for data analysis Ask for alternate solutions Slow the process down
Attributions
C C C
Members make casual inferences Members don’t seek real explanations Members make psychological judgments
C C C
Challenge assumptions Challenge judgments Ask for data to support conclusions
Put-downs (Discounts & Plops)
C C C C
A member’s comments are ignored Members are not listening The meaning of a suggestion is missed Sarcasm is noted
C C C C
Encourage active listening Encourage equal participation Talk to parties privately Promote uniform idea consideration
Wanderlust (Tangents & Digressions)
C C C
Conversations stray from the main topic Sensitive issues are avoided Group pursues tangents
C C C
Follow a written agenda Reinforce team operating guidelines Redirect the discussion
Feuding
C C C
Win-lose hostilities emerge The team takes entrenched sides Some members become spectators
C C C
Confront the adversaries alone Reinforce team operating guidelines Replace the guilty parties if necessary
Risky-Shift
C
Expansive and expensive remedies are suggested (using company money)
C
Ask “If this were my personal money would I still spend it?”
All of the above problem areas can be minimized with proper team training and awareness.
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Facilitation Techniques A number of additional techniques are reviewed in the following material.
Brainstorming Brainstorming is an intentionally uninhibited technique for generating creative ideas when the best solution is not obvious. A facilitator or group leader is necessary for this activity. Some of the key aspects of brainstorming are discussed below:
C Generate a large number of ideas: Don’t inhibit anyone. Just let the ideas out. The important thing is quantity, but record the ideas one at a time. C Free-wheeling is encouraged: Even though an idea may seem half-baked or silly, it has value. It may provoke thoughts from others. C Don’t criticize: There will be ample time after the session to sift through the ideas for the good ones. During the session, do not criticize ideas because that might inhibit others.
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Brainstorming (Continued) C Encourage everyone to participate: Everyone thinks and has ideas. So allow everyone to speak up. Speaking in turn helps. C Record all the ideas: Appoint a recorder to write down everything suggested. Don’t edit the ideas, just jot them down as they are mentioned. Keep a permanent record that can be read later. C Let ideas incubate: Allow the subconscious mind to be creative. Give it time. Don’t discontinue brainstorming sessions too soon. Consider adding to the list at another meeting. C Select an appropriate meeting place: A place that is comfortable, casual, and the right size will greatly enhance a brainstorming session. C Group size: The ideal group size is 4-10 people. Brainstorming does not necessarily solve problems or create a corrective action plan. It can be effectively used with other techniques such as multivoting to arrive at a consensus as to an appropriate course of action.
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Nominal Group Technique The nominal group technique (NGT) brings people together to solve problems, but limits initial interaction among them. The concept is to prevent peer or social pressures from influencing the generation of ideas. Hence, the term “nominal” is used to describe the limiting of communications. To conduct a NGT problem solving meeting:
C A facilitator or moderator leads the discussion C A group of five to nine individuals are assembled C A problem is presented C Before any discussion, all members create ideas silently and individually. Usually they are noted on a sheet of paper. C The facilitator then requests an idea from each member in sequence. Each idea is recorded until ideas are exhausted.
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Nominal Group Technique (Continued) C Like brainstorming, no discussion is allowed at this point C The clarification, support, and evaluation of ideas is then permitted. Expanding on the ideas of others is encouraged. C Voting for the best solution idea is then conducted (rank ordering, priority ratings, etc.). Several rounds of voting may be needed. The facilitator should allow about 60 to 90 minutes for a problem solving session. As with brainstorming sessions, the facilitator should avoid trying to influence the problem solving process. The advantage of this technique is that the group meets formally, and yet encourages independent thinking.
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Multivoting Multivoting is a popular way to select the most popular or potentially most important items from a previously generated list. Often, there are too many items for a team to work on at a single time. It is often worthwhile to narrow the field to a few items worthy of immediate attention. Multivoting is useful for this objective and consists of the following steps: 1. Generate and number a list of items 2. Combine similar items, if the group agrees 3. If necessary, renumber the list 4. Allow members to choose several items that they feel are most important. Each member might have a number of choices equal to one-third of the total items on the list.
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Multivoting (Continued) 5. Members may make their initial choices silently and then the votes are tallied. This is usually done by a show of hands as each item is announced. 6. To reduce the list, eliminate those items with the fewest votes. Group size will affect the results. Items receiving 0-4 votes might be eliminated altogether. It should be noted that most problem solving teams can only work on two or three items at a time. The items receiving the largest number of votes are usually worked on or implemented first. The original list should be saved for future reference and/or action.
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Force Field Analysis A useful tool for problem identification and resolution is force field analysis. Eitington provides a description of the process used to perform a force field analysis: 1. The process starts with a desire to understand the forces acting on a goal 2. Determine the forces favoring the desired goal (driving forces) 3. Determine the opposing forces to the desired goal (restraining forces) 4. Add to the driving forces to overwhelm the restraining forces, or 5. Remove or weaken the restraining forces, or 6. Do both (strengthen driving forces and weaken restraining forces)
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Force Field Analysis (Continued) Consider an example of a force field analysis on reducing student smoking: Driving forces parental pressure peer pressure fear of addiction fear of cancer other bad effects taxes on smoking fire hazards in dorms advertising
Restraining forces free time peer pressure addiction exam time habit parties social status advertising
On the driving forces side, the government is forcing higher taxes on smoking. Tobacco advertisement has been severely restricted. Several high profile court cases have gone against the cigarette industry. On the restraining forces side, cigarettes advertisement on television, billboards, racing, or almost everywhere else is being banned.
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Conflict Resolution Conflict is the result of mutually exclusive objectives or views, manifested by emotional responses such as anger, fear, frustration and elation. Some conflicts are inevitable in human relationships. When one’s actions may be controlled by the actions of another, there is opportunity for conflict. Common causes of conflict include: • • • • • • • • • •
Organizational structure Value differences Role pressures Perceptual differences Divergent goals Status threats Personality clashes Differences in ideals Changes in procedures Discrepancies in priorities
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Conflict Resolution (Continued) Conflicts may be categorized as to the relationship between the parties involved in the conflict. The relative power or influence between parties is a factor both in the cause and the resolution of the conflict. Categories of conflicts are: • • • • • •
Intrapersonal - within an individual Interpersonal - between any two people Intragroup - within a group Intergroup - between groups Interdepartmental - between departments Intercompany - between companies
The results of conflicts may be positive in some instances, negative in some, and irrelevant in others. Irrelevant conflicts occur when the outcome has neither positive nor negative effects for either party.
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Conflict Resolution (Continued) Positive conflicts result in: • • • • • • • •
A combined desire to unite and improve Win - win situations Creative ideas brought forth Better understanding of tasks, problems Better understanding of other’s views Wider selection of alternatives Increased employee interest and participation Increased motivation and energy
Negative conflicts result in: • • • • • •
Hostile, impulsive drives to destroy Win - lose situations Lose - lose situations Undesirable consequences Isolation Loss of productivity
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Conflict Resolution (Continued) Individuals may use a number of ways to deal with conflicts depending upon the circumstances and the relationships involved. Whether a conflict resolution method is appropriate or effective will also depend on the situation. Conflict resolution can be depicted in a two dimensional model, adapted from the ThomasKilmann Conflict Mode Instrument:
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Conflict Resolution (Continued) • Avoiding is unassertive and uncooperative - the individual withdraws from the situation. (You lose, I lose). • Accommodating is unassertive but cooperative - the individual yields to the wishes of others. (You win, I lose). • Competing is assertive and uncooperative - the individual tries to win, even at the expense of others. (You lose, I win). • Collaborating is assertive but cooperative - the individual wants things done their way, but is willing to explore solutions which satisfy the other person’s needs as well. (You win, I win). • Compromising is intermediate in both assertiveness and cooperativeness - the individual is willing to partially give in to reach a middle position, splitting the differences, and partially satisfying both parties. (Neither win or lose). There is no specific right or wrong method for handling conflicts. The method that works best depends upon the situation.
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Communication Skills An effective quality professional must be a “communicator,” or must learn to be one. Motivating and collaborating with people are essential responsibilities. At the manager level, a professional will be the information hub for his/her department or team. The manager will operate as a:
C C C C C
Monitor of external information from peers or experts Monitor of internal information from subordinates Disseminator or distributor of information Spokesperson to outsiders Decision maker from gathered information
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Communication Skills (Continued) A manager, or group leader, will have many opportunities to process, receive, and pass on information. The four basic purposes of such communications are:
C To influence employees to work for the organization C To inform employees by providing necessary information for job performance C To control the organization’s progress toward the objectives C To inspire employees through displays of values, attitudes, or modeling
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Downward Flow of Communications Managers must relay information and give orders and directives to the lower levels. There are normally five types of information sent down through the channels:
C C C C C
Instructions for subordinates Rationale for the instructions The vision and mission of the company Policies and procedures of the company Performance feedback to the employees
It has been stated that information overload can be a problem for many employees. There is too much of it, and thus, the information is not retained. Furthermore, the lack of openness between managers and employees can be damaging. It takes time for the manager to keep subordinates informed. Another detractor in downward communications is the filtering process. A message from the highest officer of the company will be distorted greatly if it goes through multiple organizational layers.
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Upward Flow of Communications Upward communication consists of information relayed from the lower levels to the higher levels of the company. This gives the higher levels a chance to learn about what is happening in the lower levels. To encourage more reliable upward communications, top level managers can have open door policies, surveys, questionnaires, suggestion systems, breakfast meetings, shift meetings, and the like. Misleading information has many origins and causes. There are three important reasons why a manager may not receive accurate and complete information:
C Subordinates may withhold information that tends to discredit them. C There may be a tendency to tell a supervisor, what he or she wants to hear C An incumbent manager is not always surrounded by allies.
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Horizontal Communications Horizontal communication refers to the sharing of information across the same level of the organization. The production engineer shares information with production planning. The planning group, in turn, shares information with manufacturing. This is a very important part of the communications process.
Formal and Informal Communications Formal communications are official company sanctioned methods of communicating to the employees. Formal methods can occur up, down, or across the organization. The informal communication link in a company is the grapevine. This rumor mill can be either valuable or detrimental to communication flow. It is generally advisable to avoid it.
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Special Communication Roles Gatekeepers are described as individuals who are at the crossroads of communications channels. They are centers of information, normally because of their jobs. Boundary spanners are individuals who have positions that link them with others outside of their work units.
Communication Forms The spoken word via the telephone, face-to-face discussions, formal briefings, videotapes, and even the internet are forms of verbal communications. Examples of written communications include letters, reports, computer messages and e-mail. The written forms can be described as one-way channels. There are some forms of verbal communications that could be one-way, not two-way. This can occur with a highly directive boss. Face-to-face meetings generally allow for immediate feedback from the receiver to the sender.
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Communication Forms (Continued) There are a variety of nonverbal communication signals from people that the manager might be able to pick up on from a face-to-face or group meeting. The nonverbal signals include:
C Hand movements C Eye contact C Body posture
C Use of interpersonal space C Head movements C Leg positions
In the use of interpersonal space, certain cultures are comfortable with a set spacing. Note that not all verbal signals really mean what others claim them to mean. Although nonverbal signals can be spontaneous, some nonverbal signals are conscious and deliberate. The ability to explain and to clarify details have long been recognized as important abilities. Speaking and writing abilities are also essential for leadership success. Listening, the other half of the communication concept, has received far too little attention. Effective quality professionals have learned the art of listening.
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Communication Effectiveness Communication effectiveness includes:
C C C C C
Strategies Media choices Appropriate vehicles for different situations Open-ended and closed-response questioning Listening strategies
Media Choices The methods used to communicate ideas are:
C Verbal communication: in face-to-face discussions, meetings, phone conversations, speeches, etc. C Written communications: reports, memos, e-mail, letters, etc.
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Vehicles for Different Situations Reprimanding an employee should be done in private and is typically done verbally. Second or third offenses should be done in person with the employee and documented in writing with a copy given to the employee. Business agreements may be made verbally, but must always be followed with a letter to assure both parties have the same understanding of the agreement.
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Open-Ended and Closed-Responses Skillful questioning is of great value to the manager. Scholtes provides an initial framework of questions:
C What is the purpose of the project or job? C How do you know that you are making a difference? C What methods are you using? The use of open-ended questions will allow for some discussion and probing rather than just a simple “yes” or “no” answer. Examples are as follows:
C C C C C C C
Why? Ask “why” five times. What is the purpose? What will it take to accomplish the project? Will someone care? What is your theory on the subject? What data do you have? Where did your data come from?
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Listening Strategies Active listening is defined as helping find the source of problems or meanings. A passive listener will respond in a manner that will discourage the message sender from saying more, except defensively. Ten tips for good listening: 1. 2. 3. 4. 5. 6. 7. 8. 9. 10.
Stop talking Put the message sender at ease Show that you want to listen Remove listening distractions Empathize with the person Be patient with your response Hold your own temper Avoid argument and criticism Ask questions Stop talking
Most people would rather hear themselves speak as opposed to listening to someone else. The good news is listening skills can be learned.
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Communications in a Global Economy In today’s global economy there is an ever increasing need to communicate with customers, suppliers, and colleagues abroad. It has been stated, in a business sense, the world is no longer round (spherical), it is flat. The major advance in this area is the increased use of the high speed internet.
Language Issues Other than an abundance of national and local tariffs, there is no greater restriction on international business than language. The following precautions should be considered for correspondence:
C C C C C C C C C
Avoid words that have multiple meanings Maintain consistency of terminology Stick to a logical sequence of events Do not use complex or compound sentences Do use simple direct sentences Avoid abbreviations, acronyms, and contractions Avoid puns, slang, and idiomatic expressions Be especially careful with contract language Avoid Latin abbreviations (e.g., i.e., etc.)
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Time Zones For virtual team meetings, hand-off international business activities, and synchronous on-line discussions, time can be especially critical. Even with certain asynchronous e-mail correspondence, an awareness of time (or timing) can be critical. Routine email transmission between the U.S. and Korea or India can easily delay shipments by two days. The best advice is to maintain consistency in response times. In the case of international work teams working on the same or similar service or manufacturing functions, this can entail a pre-set, transition time. In certain selected areas such as finance, stock trading, and commodity futures, speed can be an overwhelming competitive advantage. Time, in this case, relates to when markets are open.
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Cultural Considerations E-business or B2B commerce must be aware of cultural differences. Certainly any form of prejudice or discrimination must be avoided. Some considerations:
C There can be wide differences in syntax and discourse patterns. C Technology can vary in availability and acceptance. C Charts and videos can be useful. C Making language and intentions visible helps. C There are worldwide differences in food, drink, and fashion. In some cases these should be considered and in other cases they should be avoided. C Religion and human rights issues are often sensitive areas and should be avoided. C Cultural considerations can have an impact on both timing issues and business practices. C Many companies design programs to help employees bridge the cultural gap with co-workers.
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Customer Relations Everything starts and ends with customers. Customers define quality and set expectations. They rightfully expect performance, reliability, competitive prices, ontime delivery, service, and clear and accurate transactions. To succeed, a business must identify their appropriate market focus. They can do this best by identifying their customers and determining their requirements. There are two main types of customers: external and internal. The relationship that management can develop with either basic type will affect the company’s ability to be effective in delivering customer satisfaction.
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Internal Customers An internal customer can be defined as anyone in the company who is affected by the product or service as it is being generated. The internal customer is sometimes forgotten. Research has shown that management practices which relate to employee satisfaction, will also impact customer satisfaction. Internal employee communications can be improved through the following options:
C C C C C C C
Company newsletters: Corporate news Story boards: A board display, memos, letters, etc. Team meetings: Share business news Posting customer letters Staff meetings: Share the information Display of goals, progress charts, etc. Quality awards from suppliers
To stay competitive in this environment, training of the entire workforce is required. Employee surveys can serve as a tool for overall improvement.
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External Customers External customers include three types: end users, intermediate customers, and other impacted parties. External customers may be segmented in many ways in an attempt to better understand their requirements and identify possible market niches. Once a customer purchases a service or a product from the company, the work should start to retain them for further purchases. The value of a loyal customer is not measured on the basis of one gigantic purchase, but rather on his/her lifetime worth. Listening to the customer results in information on customer expectations, priorities of expectations, and needs.
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External Customers (Continued) The customer’s expectations of the product can be described through an analogy similar to Maslow’s hierarchy of human needs.
C Basic: The bare essential attributes of the product or service should be present. C Expected: Some additional attributes will be provided as a part of the product. C Desired: These are attributes that are worthwhile to have, but not necessarily provided as part of the package. C Unanticipated: These are surprise attributes that go beyond what the customer expects from a purchase.
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External Customers (Continued) Customer needs are not stable, and continually change. A product or service that satisfied a certain need may generate new needs for the customer. As the customer obtains a suitable product or service, the basic needs are fulfilled, and they will look for new attributes. Juran lists customer needs as follows:
C Stated needs: What the customers say they want (a car) C Real needs: What the customer really wants (transportation) C Perceived needs: What the customer thinks is desired (a new car) C Cultural needs: Status of the product (a BMW) C Unintended needs: The customer uses the product in an unintended manner. (a BMW used to haul concrete blocks)
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Instruments to Gather Customer Data Some of the instruments available for the purpose of collecting customer information are described below:
C Surveys: A properly designed questionnaire gathers data using a consistent set of standardized questions. Usually, a sample is selected for use. C Focus groups: A small group (3 to 12 typically) of individuals is assembled to explore specific topics and questions. A time of 1 to 2 hours is normal. C Face-to-face interviews: Individual interviews of 30 to 60 minutes in length may be used. C Satisfaction/complaint cards: The return of a card prompts a reaction by the company. C Dissatisfaction sources: Some methods that voice dissatisfaction include: complaints, claims, refunds, recalls, returns, litigation, replacements, downgrades, warranty work, misshipments, etc. C Competitive shopper: Shoppers evaluate the company and competitors. CEOs may call their own offices to measure the ease of customer access.
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Customer Surveys Research on customer satisfaction can be worthwhile in helping the company efforts. The objectives of customer research vary, but a few major themes are noted below:
C C C C C
To determine what quality is To find out what competitors are doing To define quality performance measures To identify factors to give a competitive edge To identify urgent problems
Surveys can be developed in questionnaire form. An adequate number would range from 25 to 30 questions.
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Customer Surveys (Continued) For an L-Type matrix survey, the use of a numerical scale from 1 (very dissatisfied) to 10 (very satisfied) can make it easier to quantify the results Customer Satisfaction Very Dissatisfied Task
1
2
3
4
5
Very Satisfied 6
7
8
9
10
On Schedule Good Product Friendly Prompt
Scores from survey forms can be accumulated using a variety of Likert scales. If a number can be ascribed to a product or service, then that attribute can be evaluated for changes and trends. A well designed and properly executed survey can be a help to the company.
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Customer Surveys (Continued) There can be problems in the use of surveys:
C Improper survey form design or poorly defined issues C Sampling errors or poor sampling techniques C Ignoring nonresponses C Using incorrect analysis methods C Failing to ask the right questions C Ignoring the results or using them incorrectly C Using too many questions (25 to 30 questions are typical)
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Customer Data Analysis Comparing customer attitudes over time or between groupings can provide insights into market niches and changes. The results of customer feedback data collection can be analyzed using a variety of tools:
C Statistical tests C Line graphs C Control charts C Matrix diagrams C Pareto analysis
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Quality Function Deployment Quality function deployment is a tool that is sometimes referred to as the “voice of the customer,” or as the “house of quality.” Quality function deployment (QFD) has been described as a process to ensure that customers’ wants and needs are heard and translated into technical characteristics. This activity should focus the product or service on satisfying customer requirements. QFD is a tool for the entire organization to use. It is flexible and customized for each case and works well for manufactured products and in the service industry. QFD provides a graphic method of expressing relationships between customer wants and design features. It is a matrix that lists the attributes a customer wants and compares it to the design features (services that satisfy customer wants). The collection of customer wants and expectations are expressed through the methods available to most any organization: surveys, focus groups, interviews, trade shows, hot lines, etc.
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Quality Function Deployment (Continued) The construction of the house follows:
C C C C C
The left side of the house has the customer needs The ceiling has the features and requirements The right side contains the customer priorities The foundation contains the target values The roof contains design feature relationships
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Quality Function Deployment (Continued) The possible benefits for using the QFD process are:
C C C C C C C C
Creates a customer driven environment Reduces the cycle time for new products Uses concurrent engineering methods Reduces design to manufacture costs Increases communications through teamwork Creates data for proper engineering documentation Establishes priority requirements Improves quality
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Quality Function Deployment (Continued)
A Hypothetical CQE Primer Example The house of quality is flexible and customized to each situation. However, the basics of QFD will remain the same: to hear the voice of the customer and to be proactive in its design.
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Supplier Selection The quality of materials and supplies determines the quality of the end product in many instances. A company can no longer buy from the lowest bidder solely on price, and then inspect and stage the material for processing approval. Today, companies are intensifying pressure to reduce idle inventory and maintain product quality. Increased cooperation between supplier and the end user is required. Suppliers may be selected by either an internal rating system or by use of an external certification model or some composite of the two. Juran describes the process of supplier evaluation as:
C The evaluation of product samples C The evaluation of the supplier’s processes
Evaluation of the Supplier Through Samples In this stage, the customer requests product samples from the supplier. Customer approval stages arise at each phase of the production process.
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Evaluation of the Supplier’s Processes There are three possible manufacturing process evaluation vehicles:
C Prior product performance C Process capability analysis C Quality system review Prior product performance assumes that the best predictor of future product quality is past performance. A process capability analysis can be performed on various products to verify that the process is capable of meeting the specifications. A quality system review may require a visit to the supplier’s site. An on-site survey is dependent on the size and resources of the customer and on the dollar volume of the supplier.
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Supplier Communications There are many ways that a producer or supplier can disappoint a customer. Planning meetings, contract meetings, and communications which review both requirements and performance are steps that can be taken to prevent supplier disappointment. Juran states that joint quality planning requires detailed discussion between customer and supplier covering three major areas:
C Economic C Technological C Managerial All three of these areas are important and are part of the up-front stated supplier expectations.
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Joint Economic Planning Meetings The economic aspects of customer-supplier conversations should concentrate on the following key elements:
C Value rather than conformance to specification C Optimizing overall quality costs
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Joint Technological Planning Meetings The following are typical of the issues covered for a fairly sophisticated product:
C C C C C C C
Agreement on specification details Agreement on the performance requirements Qualification of reliability requirements Standardization of test methods and conditions Establishment of a system of timely responses Establishment of lot identification and traceability Establishment of acceptable quality levels
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Joint Managerial Planning Meetings The prior two issues are certainly of managerial concern. Additionally, the following items fit more firmly into the conventional concepts of managerial control:
C C C C C C
Definitions of mutual responsibilities Documented reporting requirements The formalization of communication channels A formal written contract Buyer/supplier management requirements Action expected of the supplier (testing, records)
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Communications During the Contract Obviously there is a need for continuing buyer and supplier cooperation and communication during the execution phase of a contract. For standard commodities, most communications are channeled through the buyer purchasing agents and the supplier sales personnel. For complex engineered products, there may be multiple communication channels.
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Supplier Performance Assessment Supplier assessment and feedback is an essential element to both supplier and customer alike. Both objective and subjective data must be collected and analyzed to determine if corrective action is necessary. Customer ratings encourage a supplier to solve quality problems because they can:
C Demonstrate the effects of poor quality on costs C Move the supplier to probationary status C Disqualify the supplier from further business Supplier rating systems cover the spectrum from simple to complex. A wide assortment of measurements are used to provide supplier feedback:
C C C C C C
Quality metrics Timeliness metrics Delivery metrics Cost metrics Compliance metrics Subjective rating metrics
Suppliers can be rated and analyzed using many of the same techniques presented earlier for customers.
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Supplier Ratings Bhote lists 5 generic types of supplier rating systems: 1. No rating: the rationale is that purchasing and quality know which companies are good or bad. Therefore, a formal rating system is not needed. 2. Quality rating only: a rating based on the incoming inspection statistics. 3. Quality and delivery rating: graphic method. A quality rating charted against the delivery rating. 4. Quality and delivery rating: cost index method. Use of a rating system based on a fixed dollar penalty of nonconformances. 5. Comprehensive method: the measuring and rating of agreed on variables such as: quality, cost, delivery, service, etc.
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Supplier Ratings (Continued) Juran identifies how supplier ratings can be beneficial:
C To provide objective, quantitative measurement of supplier performance C To provide purchasing with information in desired categories C To provide the customer and supplier with the same grading information C To avoid drastic actions with a “special cause” supplier problem C To identify troublesome areas that require action
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Supplier Feedback Reports Most of the objective and subjective supplier feedback information can be provided in a variety of formats. Traditionally, at higher corporate levels, less detail is reported. Management reporting generally focuses on the economic factors (plus a few other key categories). The following items are representative:
C C C C C C
Total dollar value purchased Percent defect dollar to dollar value purchased Percent defect dollar recovered (for each supplier) Percent of lots or product rejected Corrective action activity (highlights or results) Composite supplier rating score (when applicable)
The above items are more easily digested in trend chart format. Obviously, where performance evaluations or rankings indicate, supplier meetings and corrective action planning may be required.
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Supplier Improvement Strategies In the past, companies bought from the lowest cost supplier, period. Financial concern is still important, but is mainly directed at the total cost, not just the price tag. Companies have found that it is mutually beneficial to develop supportive long-term relationships with their suppliers. The new trend is one of interdependence between vendor and purchaser. Vendors are selected based on quality, delivery, technology, life-cycle-cost, and management philosophy.
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Supplier Surveillance In many cases, a contract may require the supplier to present both a written plan for controlling quality and proof that the plan has been followed. There are two major surveillance approaches. One involves program auditing. The second approach is in-process surveillance which consists of monitoring the manufacturing process of the supplier, and can involve several of the following steps:
C Witnessing key events, inspections and tests
such
as
operations,
C Critical characteristic inspection by witnessing or performing C Joint troubleshooting of mutual quality related issues (Juran, 1999)
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Supplier Partnerships and Alliances The purpose of a partnership between customer and supplier is to mutually improve each other's operations in the areas of quality, costs, delivery, cycle time, response time, and other areas to ensure a mutually competitive advantage. The following definitions are important:
C Strategic alliances: The development of an association (partnership) with one or more companies. Alliances allow partners to be bigger than their parts and benefit both parties. C Partners: These are joint parties in a common business or purpose. The parties are on the same team, with equal rights. C Business partnering: There is a pooling of resources in a trusting environment focused on mutual improvement. (Poirier, 1993)
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Supplier Certification Programs The certification process comes after supplier selection and approval. It starts after the supplier begins shipment of the product. The certification process has been described by the Customer/Supplier Technical Committee of ASQ, in the following criteria: 1. The customer and supplier shall have agreed upon specifications that are mutually developed, justifiable, and clear. 2. The supplier shall have no product-related lot rejection for a significant period of time, say, one year, or significant number of lots, say 20. 3. The supplier shall have no nonproduct-related rejections for a stated period of time, say, three months, or number of lots, say, five. Nonproductrelated nonconformities like wrong counts are not as serious as product-related ones. 4. The supplier shall have no negative nonproductrelated incidents for a stated period, say, six months, or number of lots, say, ten.
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Supplier Certification Programs (Cont’d) 5. The supplier shall have a fully documented quality system. ISO 9001 is an excellent model. 6. The supplier shall have successfully passed an onsite system evaluation. 7. The supplier must conduct inspections and tests. Laboratory results are used for batch processes, and SPC is used for piece part production. 8. The suppliers shall have the ability to provide timely inspection and test data. This documentation is necessary when the product arrives. (Besterfield, 1999) Occasionally, it may be necessary to decertify a supplier as a result of a major problem. The number of suppliers can be reduced to a manageable level, thus further reducing costs.
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Supply Chain Management Traditional customer/supplier relationships have involved some assessment of incoming quality via source or incoming inspection. Obviously, there would have been some preliminary selection requirements, criteria, communications, and performance assessment activities. However, the point remained that the supplier’s quality was not to be totally trusted and must be monitored. The results of this traditional approach were inefficient use of human resources, the late discovery of problems, inflated inventories, lengthy cycle times, etc.
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Ship-To-Stock The disadvantages of traditional procurement methods have provided strong logic for ship-to-stock (STS) activities. A typical STS program can be divided into three phases (Bossert, 1988): 1. Candidacy 2. Qualification 3. Maintenance STS offers many of the following advantages:
C C C C C C C
Mutual purchaser/supplier trust Reduced inventory levels Reduced purchaser testing time and expense Reduced incoming rejects A replacement of inspection activities with audits Enhanced supplier quality responsibility A supplier quality reputation that can be broadened
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Just-In-Time STS is often a forerunner to just-in-time (JIT) procurement. If all of the controls are in place for successful STS activities, then a transition to JIT is possible. JIT consists of two principle elements: procurement and inventory. Procurement involves scheduling and receiving purchased product in a fashion that the purchased product is maintained at a near zero level. JIT procurement would focus on the same elements as STS, but with the addition of rigid:
C Forecasting C Inventory cost control C Scheduling C Freight expense controls
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Barriers to Quality Improvement The following are difficulties in many organizations:
C Concern about “Who gets the credit?” C Difficulty in answering the question: “What savings will be made with the proposed improvements that will not be made without them?” C The need to recognize that changes in one department may cause increased expenditures in another department. C The inability to estimate the costs of a proposed quality improvement C NIH: “Not Invented Here”; therefore the idea has no merit C A reluctance to increase training expenditures C Worker errors due to inadequate training or skills
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Barriers to Quality Improvement (Cont’d) C Functional departments wanting to optimize their own organizations C Separate departments budgeted dollars
competing
for
limited
C Poorly designed incentive and reward systems C Reluctance to design and install a team based approach C Management’s avoidance of the need for statistical thinking C Failure to make planned periodic improvements an integral part of the system C Failure to establish corrective and preventive action systems C Failure to identify needed improvements via audits or other means C Failure to keep adequate records
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Overcoming Improvement Barriers Almost all organizational weaknesses are systems based and must, therefore, be addressed by top management. Some considerations include:
C The current organizational status should be assessed both internally and independently C A management steering committee should be established to direct quality and other key initiatives C An atmosphere of supportive empowerment must be developed
employee
C Senior management must be role models by: C C C C
Recognizing employee accomplishments Providing adequate training Providing support and facilitation Responding to worthy recommendations
C Some form of continuous improvement methodology should be adopted
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Overcoming Improvement Barriers C Some form of corrective and preventative action system should be established C Use improvement teams to research, assess, and correct problems and exploit opportunities. should be a major consideration C The pulse of both internal and external customers must be measured C Lasting relationships and communication links with key suppliers is a must C The determination and reporting of quality costs will provide an economic measurement system C Standard operating procedures and instructions should be adapted and audited
work
C Efforts should be undertaken to break down barriers between departments and groups
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MANAGEMENT & LEADERSHIP QUESTIONS
2.1. A thorough review of the works of the major quality gurus would indicate which of the following to be the most effective way to create quality? a. Effective problem solving b. Benchmarking the best competitive practices c. Continuous process improvement d. Modern statistical control techniques 2.6. For employee involvement efforts to succeed, what may be needed? a. Increased employee incentives b. Increased basic training companywide c. Employee understanding of how they can make a difference d. The initiation of pilot projects 2.7. Consider the following network, with events marked within the circles and durations in weeks:
The critical path is: a. 1-3-6-8-10 b. 1-3-6-9-10 c. 1-4-6-8-10 d. 1-4-6-9-10
Answers:
2.1. c,
2.6. c,
2.7. c
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MANAGEMENT & LEADERSHIP QUESTIONS
2.11. Which of the following techniques are especially beneficial for the generation of ideas when solving quality and productivity problems? a. Poka - yoke b. Storming c. NGT d. PERT 2.13. The most desirable method of evaluating a supplier is: a. A history evaluation b. A survey evaluation c. A questionnaire d. Discussion with the quality manager on the phone 2.18. What is a major distinction between the CPM and PERT methods in the evaluation of project performance? a. Only the PERT method can be displayed on a Gantt chart b. The PERT technique allows for easier crashing of project time c. The PERT technique permits network relationships but CPM does not d. The PERT technique is event oriented, while CPM is activity centered
Answers: 2.11. c, 2.13. a, 2.18. d
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2.21. A key characteristic of a business partnership is: a. Sharing of critical business information b. Limited access to human resources c. Special company audits are performed d. Only plant managers agree on agendas 2.24. Which of the following items describe well functioning improvement teams? a. Members listen to what others say in the meeting b. Members often act without interdependency c. Members often have covert agendas d. Members set unrealistic objectives 2.25. The "next process is your customer" refers to: a. "Do it right" for the next operation b. Desire for better cooperation among departments c. "Zero defects" for the next process d. Process efficiency is very important
Answers: 2.21. a, 2.24. a, 2.25. b
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2.36. A critical path in a project means that: a. The project is important to the profits of the organization b. Slack times can be used to delay the ending date of the project c. Events on this path have no slack time d. The arrows and project path are always in bold print 2.37. Technical service to suppliers is: a. A great public relations gesture when personnel are available b. A greater benefit to the company than it is to the supplier c. A support feature for which suppliers are normally charged d. An optional luxury which is not a company responsibility 2.38. In planning for quality, an important consideration at the start is: a. The relation of the total cost of quality to the net sales b. The establishment of a company quality policy or objective c. Deciding precisely how much money should be spent on quality d. The selling of the quality program to top management
Answers: 2.36. c, 2.37. b, 2.38. b
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III. QUALITY SYSTEMS
OUR PLANS MISCARRY BECAUSE THEY HAVE NO AIM. WHEN A MAN DOES NOT KNOW WHAT HARBOR HE IS MAKING FOR, NO WIND IS THE RIGHT WIND. SENECA (4 B.C. - 65 A.D.)
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Quality Systems Quality Systems is presented in the following topic areas:
C C C C C C
Quality system elements System documentation Quality standards and guidelines Quality audits Cost of quality Quality training
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Historical Context Over the last sixty years there has been a tremendous shift in the way that companies in the U.S. must operate. Due to the huge vacuum of industrial production after World War II, the unscathed U.S. industrial base was able to become the world’s best. Goods could not be made fast enough. Our management style (the Taylor system) was examined and copied in many instances. The rise of big U.S. corporations began in the 1950s and continued to the early 1970s. During this period, a certain big business mind-set and management style developed. Running a big business became a numbers game. During this period, foreign competitors began to eat our lunch in a large number of technical and manufacturing areas. Since the mid 1970s, many U.S. companies have started to revive. They reeled from the initial shock of lost markets and responded. Challenges to U.S. companies abound in the areas of quality, productivity, reliability, communications, responsiveness, technology, costs, and customer satisfaction.
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The Quality Function The quality department has a basic function in an organization: to coordinate the quality efforts. The quality department, in most organizations, plans, measures, analyzes and reports quality. It is a staff function which supports other departments in the continuous improvement of products and services. The common functions of a quality organization include: Quality control. A management function that is intended to control or regulate the process in order to prevent defective products from being made. Quality assurance. A planned and systematic action to provide adequate confidence that a product will conform to requirements. Inspection. An appraisal activity where products are inspected (or tested) to determine whether they conform to requirements. Reliability. A function to determine the probability of a product performing its intended function for a specified time interval under stated conditions.
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The Quality Function (Continued) Often under the quality assurance organization, there are five additional functions: Quality engineering. The main planning function of quality assurance. Quality audit. An independent evaluation of various aspects of quality performance. Procurement quality. Assures that new materials and purchased parts are acceptable prior to release. Metrology measurement. Assures that equipment is calibrated via standards traceable to the National Institute of Standards and Technology. Administration. Originates the reports, procedures and policies used to support other functions in the company. This is often a valuable feedback loop.
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Systems From an organizational standpoint, a system is defined as a series of actions, activities, elements, components, departments, or processes that work together for a definite purpose. Business systems are made up of a variety of processes.
Quality Systems A quality system entails all of the activities that are undertaken to assure that a product or service meets required standards. Sometimes the systems are formal (written), and sometimes they are informal (assumed). Some of the main elements of a quality system for a manufactured product are:
C C C C C C C C C C
Management responsibility Raw material purchasing and control Incoming inspection of raw materials Process control Final inspection Control of nonconforming product Calibration control Document control Records Corrective/preventive actions
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Quality Systems (Continued) Generally, any large group will require a formal, documented quality system. It is simply not possible to keep everyone informed of the correct procedures and management philosophy. One definition of a quality system is: The organizational structure, responsibilities, procedures, processes, and resources for implementing quality management. ANSI/ISO/ASQ Q9000-2000 has expanded the term “quality system,” to “quality management system.” This Standard states: “The quality management system is that part of the organization’s management system that focuses on the achievement of results, in relation to the quality objectives, to satisfy the needs, expectations and requirements of interested parties, as appropriate.”
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Quality Systems (Continued) The keys to a proper quality system, then, are:
C It is companywide C It provides an operating work structure C It contains documented technical and managerial procedures C It guides the coordinated actions of people, machinery and information C It assures customer quality satisfaction and economical costs
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Elements of a Quality System All elements of a quality system flow from top management, to the product, through a number of elements. These major elements are discussed below:
Quality Policy The top management of a company establishes the intention and direction of a company to meet customer’s needs through the quality policy. The quality policy states how they intend to satisfy the customer. The quality policy is the foundation of the total quality hierarchy
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Elements of a Quality System (Continued) Quality Management Quality management is that portion of management that implements the quality policy. In many enlightened organizations, the implementation of the quality policy is the function of all management and employees.
Quality System The quality system is the total organizational structure, directed by quality management to fulfill the quality policy. The quality system consists of employees and other resources directed through procedures.
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Elements of a Quality System (Continued) Quality Assurance Quality assurance is planned and systematic actions that provide confidence that a product or service will satisfy given requirements for quality. Some typical quality assurance activities are:
C C C C C C
Establish customer needs/expectations Convert customer needs to specifications Control of incoming materials Monitor processes and procedures Final testing of product or service Warranty or service support of product or service
Quality Control Quality control operations are those techniques and activities that monitor and control quality. Typical quality control techniques and activities are:
C C C C C
Receiving inspection In-process inspection Final inspection Internal audit Supplier control
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Quality System Flow TOP MANAGEMENT
QUALITY POLICY
The quality policy is established by top management. It is the overall quality intentions and directions of an organization regarding quality.
QUALITY MANAGEMENT
Quality management is the management function that determines and implements the quality policy.
QUALITY SYSTEM
The quality system is the organizational structure, responsibilities, procedures, processes and resources for implementing quality management.
QUALITY ASSURANCE
QUALITY CONTROL
Quality assurance is all of the planned and systematic actions to provide adequate confidence that a product or service will satisfy given requirements for quality.
Quality control is the operations, techniques and activities of quality assurance that are used to fulfill requirements for quality of the product or service.
PRODUCT/SERVICE
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III. QUALITY SYSTEMS QUALITY SYSTEM DOCUMENTATION
Documentation of the Quality System The document set that comprises the quality system can be organized in many different ways. Most organize the quality documentation into a hierarchy. The top of the pyramid is the quality manual. The quality manual records management’s quality policy and contains information on how the company will meet the requirements of ISO or any other standard. Tier two represents the quality procedures. These procedures are the focal point of the system, since they describe the responsibilities of the various personnel and the administrative system used to accomplish the tasks. Thus, the quality manual details what is to be done, the quality procedures describe who will do it. Finally, tier three illustrates the work instructions that describe how to do the tasks. The work instructions detail the specific steps to accomplish the goals defined in the quality manual and the quality procedures. Some companies use four tiers with the last level representing the required forms and records.
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Quality Documentation Pyramid
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Quality System Components The documented portion of the quality system should contain the following four components:
C Quality policy: The quality policy should be a prominent part of the quality system so that the employees are informed of management’s direction and “vision.” C Responsibilities: The documented system also should describe and define the responsibilities of everyone in the organization responsible for quality. C “How to do it”: The documented quality system should describe how the various tasks are to be performed. C Verification: The documented quality system should also describe how the quality of the product is verified. One of the purposes of a formal quality system is to document and freeze the operations of the company. It is important to make sure that the formalized systems are the best.
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Types of Documents A formal quality system is characterized by formal instructional documents. These documents provide direction to the employees on how to accomplish a task, who is responsible for performing those tasks, or how the company systems work. There are various names for these documents. Some of the names are:
C C C C
Standard operating procedures Procedures Work instructions Manuals
Many companies have spent considerable amounts of effort and money to develop these documents. This is because good documentation is useful, and, in fact, necessary to the continued success of a company.
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Types of Documents (Continued) The formal quality system contains procedures or instructions that define and operate the system. There are several types of documents that are used in quality systems. These are shown in Table below. Document Type
Common Name
Policy documents: Documents that describe the overall company quality Quality policy, commitment to quality and manual quality system management organization. “Ways of doing business” documents: Documents that describe how the company quality management system operates.
Quality procedures
Technical documents: Documents that describe how to do specific tasks such as equipment operation, administrative steps, etc.
Work instructions
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General Characteristics of Documents All documents used in the quality system have similarities. The basic content of any good quality procedure or instruction should include:
C Purpose of the document C Basis of the document C Scope of the document In addition, the documents should contain the information necessary to convey the intended message. Each document has a goal, according to the type. The documents should be generated so that the goal is accomplished in the least amount of effort.
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III. QUALITY SYSTEMS QUALITY SYSTEM DOCUMENTATION
Quality Manual The quality manual is a policy document generated principally by upper management to outline how the company is to operate. The goal of the quality manual is to inform company employees and customers of the management vision and approach to operating the business. It should define how management intends to satisfy the customer for continued business success. The key elements of the quality manual are:
C Policy statement C General descriptions of policy implementation C Correlation of policy and implementation to applicable quality standards The quality manual is most frequently organized along the outline of ISO 9001:2000 or other applicable standard(s).
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Quality Procedures Quality procedures are “ways of doing business” documents. Sometimes these are called standard operating procedures (SOPs). Quality procedures should define management or administrative processes in a manner that supports the company policy. The quality procedures should:
C C C C C
Be consistent with company policy Describe the functional organization Outline responsibilities of personnel Be implemented Be understood by all employees
Quality procedures are the real focal point of the document system. They define the company organization, and how the company quality policy will be implemented to best satisfy the customer. Procedures tell the operating entities what they are supposed to do, and describe their interfaces.
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III. QUALITY SYSTEMS QUALITY SYSTEM DOCUMENTATION
Documentation Systems A documentation system can be divided into two major components:
C Configuration management (for design) C Document control (for design and other companies)
Configuration Management Juran (1999) describes configuration management as: “The collection of activities needed to define, identify, manage, record, or approve the hardware and software characteristics of a product.” Configuration management can be described via two questions:
C What constitutes the product at any point in time? C What changes have been made to the product?
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Configuration Management (Continued) According to Cox (1995), configuration management consists of four basic elements:
C Configuration identification: the process of defining and identifying every element of the product. C Configuration control: to manage the change order process from design to implementation. C Configuration accounting: the documenting of the approved configuration identification, and the implementation status of the changes. C Configuration audits: a comparison of the product against the engineering specifications in order to determine compliance.
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Configuration Identification The starting point for a configuration is called the baseline. There are three levels to a baseline:
C Functional baseline: general requirements of the product C Allocated baseline: defines the general requirements for a subsystem in the overall product C Product baseline: defines the detailed requirements of the system or item The baseline documents are very detailed. They will include all of the original drawings, specifications, tests, procedures, parts, materials, etc.
Configuration Control Once the product baseline has been approved (or created), changes to the design will fall under configuration control. Ideally, there will be established procedures for coordination of the change order. Any changes may have to go through the project engineer, with signatures from other key departments.
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Configuration Accounting Configuration accounting is the tracking of all proposed changes and the implementation status of every approved change. The details of every change are recorded and reviewed for existing and future compatibility. A department, perhaps the quality department, will have the responsibility of verifying that the changes have been implemented and that documentation is completed.
Configuration Audits This could consist of audits of the documentation system for completeness and accuracy, or audits of the product to verify engineering specification accuracy.
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Documentation Control The information required under configuration management could be immense. Information could be available from all parts of the organization including:
C C C C C C C C C C
Contracts design input Design specifications Process details Engineering changes Inspection and test data Supplier data Final inspection data Field data Failure data scrap Warranty charges, etc.
Configuration management of procedures, forms, and records often requires the documentation to be in written form. Thus, a method for filing, storing, and retrieving the documents is needed. Even an electronic software documentation system requires organization.
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Revision Control Keeping track of revisions, and ensuring their availability are two of the more challenging tasks of a quality system. They are challenging because they require attention to minor details. The first step of revision control is deciding how to mark the documents. There are two principle methods of revision marking:
C Revision control by sections C Revision control by total document Revisions of longer documents, like the quality manual, are usually maintained section by section. That is, a single quality manual may have a number of sections, each with a different revision date. Total document revision control is frequently used for quality procedures and work instructions. This means that a single change requires the generation and distribution of the total document.
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Marking Changes ISO 9001:2000 (paragraph 4.2.3c) requires that changes to the quality system documents be identified along with the revision level. Change markings can occur throughout the document. A common change marking is to underline additions and strike-out words/phrases that have been eliminated. Most word processors will do this automatically. ISO 9001:2000 allows documentation to be in any form or medium (paragraph 4.2.1, Note 3). Many companies are now using computer network systems to distribute and control the documents. Computer distribution has one danger. Employees have a habit of printing the document and keeping that version handy. This means that revision control can be lost.
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Document Formats The formats of all quality system documents should be consistent. This allows employees and auditors to know where items are found, without confusion. In addition, constant formats make a quality system look professional. Format consideration includes the major headings. These headings should be consistent within the same document type.
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Correlation Matrix of Documents Some companies choose to have a correlation matrix to track requirements. In the event a company is ISO 9001:2000 certified, every requirement of the standard should be identified and “broken-out.” The sequence can go as follows:
Specific ISO 9001:2000 Requirement Addressed in which section of the quality manual, including who is responsible?
Correlated to any necessary procedures including equipment, records and responsibilities?
Connected to any specific work instruction, providing adequate details to perform the work, record information, etc.?
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III. QUALITY SYSTEMS QUALITY SYSTEM DOCUMENTATION
ISO 9001:2000 Records A listing of required ISO 9001:200 records is shown on Primer page III - 18.
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Quality Standards and Other Guidelines Standards are measures of excellence against which comparisons are made. Quality standards can be government or industry endorsed descriptions of essential characteristics for an item or activity. Quality standards may be product specific, user specific, or generic and are approved by a recognized authority. Examples of standards include:
C ISO 9001:2000 Quality Management Systems Requirements C ISO/TS 16949 Quality Management Systems Particular requirements for the application of ISO 9001:2000 for automotive production and relevant service part organizations Although adherence to quality standards has become very widespread, a large amount of business is conducted using only requirements and specifications.
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Requirements A requirement is a formal statement of a need and the mandatory and expected way to attain it. It can also represent an accomplishment level to achieve specific objectives for given conditions. A requirement can be a contractually binding technical prerequisite stated in approved specifications. Note that registration to a quality standard may also be a requirement to conduct business with a company.
Specifications A specification is a mandatory requirement. A specification clearly and accurately describes essential technical requirements and verification procedures for items, materials and services. When invoked by a purchase order or contract, it is legally enforceable and its requirements are binding.
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Industry Standards Industry standards are numerous. Some industries have several associations that publish standards. Industry standards are developed to rationalize and simplify the design, manufacturing, service and use of that industry’s output. For consistency, industry standards should be based on international or national models. However, they are often not presented in a format that is consistent from industry-to-industry. Some examples explaining the character of industry standards:
C Many industries have accepted the ISO 9000 series standards C The automotive industry has modified ISO 9001 (ISO/TS 16949) C The steel industry has standardized compositions and properties
alloy
C Most industries accept the test methods of ASTM
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International/Industry Standards ISO/TS 16949 is an example of an international standard that has been modified and adopted as an automotive industry standard. ISO/TS 16949 is ISO 9001:2000 in its entirety with significant additions to many elements. This Standard replaces QS-9000 (1998). Additionally, six other documents may be required by Chrysler, Ford, General Motors, and other OEMs:
C C C C C C
Quality System Assessment APQP Reference Manual PFMEA Reference Manual Production Part Approval Process Manual Measurement System Analysis Reference Manual Fundamental SPC Reference Manual
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III. QUALITY SYSTEMS QUALITY STANDARDS
Industry/National Standards American National Standards Institute (ANSI) and American Society of Mechanical Engineers (ASME) have established and executed a quality assurance standard for the design, construction, and operation of nuclear power plants. This Standard, ANSI/ASME NQA-1, is an example of a national standard that is also an industry standard.
Other Standards Each organization must determine which standard(s) are applicable to their business. Included in the decision are both regulatory and customer requirements. The organization must also determine whether it will:
C Ignore the quality system requirements C Comply with some or all of the requirements C Comply with the requirements and obtain third-party registration or accreditation verifying that they meet the requirements There are many other quality system standards which apply to specific industries.
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ISO 9000:2000 The ISO 9000 Quality Management Standards were revised and published by ISO in December, 2000. The three new ISO Standards are: ISO 9000:2000, Quality Management Systems – Fundamentals and Vocabulary ISO 9001:2000, Quality Management Systems – Requirements ISO 9004:2000, Quality Management Systems – Guidelines for Performance Improvements
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ISO 9001:2000 Summary 1
2 3 4
5
6
7
8
Scope 1.1 General 1.2 Application Normative reference Terms and definitions Quality management system 4.1 General requirements 4.2 Documentation requirements Management responsibility 5.1 Management commitment 5.2 Customer focus 5.3 Quality policy 5.4 Planning 5.5 Responsibility, authority and communication 5.6 Management review Resource management 6.1 Provision of resources 6.2 Human resources 6.3 Infrastructure 6.4 Work environment Product realization 7.1 Planning of product realization 7.2 Customer-related processes 7.3 Design and development 7.4 Purchasing 7.5 Production and service provision 7.6 Control of monitoring and measuring devices Measurement, analysis and improvement 8.1 General 8.2 Monitoring and measurement 8.3 Control of nonconforming product 8.4 Analysis of data 8.5 Improvement
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ISO 9001: 2000 Summary ISO 9001:2000 is summarized on Primer pages III - 23 through III - 30.
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Malcolm Baldrige National Quality Award The Malcolm Baldrige National Quality Award was modeled after the Deming Prize in Japan and focuses on organizational excellence. The systems model is now called the Baldrige National Quality Program (BNQP) but the presented award is still called the MBNQA. Core values and concepts are based on:
C Visionary Leadership: Senior leaders set directions, create a customer focus, create methods for achieving excellence, and build knowledge and capabilities. C Customer Driven Focus: Understanding today’s customer desires and anticipating future customer desires and marketplace offerings. C Organizational and Personal Learning: Adopting a well-executed approach to learning including continuous improvement and adaptation to change. C Valuing Employees and Partners: Committing to employee satisfaction, development, and well-being. Building internal and external partnerships to better achieve overall goals.
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MBNQA (Continued) C Agility: Creating a capacity for rapid change and flexibility. C Focus on the Future: A strong future orientation and willingness to make long-term commitments to key stakeholders. Seeking opportunities for innovation. C Managing for Innovation: Making meaningful changes to improve products, services, and processes. Creating new value for stakeholders. C Management by Fact: Measurement and analysis of performance, critical data, key processes, outputs, and results. C Public Responsibility and Citizenship: Adopting a practice of good citizenship, business ethics and protection of health, safety, and the environment. C Focus on Results and Creating Value: Developing performance measurements that focus on key results and create value for all stakeholders. C Systems Perspective: Managing the whole enterprise, to achieve performance improvement.
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MBNQA (Continued) The Criteria for the MBNQA includes voluntary compliance as well as customer or organizational mandatory compliance requirements. Organizations are increasingly seeking compliance with these models as a result of not only client driven motivations but for organizational prestige and improvement. The purposes of the Criteria include:
C To provide a basis for organizational selfassessments C To actually achieve the Baldrige award C To provide feedback to applicants C To help improve organizational performance practices and capabilities C To facilitate information sharing of the best U.S. practices C To serve as a working tool for understanding and managing performance C To serve as a guide for planning and training
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MBNQA (Continued) The criteria are designed to help organizations use an integrated approach to organizational performance management that results in: • Ever-improving value to customers, contributing to marketplace success • Improvement of overall organizational effectiveness and capabilities
C Organizational and personal learning The Baldrige award eligibility categories now include:
C C C C C
Manufacturing businesses Service businesses Small businesses Education institutions Health care organizations
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MBNQA (Continued) The Malcolm Baldrige 2006 categories, items, and point values. are shown in the table below. 2006 Categories/ Items 1
Point Values
Leadership 1.1 1.2
2
Senior Leadership Governance and Social Responsibility
120 70 50
Strategic Planning 2.1 2.2
3
Strategy Development Strategy Deployment
85 40 45
Customer and Market Focus 3.1 3.2
4
Customer and Market Knowledge Customer Relationships and Satisfaction
85 40 45
Measurement, Analysis, and Knowledge Management 4.1 4.2
5
Measurement, Analysis, and Review of Organizational Performance Information and Knowledge Management
90 40 45
Human Resource Focus 5.1 5.2 5.3
6
Work Systems Employee Learning and Motivation Employee Well-Being and Satisfaction
85 35 25 25
Process Management 6.1 6.2
7
Value Creation Processes Support Processes and Operational Planning
85 45 40
Results 7.1 7.2 7.3 7.4 7.5 7.6
Product and Service Outcomes Customer-Focused Outcomes Financial and Market Outcomes Human Resource Outcomes Organizational Effectiveness Outcomes Leadership and Social Responsibility Outcomes
Total Points
450 100 70 70 70 70 70
1000
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Baldrige and ISO 9001 Comparisons Selected Criticisms for ISO 9001 and MBNQA ISO 9001
MBNQA
1. Does not assure world class performance
1. Past winners have not solved all business problems
2. Narrow quality documentation focus
2. Quality documentation requirements are not spelled out
3. Minimal effort to improve company efficiencies
3. Winning the award may displace more important objectives
4. Not helpful for high-tech companies
4. Can create an internal strain on resources
5. Automotive industries require additional ISO/TS 16949 registration
5. The sharing requirement costs money and might aid competitors
6. Products produced may not capture customer desires
6. A winning company’s products may not be superior to competitors
7. Registration costs may be high ($150-200,000)
7. Award costs can be staggering ($500,000 and up)
Requirement Comparisons for ISO 9001 and MBNQA ISO 9001
MBNQA
1. Adequate quality systems
1. Best-of-the-best quality systems
2. Objective evidence of meeting requirements
2. Clear evidence of product quality
3. Completely controlled and current documentation
3. Clear evidence of customer’s perception of company superiority
4. Periodic surveillance audits that verify compliance
4. Historic trends must support a single audit (Juran, 1999)
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III. QUALITY SYSTEMS QUALITY AUDITS
Audit Purpose and Benefits The purpose of quality auditing is to examine the effectiveness of management directed control programs. The philosophy of quality assurance programs is based on prevention rather than detection of problems. Where problems do occur, emphasis is on:
C Early detection of the problem C The depth of the problem C Discovery of the root cause of the problem Management implements control programs to:
C Prevent problems C Identify problems C Prevent the reoccurrence of problems Quality problems result in:
C Customer dissatisfaction C Lost profits C Loss of employee morale
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Audit Purpose and Benefits (Cont’d) Quality auditing provides management with objective feedback based on facts, enabling management to make informed decisions. The primary directive of an audit is to be beneficial to the function being audited. Examples of specific auditing purposes are to determine that:
C C C C C C C C C
Products are fit for use Adequate written procedures exist and are utilized There is adherence to regulatory requirements Product or system deficiencies are identified There is conformance to specification Remedial action is taken and the result is effective Information is obtained to identify and reduce risks There is effective use of company resources Standardized organizational practices exist
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Audit Philosophy Quality audits are formal, systematic, and independent. The results of the audit are based on facts. The effectiveness and integrity of an audit depend heavily upon the skills and training of the auditor(s). The new audit philosophy is centered around two main themes:
C Auditors must be fact-finders, not fault-finders C Audits should not be conducted in a covert manner; avoid secrecy
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Types of Audits Quality auditing is concerned with three general types of audits. The system audit, the process audit, and the product audit. Each of these general categories of audits will be discussed in more detail on the following pages of this Section.
SYSTEM AUDIT
PROCESS AUDIT
PRODUCT AUDIT
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System Audits A system audit is the largest and most extensive of audits. System audits are conducted to verify, through objective evidence, whether or not the quality management systems and organizational plans are indeed carried out to the requirements set forth. System audits may be external (supplier) or internal (in-house).
Process Audits A large and significant portion of the system audit is devoted to the process audit. One or more processes may be audited during the systems audit. The process audit, conducted by itself, is a convenient audit, often yielding swift results. Process audits:
C C C C C
Are less extensive than system audits Usually concentrate only on specific processes May be performed internally or externally Require less planning than the system audit Can be very helpful in improving a process
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Product Audits The product audit is an assessment of the final product or service and its “fitness for use” evaluated against the intent of the purpose of the product or service. Product audits are customer oriented (from the customer's point of view). Product audits may be performed by as few as one auditor or by as much as a large team (or even many teams) of auditors. Product audits may be performed internally or externally.
Internal Audits An internal audit is performed within an organization to measure its own performance, strengths, and weaknesses against its own established procedures and systems. An internal audit may be performed by inhouse personnel. An internal audit is considered to be a first-party audit.
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External Audits An external audit is an audit by company directive and performed on an outside source, such as a supplier. The external audit may be performed by company representatives; or the company may hire outside auditors to conduct the supplier audit. However, product knowledge, contracts, purchase agreements, and secrecy agreements make it more common for the company conducting the audit to send personnel from it's own auditing staff to perform an external audit.
Third Party Audits A third-party audit is when an outside source, or a thirdparty, is used to conduct the audit. The third-party audit is used to obtain a more independent and objective assessment or achieve certification to a recognized standard.
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Specific Objective Audits Some examples of specific objectives audits follow: Assessment: Sometimes used to indicate a less formal means of measuring and reporting than the normal audit. An assessment is usually limited in scope. Compliance: This is a type of audit which verifies whether or not the audit systems, processes, or products, satisfy the requirements as set forth in the contractual agreements and standards. Pre-Award Survey: A system audit may be conducted as a condition of accepting a new supplier prior to contract award. Procedural Audit: A procedural audit is a form of the compliance audit which verifies documented and formal procedures. Quality System Review: System audits resulting from significant changes affecting product quality. This type of audit may be necessary if product quality declines or there are critical changes in management.
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General Audit Matrix Audit Type Audit Name
Process
Product
System
Compliance Audit
C
NA
C
Corporate Audit
C
C
X
External Audit
C
C
X
Extrinsic Audit
C
C
X
Full Scope Audit
C
C
X
Informal Audit
C
C
C
Internal Audit
C
C
C
Management Audit
C
C
X
Pre-award Survey
C
C
X
Procedure Audit
C
NA
X
Process Audit
X
NA
NA
Product Audit
NA
X
NA
Quality Audit
C
C
X
Quality Program Evaluation
C
C
X
Self Audit
C
C
C
Supplier Audit
C
C
C
Surveillance Audit
C
X
X
NA
NA
X
C
C
C
Unannounced Audit
NA
NA
NA
X = Normal Audit Type
C = Audit Possibility
Systems Audit Third-Party Audit
NA = Not Applicable
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System Audit Matrix Type
Subject
Extrinsic
A company is the subject of a customer audit
External
Supplier
External
Potential supplier
External
Systems or Management Audit
In-depth quality management systems and compliance
Internal or External
Assessment Audit
More limited in-depth than the system audit
Internal or External
Total quality program effectiveness.
Internal or External
Compliance Review
Verification of effectiveness of quality management system
Internal or External
Full Audit
Entire company or product from design development to end of product life
Internal or External
Vendor Survey Pre-award Survey
Appraisal
Application
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Audit Program Administration Top management has the responsibility for establishing and authorizing the organizational auditing program. The audit authority (or audit manager) should establish clear objectives for the audit program and for the specific audit types. Audit manager duties include:
C Establish the objectives of the audit program C Establish the responsibilities and procedures C Ensure adequate resources C Ensure the implementation of the audit program C Ensure that audit program records are maintained C Monitor, review, and improve the audit program The audit program should be periodically reviewed and evaluated by management.
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Auditing Standards ISO 19011:2002 ISO 19011:2002 combines criteria for both quality and environmental systems auditing. The following topics are addressed in ISO 19011:2002:
C C C C
Standards - to be used in the audit process Auditors - criteria for an auditor skill levels Monitoring / maintenance of auditor performance A code of ethics
ISO 9001:2000 ISO 9001:2000 quality standards provide international requirements as to what elements are to be audited. ISO 9001:2000, Section 8.2.2, identifies the requirement to perform internal audits and addresses the following elements:
C C C C
Requirements for documented internal audit plans Records of the results of internal audits Evidence of review of the results Identification of corrective actions and follow up
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Lead Auditor Responsibilities C C C C C C C C C C C C
Assisting in the selection of other team members Maintaining the ethics of the audit team Defining the requirements of each audit assignment Complying with applicable auditing requirements Preparing the audit plan Preparing working documents Briefing the other auditors Representing the audit team with the auditee Reviewing documentation Reporting critical nonconformities Reporting obstacles in performing the audit Submitting the audit report
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Auditor Responsibilities C C C C C C C C C C C C C C
Complying with the applicable audit requirements Communicating and clarifying audit requirements Carrying out assigned responsibilities effectively Maintaining objectivity and confidentiality Remaining within the audit scope Cooperating with and supporting the lead auditor Acting in an ethical manner Collecting and analyzing evidence Retaining and safeguarding documents Documenting any observations Noting areas more extensive auditing Answering relevant questions Verifying the effectiveness of corrective actions Reporting the audit results
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Client Responsibilities C Determines the audit need, scope, and purpose C Initiates the audit C Determines the auditing organization C Receives the audit report C Determines follow-up action
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Auditee's Responsibilities C C C C C C
Informing employees about the audit Appointing staff to accompany the audit team Providing resources needed by the audit team Cooperating with the auditors Providing access to the facilities and material Determining and initiating corrective actions
Audit Scope The client makes the final decisions on the scope and depth of the audit, which quality system elements, physical locations, and organizational activities are to be audited within a specified time frame. The resources committed to the audit should be sufficient to meet its intended scope and depth.
Audit Frequency The need to perform an audit is determined by the client, taking into consideration changes in management, organization, policies, techniques, technologies, as well as changes to the system itself, and the results of other recent audits. Within an organization, internal audits may be organized on a regular basis for management or business purposes.
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Preparing the Audit The audit plan should:
C C C C C C C C C C C C
Be approved by the client Be communicated to the auditors and auditee Be designed to be flexible (permitting changes) Define the place and date of the audit Include the audit objectives and scope Stipulate reference documents Identify audit team members and assign tasks Define the language of the audit Define the duration of the audit Provide an anticipated auditee meeting schedule Identify confidentiality requirements Stipulate audit report distribution and date
The working documents, facilitating the audit, may include:
C Flow charts C Checklists and reporting forms
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Flow Chart Usage The starting point for a system or major process audit is an important decision. If there is sufficient audit time, a good place to start is at the beginning. If the final results are of more importance and the auditor already has some knowledge of the activities, beginning at the end may be desirable. These widely used and highly effective forms of field investigative activities are called tracing (or tracking). The use of flow charts is often helpful with either trace forward or trace backward audits. If the needed flow charts exist, they can be requested and followed for accuracy and compliance. If they do not exist, the auditor may find it very helpful to create one during the tracing process. A flow chart is an effective document for evidence of compliance or adequacy. A comparison table of auditing approaches is shown in the Primer.
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Checklists A checklist is one of the distinguishing features between an audit and other less formal methods of performance monitoring. The checklist serves as a guide to each member of the audit team, in order to ensure that the full scope of the audit is adequately covered. It also provides a place for recording data collected during the field work. Checklist questions are not open ended questions to be discussed in the field; rather they are the individual facts necessary to form conclusions. Checklist questions must be precise, measurable, and factual.
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Executing the Audit The Opening Meeting C C C C C C C
Introduces the audit team to the auditee's Reviews the scope and the objectives of the audit Summarizes the methods and procedures Establishes communication links Discusses the resources and facilities needed Sets the time and date for the closing meeting Clarifies any unclear details of the audit plan
Evidence Collection C C C C
Interviews Physical evidence Examination of documents and records Observation of activities and conditions
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Executing the Audit (Continued) Interviews Most of the information obtained during the audit will be by questioning auditee personnel. The auditor should determine not only compliance, but also how adequate the compliance is. Most of the questions should allow for some discussion and probing rather than just a simple “yes” or “no” response. This gives the auditee the opportunity to elaborate and possibly provide other supporting documentation or evidence.
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Executing the Audit (Continued) Physical Evidence Verification of formal controls such as methods, practices, procedures, policies and documentation is done through field work. The auditor(s), accompanied by the designated auditee representative, physically go to the facility or location where the production or service is occurring (plant floor, department, or customer service area). The act of verification by the auditor is the most important aspect in the performance of the audit.
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Executing the Audit (Continued) Verifying Documents and Records In the performance of the audit, any supporting auditee documentation should be noted beneath the corresponding checklist question. The auditor may review the documentation at the time it is presented. It is best if supporting documentation has been previously obtained and reviewed during the audit planning phase. When recording document data, the following items should be included:
C C C C
Location of the document sampled Identification of the record or document The time and date Any observations which may affect the document
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Executing the Audit (Continued) Observation Techniques Audit observation is the act of recognizing and confirming a fact or occurrence by some objective or subjective measurement. Particular attention should be given to the recording of details that may potentially result in either positive or negative audit findings. These observations should be traceable to time, location and conditions under which they were made. Whenever possible, the auditor should obtain an acknowledgment from the auditee escort All audit observations should be:
C C C C C C
Documented and reviewed Clear and concise Supported by evidence Identified in terms of the specific requirements Reviewed by the lead auditor with the auditee Acknowledged by the auditee’s management
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Closing Meeting with Auditee At the end of the audit, prior to preparing the audit report, a meeting with the auditee's senior management should be held, to present audit observations to the senior management in such a manner that they clearly understand the results. The lead auditor should present observations and the audit team's conclusions. Records of the closing meeting should be kept.
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Audit Report Preparation The lead auditor is responsible for the accuracy and completeness of the audit report. The audit report should:
C C C C C C C C C C C
Reflect both the tone and content of the audit Be dated and signed by the lead auditor Contain the scope and objectives of the audit Contain details of the audit plan Identify the audit team Identify the auditee's representative List audit dates Identify the specific organization audited Identify the reference documents Describe observations of nonconformities Express a judgment of the extent of compliance
Report Distribution The audit report should be sent to the client by the lead auditor. It is the client's responsibility to provide the auditee's senior management with a copy.
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Audit Completion The audit is completed upon submission of the audit report to the client.
Corrective Action Follow-up The auditee is responsible for determining and initiating the corrective action needed to correct the cause of a nonconformity. Corrective action, and subsequent follow-up audits, should be completed within a time period agreed to by the client and the auditee, in consultation with the auditing organization.
Record Retention Audit documents should be retained according to the agreement between the client, the auditing organization and the auditee, and in accordance with any regulatory requirements.
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Glossary of Audit Terms Appraisal: A form of the quality system audit, normally conducted to examine the total quality program effectiveness and implementation. Assessment: Another term for the quality audit, sometimes used to indicate a less formal means of measuring and reporting than the full audit. Audit: An independent, structured, and documented evaluation of the adequacy and implementation of an activity to specified requirements. Auditee: The organization to be audited. The auditee may be another group within the firm, or it may be an entirely separate organization. Auditor: A person who is qualified and authorized to perform all or part of an audit.
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Glossary of Audit Terms (Continued) Client: The person or organization requesting or sponsoring an audit. Examination: A measurement of goods or services to determine conformance to some specified requirement. Finding: An audit conclusion which identifies a condition having a significant adverse effect on the quality of the goods or services produced. Follow-up audit: A subsequent audit which verifies that some corrective action has been performed as scheduled, and determining that the action was effective. Lead auditor: A person who is qualified and authorized to direct an audit. Objective evidence: Qualitative or quantitative information, records, or statements of fact which are based on observations, measurements, or tests that can be verified.
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Glossary of Audit Terms (Continued) Observation: An audit observation identifies a condition which is not yet causing a serious degradation of quality. Process audit: The evaluation of a process operation against established instructions and standards. It also measures the effectiveness of process instructions. Product audit: The examination, inspection, or testing of a product which has been accepted previously for the characteristics being audited. Quality system audit: A structured activity performed to verify that one or more portions of a quality program are appropriate and being implemented effectively. Quality (system) survey: An activity conducted prior to a contract award and used to evaluate the overall quality capability of a prospective supplier or contractor. Verification: The act of reviewing, inspecting, testing, checking, auditing, or otherwise establishing and documenting whether items, processes, services or documents conform to specified requirements.
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Traditional Cost Concept Most companies utilize financial reports which compare the actual costs to the budgeted costs. The difference is called a variance and, if significant, may prompt management action. Shown below is a schematic of a traditional corporate financial structure which indicates areas where a quality cost program will operate.
Profit Revenues
Selling Costs General and Administrative Costs Fixed and Miscellaneous Expenses
Area of Concentration of a Quality Cost Program
Cost of Goods Sold Overhead Cost Cost of Goods Produced
Indirect Labor Indirect Materials Direct Labor Direct Materials
Prime Cost
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Origin of Quality Cost Measurements In the 1950s and 1960s, some enlightened companies began to evaluate and report quality costs for a variety of reasons. What resulted was a method of defining and measuring quality costs and reporting them on a regular basis (monthly or quarterly). The quality cost reports became a vehicle to:
C Determine the status of cost control efforts, and C Identify additional opportunities for reducing the cost of quality by systematic improvements Since the costs of quality are high (some authorities say 15% to 25% of total costs), the opportunity for improvement should easily capture the attention of management.
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Quality Cost Categories Prevention costs: The costs of activities specifically designed to prevent poor quality in products or services. Appraisal costs: The costs associated with measuring, evaluating, or auditing products or services to assure conformance to quality standards and performance requirements. Failure costs: The costs resulting from products or services not conforming to requirements or customer/user needs.
C Internal failure costs: Failure costs which occur prior to delivery or shipment of the product, or the furnishing of a service, to the customer. C External failure costs: Failure costs which occur after deliver or shipment of the product, or during or after furnishing of a service, to the customer.
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Three Levels of Product Costs
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Costs Category Examples Listings of prevention, appraisal, and failure costs are shown on Primer pages III - 56/57.
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Optimum Quality Costs The total quality curve is depicted in the theoretical model below (Juran, 1999). The minimum level of total quality costs occurs when the quality of conformance is 100%. The model illustrates that as prevention and appraisal costs increase, the failure costs will decrease until an optimum point is reached.
Most companies initially find that they are woefully to the left of the optimum quality cost point.
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Optimum Quality Costs (Continued) Listed below are some typical quality cost ratios for American companies. Cost Category
Percent of Total
Prevention Appraisal Internal Failure External Failure
0-5 10 - 50 20 - 40 20 - 40
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Optimum Quality Costs (Continued) 30 28
Total Cost of Quality Sales
26 24
Program Start
22
Total Failure
20 18 16 14
Internal
12
Failure
10 8
Appraisal
6 4 Prevention
2 0
1
2
3
4
5
6
7
8
9
10
Time
Hypothetical Quality Costs Trends Over Time The implementation of preventative measures to control quality often take time. Appraisal measures are initially undertaken which cause internal failures to increase but external failures (and total failures) to decrease. However, a small increase in prevention methods will normally create a large decrease in total quality costs.
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Quality Cost Improvement C Define the company quality goals and objectives: C The relative position desired among competitors C The type of long-term quality reputation desired C Translate the quality goals into quality requirements which represent the real workplace. C Develop realistic programs and projects consistent with the company goals C Set up quality cost categories of prevention, appraisal, and failure to accumulate costs C Arrange for accounting to collect and present quality costs C Analyze the quality cost data for major improvement candidates C Utilize the Pareto principle to isolate specific vital areas for investigation.
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Quality Cost Comparison Bases Quality costs should be related to two or three comparisons bases. Some examples are:
C Labor bases: C Total direct labor (worked) C Standard labor (planned) C Manufacturing cost bases: C Shop cost of output C Direct labor C Direct material C Indirect costs C Manufacturing cost of output C Including the total shop cost of output C Production engineering costs and expenses C Provision for complaints C Packing and shipping C Sales bases: C Net sales billed C Contributed value C Unit bases: C Quality costs, dollars per unit of production C Quality costs related to production
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Typical Quality Cost Report Quality Cost Report for September 2006 Dollars ($)
Percent of Total
Prevention Costs Quality Control Administration Quality Control Engineering Other Quality Planning Training
5250
2.1
14600
5.9
1250
0.5
2875
1.2
23975
9.7
Inspection
55300
22.3
Test
23800
9.6
Vendor Control
1700
0.7
Measurement Control
1950
0.8
Materials Consumed
375
0.2
Product Quality Audits
800
0.3
83925
33.8
66500
26.8
Total Prevention Appraisal Costs
Total Appraisal Internal Failure Costs Scrap Repair, Rework
1900
0.8
Vendor Losses
2500
1.0
Failure Analysis Total Internal
4000
1.6
74900
30.1
14500
5.8
7350
3.0
External Failure Costs Failures - Manufacturing Failures - Engineering Failures - Sales Warranty Charges Failure Analysis Total External Total Quality Costs
4430
1.8
31750
12.8
7600
3.1
65630
26.4
248430
100.0
94900
8.1
Bases Direct Labor Conversion Cost Sales
476700
40.8
1169082
100.0
Ratios Internal Failure Costs to Direct Labor
78.9
Internal Failure Costs to Conversion
15.7
Total Quality Costs to Sales
21.3
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Advantages of a Quality Cost System C C C C C C C
Provides a single overview of quality Aligns quality and company goals Provides a problem prioritization system Provides a way to distribute quality costs Improves the effective use of resources Provides emphasis for doing the job right Helps to establish new product processes
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Limitations of a Quality Cost System C C C C C C C
Cost measurement does not solve quality problems Quality cost reports do not suggest specific actions Quality costs are susceptible to mismanagement It is difficult to match effort and accomplishments Important costs may be omitted from cost reports Inappropriate costs may be included in cost reports Many costs are susceptible to measurement errors
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Other Quality Cost Pitfalls C Perfectionism in the numbers C Other data pitfalls C Inclusion of non-quality costs C Implications of reducing quality costs to zero C Reducing quality costs but increasing total company costs C Understatement of quality cost C Inconsistency of measurement
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Pareto Analysis of Quality Costs Pareto analysis is widely used to analyze quality costs; particularly failure costs. Corrective action, in the form of problem solving techniques and prevention methods, is undertaken on the major defect categories first. 9 8.5
8 7 6 3.4
5 4 3
3 2
1.8 1.2
1
1
0.8 0.5
0.2
0
Problem Categories Pareto Analysis of Cylinder Block Scrap
0.2
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Taguchi's Loss Function Taguchi contends, as product characteristics deviate from the normal aim, losses increase according to a parabolic function.
All Bad
LSL
USL
LSL
All Good
USL
All Bad L
Traditional Concept
Target
Y
Taguchi Concept
Traditional and Taguchi Loss Concepts Formula: L = K (Y - T)2 Where: L = loss in dollars K = cost coefficient
T = target value Y = actual quality value
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III. QUALITY SYSTEMS QUALITY TRAINING
Quality Training Management must be aware of the importance of having thoroughly trained employees to perform operations where product and service quality are at stake. Good training is a planned and ordered process where the trainee is guided along a path of learning. This means that a supervisor must ensure that those who are to train new employees are themselves clear about duties and that the process of training is properly supervised. The quality engineer may be involved in either departmental development training or training for the entire plant workforce. The need for training may arise from direct management requests, self perceived needs, or from workforce performance.
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Training to Reduce Defects When employees attempt to perform tasks for which they have not been adequately trained, quality objectives cannot be economically reached. Proper training reduces both errors and costs. There are three general conditions that lead to workmanship defects: lack of skill or training, misunderstanding instructions, and carelessness.
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Training for Customer Interface Elements of a good program include:
C C C C C C C C C C
Teach skills that are distinctive to the company All employees are treated as career employees Regular retraining is required Time and money are allocated for training Provide on the job training Teach new skills Use training for strategic changes Training is not cut when times are tough The customer interface level is involved Training is used to teach vision and values
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Training Needs Assessment Delineation of training needs must come before the preparation of course content, the selection of materials and aids, the teaching methods, and even before any other training program planning. A formal training needs analysis (TNA) should be conducted to assess the gaps in current performance and ideal performance. The TNA will collect information for evaluation on:
C Current activities and performance C Future activities and ideal performance If a gap in performance exists, the decision should be made to:
C C C C C C
Provide for training Select the proper subject content for training Allocate the necessary resources for training Determine the number of employees to be trained Determine the amount of training to be provided Collect information on the effectiveness of training (Smith, 1987)
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III. QUALITY SYSTEMS QUALITY TRAINING
Training Needs Assessment (Continued) The procedures and the amount of information for each TNA can vary substantially. Smith (1987) has developed a three step TNA procedure:
C Surveillance: This is having one’s “ears” to the ground by using a variety of documents on the state of the company. C Investigation: Some of the techniques in this step are: C C C C C C C C
data
gathering
Personal observations Interviews: group, individual Questionnaires: checklists, ratings Records of activities Work samples Performance appraisals Work studies Psychological tests
C Analysis: This is the detailed analysis of the data collected.
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III. QUALITY SYSTEMS QUALITY TRAINING
Training Guidelines There are several broad guidelines that should be considered in developing an industrial training program.
C Continuously educate all organizational levels in the skill, knowledge, and attitudes needed to do quality work. C Place a great emphasis on teaching skills such as the ability to cooperate, to share a mutual understanding, to work together, and other basic social skills. C Provide for continuous learning. Training is never complete. C Include all levels of personnel from the janitor to the president. If the training involves management commitment, start there first.
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III. QUALITY SYSTEMS QUALITY TRAINING
Training Principles Training is the primary method used by management to develop increased capability in job performance. There are some underlying principles which can be used to enhance the effectiveness of training.
C Objectives should be expressed in performance terms as much as possible. C Learners should receive immediate feedback in understandable terms about the correctness of their responses. C Training programs must be audited and validated, then modified if they do not achieve their objectives. C Training programs must be adapted to the individual as much as possible. C Learners must be involved by having the material expressed in ways that are directly relevant.
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III. QUALITY SYSTEMS QUALITY TRAINING
Training Effectiveness Training employees is a costly venture for any company. In addition to the dollar costs of the training consultant, the per person cost of the employee must be considered. For a two day in-house training program, the costs include: Trainer: Workshop cost per day, transportation, lodging, and expenses
including
Employees: The daily salary or hourly base for each employee at the workshop Temps: The cost to provide a replacement for a regular employee who is at the workshop Room: Cost of the room, including refreshments Preparation time: Costs of salary and hourly employees in preparing for the workshop TNA costs: The costs involved in conducting the TNA which led to the workshop. These costs should include materials and travel. Juran (1993) states, “The ultimate measure of the value of training is the degree of success in applying the concepts.”
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III. QUALITY SYSTEMS QUALITY TRAINING
Training Effectiveness (Continued) There are several simple evaluations of training effectiveness that are frequently used:
C “Smile” evaluations provide a reaction to the trainer’s impact, but with little guarantee that learning can be transferred to the job. C A post test exam of the workshop tests a number of objectives at the end of the workshop. C A third simple method to test for effectiveness would be to have a pre-test and a post-test. The pre-test is conducted at the start of the workshop, with the post-test conducted at the end of the workshop. The difference in test scores would be an indication of effectiveness.
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III. QUALITY SYSTEMS QUALITY TRAINING
Training Deterrents Many people have a resistance to learning new things and training specialists need to be aware of this tendency. Trainee attitudes are extremely important in learning ability and speed. Employees are sometimes reticent about asking questions because of fear of appearing dumb. Fear and anxiety are ever present deterrents to learning and can freeze performance. Sympathetic and supportive relationships between instructors and learners are essential to reduce fear and anxiety. Such relationships should include a constructive tolerance for mistakes.
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III. QUALITY SYSTEMS QUESTIONS 3.2. Quality policies are principally issued by management to: a. b. c. d.
State the position of the company on quality Ensure people are reminded about quality Provide detailed instructions in regard to quality Ensure customer satisfaction
3.5. Which of the following is the best definition of configuration management? a. b. c. d.
The collection of all product related information and activities A documentation system A record keeping system for order change A product production management plan
3.7. The percentages of total quality cost are distributed as follows: prevention 12%; appraisal 28%; internal failure 40%; and external failure 20%. One would conclude: a. b. c. d.
More money should be invested in prevention Expenditures for failure are excessive The amount spent for appraisal seems about right Nothing
Answers: 3.2. a, 3.5. a, 3.7. d
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III. QUALITY SYSTEMS QUESTIONS 3.10. When an auditor or group independent of the company, the company's customer, suppliers or any party involved with the company conducts an audit, that audit is called which of the following? a. b. c. d.
An internal audit An external audit A system audit A third-party audit
3.11. The short-term effect of a dramatic increase in prevention costs would be: a. b. c. d.
An increase in total quality costs A decrease in appraisal costs An increase in external failure costs A decrease in internal failure costs
3.17. The follow-up on the need for corrective action, identified in an audit report, is most clearly the responsibility of which of the following? a. b. c. d.
The client's upper management The auditee's upper management The lead auditor The operating area in which finding was made
Answers: 3.10. d, 3.11. a, 3.17. b
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III. QUALITY SYSTEMS QUESTIONS 3.21. A checklist will often permit the audit team to achieve which of the following? a. b. c. d.
A flexible audit format The identification of noncritical processes The effective use of time The determination of corrective action steps
3.23. Which of the following is the best method for developing materials for a training program on the gaps in performance? a. b. c. d.
Secure a workshop trainer Review a record of activities Set up a one shot case study Allocate employees for training
3.26. The purpose of a quality manual is to: a. b. c. d.
Use it as a basis for every quality decision Standardize the quality methods and decisions of a company Provide a written basis for rejection of lots Make it possible to handle every situation in exactly the same manner
Answers: 3.21. c, 3.23. b, 3.26. b
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III. QUALITY SYSTEMS QUESTIONS 3.35. In order to evaluate the internal effectiveness of the customer order planning function, which of the following audits is most appropriate? a. b. c. d.
Product audit Process audit Management audit System audit
3.36. Which of the following elements are NOT a basic part of configuration management? a. b. c. d.
Configuration control Configuration audits Configuration accounting Configuration design
3.37. If shop floor employees are exposed to new assembly techniques, the best instructional proficiency evaluation would be: a. b. c. d.
Observation of performance results Testing of assembled products Oral and written testing of the operators Training evaluation by the instructed employees
Answers: 3.35. b, 3.36. d, 3.37. a
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IV. PRODUCT AND PROCESS DESIGN
THERE IS NO SUCH THING AS ABSOLUTE CERTAINTY, BUT THERE IS ASSURANCE SUFFICIENT FOR THE PURPOSE OF HUMAN LIFE. JOHN STUART MILL 1859
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IV. PRODUCT AND PROCESS DESIGN QUALITY CHARACTERISTICS
Product and Process Design Product and Process Design is presented in the following topic areas:
C C C C C
Quality characteristics Design review Technical drawings Design verification Reliability and maintainability
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IV. PRODUCT AND PROCESS DESIGN QUALITY CHARACTERISTICS
Classification of Quality Characteristics Quality characteristics are the desired customer-based properties for a product or service. Companies also use quality characteristics to define, for the consumer, the product or service a company is offering. Quality characteristics are used to establish product differentiation in the marketplace. Often, these quality characteristics define the company as well as the product.
C Products: Reliability, safety, ease of use, aesthetics, performance, and durability. C Service: Promptness, knowledge, access, satisfaction, and accuracy.
credibility,
Companies use quality characteristics to define their strategic vision with their customers.
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IV. PRODUCT AND PROCESS DESIGN QUALITY CHARACTERISTICS
Product Quality Characteristics Topic
Example
Reliability
Mercedes Benz
Safety
BMW/Volvo
Ease of use
Voice activated cellular phones
Aesthetics
Lincoln - What a luxury car should be
Performance
Pontiac - We build excitement
Durability
Maytag - World’s loneliest repair man
Service Quality Characteristics Topic
Example
Promptness
Roto-Rooter - 1 hour emergency service
Knowledge
Most law firm ads
Credibility
A spokesperson with integrity Over 100 years experience
Access
H&R Block (25 zillion offices)
Satisfaction
Hotels (100% satisfaction guarantee) Burger King - Have it your way
Accuracy
First time, every time
Initial quality characteristics come from two sources. One source is from the company's strategic plan or vision. The second source is the customer.
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IV. PRODUCT AND PROCESS DESIGN QUALITY CHARACTERISTICS
Product and Process Characteristics Quality characteristics are used to develop product and process characteristics. Quality characteristics are most often too fuzzy to provide direct input into the design process. Product and process designers need well-defined criteria to proceed with a design project. Changing quality characteristics into product and process characteristics is known as developing the design specification. Examples are illustrated below: Product /Process Characteristic
Design Specification
C Timeliness/Promptness C Normal service C Emergency service
24 hours a day Every day of the year Service within 1 hour
C Portability C Lightweight C Fits in pocket
less than 8 pounds 5 ounces 1 x 3 x 4 inches
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IV. PRODUCT AND PROCESS DESIGN QUALITY CHARACTERISTICS
Characteristic Classifications Often, product features are graded or evaluated at or near the time of design as to relative importance. These characteristics may be measured by attribute or variable techniques and may be somewhat independent of defect categories. This system requires a determination of the importance of individual features or properties of a product or service. The distinction can be as simple as satisfactory or not satisfactory. It can also be as complex as a number of classes of seriousness such as: critical, major, minor, or incidental.
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IV. PRODUCT AND PROCESS DESIGN QUALITY CHARACTERISTICS
Characteristic Classifications (Cont’d) Consider the following matrix. Characteristic Current to BOK Aligned to BOK
Critical
Major
Minor
U U U
< 3 minor errors/Section Correct answers to questions
U U
Ring metal opens easily Durability of binder Consistency of font size
Incidental
U U
According to Gryna (2001), quality characteristics may also include sensory characteristics. One important portion of this application are visual characteristics. Some approaches to define limits in this area include:
C Photographs of acceptable limits C Physical standards for assigned limits C Assigned inspection conditions
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IV. PRODUCT AND PROCESS DESIGN DESIGN REVIEW
Design Inputs It is important to recognize that a design is intended to satisfy customer needs. The customer is a mixture of both internal and external users. The internal customer provides the strategic and product requirements of the company and the external customer provides their specific product requirements. Examples of internal customers and their requirements are detailed below: Internal Customer
Requirements
Sales
Cost and quantity
Quality
Reliability and quality levels
Top management
Profit and gross margin
Manufacturing
Manufacturability requirements
Service
Serviceability requirements
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IV. PRODUCT AND PROCESS DESIGN DESIGN REVIEW
Design Inputs (Continued) Examples of external customers and their requirements are illustrated below: External Customer
Requirements
End user
Quality characteristics
Dealers, distributors
Service, storage, and delivery
Regulatory agencies
Safety, emissions
The early process/product definition phase is often referred to as the design concept phase. During this phase, quality characteristics (ideas) are turned into written process or product design specifications. One quality tool used to translate customer ideas into design specifications is quality function deployment (QFD).
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IV. PRODUCT AND PROCESS DESIGN DESIGN REVIEW
Design Inputs (Continued) Both ISO 9001:2000 and ISO/TS 16949:2002 require a company to control design inputs related to the product., including applicable statutory and regulatory requirements. It would be impractical (as well as almost impossible) for the design procedure to provide all details in developing the design specification. Usually, the design procedure includes a design input checklist.
Example Design Input Checklist Customer drawings Customer contract Market research results Tooling, gages, fixtures, facilities Quality system requirements Training requirements Sales (volume) projections Manufacturability requirements Safety requirements Product performance requirements Quality requirements Price, cost, gross margin Warranty, repair, return history
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IV. PRODUCT AND PROCESS DESIGN DESIGN REVIEW
Design Inputs (Continued) Each area of the checklist is reviewed to develop the design specification. An essential success factor is ensuring that the design specifications are quantified with a tolerance. An inability to quantify a design specification usually means that the requirements are not well understood. Additionally, some areas may need to be determined later. Both of these issues create risks in the design process.
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IV. PRODUCT AND PROCESS DESIGN DESIGN REVIEW
Design Review Design specifications may be developed with an iterative approach, in phase, or in stages. An example of the sequence of design specifications development is:
C C C C
System Subsystem Module (printed circuit board, software, etc.) Component or material
Once the design specification phase starts to take shape, a design review should take place. A design review is usually considered mandatory when the design specification (concept phase) is complete, or complete enough to assign engineers to the task of making the design specifications real prototypes.
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IV. PRODUCT AND PROCESS DESIGN DESIGN REVIEW
Design Review (Continued) A design review is a documented, comprehensive, and systematic examination of the design progress to ensure it is capable of fulfilling the design inputs and the design specification. The review communicates design project status, progress, results, and changes, and also identifies potential and real areas of risk. The design review process is established by management policy or customer specifications, or both. Often a product design requires trade-offs between conflicting aspects of reliability, maintainability, cost, weight, ease of manufacture and performance. The final decision on a product design, therefore, depends heavily upon the experience of members of the design team.
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IV. PRODUCT AND PROCESS DESIGN DESIGN REVIEW
Design Review (Continued) The membership and responsibilities of a typical design review committee are shown below: Member
Review Phase I
Chairperson (of design function)
Responsibility
II III IV V
X X X X X
Calls and conducts reviews; issues all reports
Design engineer (of this product)
X X X X
Prepares and presents the design approach
Independent design engineer
X X X X
Reviews and verifies adequacy of design
Customer or marketing representative
X X X X X
Reliability manager or engineer
X X X X X
Materials/stress engineer Human factors/safety engineer Manufacturing engineer Quality engineer or quality representative Test engineer Others
Ensures that the customer's viewpoint is represented Evaluates the design for reliability
X
Verifies stress calculations and material usage
X X
Ensures product safety in use and manufacture
X X X X X X X X
X
Ensures cost effective manufacture Reviews inspection and test capabilities Presents test procedures and results As required
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IV. PRODUCT AND PROCESS DESIGN DESIGN REVIEW
Design Review (Continued) Each review committee has a designated chairperson (not the design engineer) who has general management experience, design understanding, and technical knowledge of the various disciplines involved. The design review considers all important factors in the creation of a mature product design.
C C C C C C C C C C C C
Are customer performance requirements met? Is the design as simple as possible? Are proven components and configurations used? Are manufacturing tolerances adequate? Is the manufacturing process capable? Are approved parts used in all practical cases? Are environmental requirements met? Are operational conditions considered? Are maintainability features present? Are there provisions for testing and inspection? Have potential failure modes been analyzed? Has a worst-case analysis been conducted?
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IV. PRODUCT AND PROCESS DESIGN DESIGN REVIEW
Design Review (Continued) The design process goes through several phases. Examples of typical design phases and purposes are: Design Phase Concept
Purpose Acquire and document design inputs Design Convert design inputs into documented specifications Prototype Convert design specifications into hardware Pre-production Pilot runs, capability analysis studies and confirmation Deployment Full production Final Determine the success of meeting the design inputs
Design reviews should be conducted at the end of each phase. It is important that relevant stakeholders attend the design review. There should be a consensus among the relevant stakeholders, that each phase has been successfully completed, and the project is ready to move forward to the next step. A major component of design reviews is the qualification process, which falls into two general categories, verification and validation.
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IV. PRODUCT AND PROCESS DESIGN DESIGN REVIEW
Design for Six Sigma (DFSS) Design for six sigma (DFSS) is the suggested method to bring order to product design. Hockman (2001) and Suh (1990) noted that 70% to 80% of all quality problems are design related. Emphasis on the manufacturing side alone will concentrate at the tail end of the problem solving process. The emphasis should be at the front end. Problem solving at the downstream end is more costly and time consuming than fixing it at the source.
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IV. PRODUCT AND PROCESS DESIGN DESIGN REVIEW
Design for Six Sigma (Continued) One of the ways to increase revenues must include introducing more new products to sell to customers. Cooper (1993) states that new products account for a large percentage of company sales (40%), and profits (46%). Of course, not every new product will survive. Two studies provide some statistics. Development Items
Study A
Study B
New product ideas
7
11
Products entering development
4
3
Products launched
1.5
1.3
Successful products
1
1
The table indicates that a large amount of ideas are needed. These ideas are sorted, screened, and evaluated in order to obtain the most feasible options to enter the development stage, pass into the launch stage, and become successful products.
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IV. PRODUCT AND PROCESS DESIGN DESIGN REVIEW
Design for Six Sigma (Continued) Cooper (1996) provides more details of how winning products are obtained: 1. A unique, superior product: This is a product with benefits and value for the customer. 2. A strong market orientation: An understanding of customer needs and wants exists. 3. Predevelopment work: Up front activities such as screening, market analysis, technical assessment, market research, and business analysis are vital. 4. Good product definition: A company must have good product and project definition. 5. Quality of execution: The development process must be executed with the proper amount of correctness. 6. Team effort: Product development is a team effort that includes R&D, marketing, and operations. 7. Proper project selection: Poor projects must be killed at the proper time.
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IV. PRODUCT AND PROCESS DESIGN DESIGN REVIEW
Design for Six Sigma (Continued) 8. Prepare for the launch: A good product launch is important and resources must be available for future launches. 9. Top management leadership: Management must provide guidance, resources, and leadership. 10. Speed to market: Product development speed is the weapon of choice, but sound management practices should be maintained. 11. A new product process: This is a screening (stage gate) process for new products. 12. An attractive market: An attractive market makes it easier to have a successful product. 13. Strength of company abilities: The new product provides a synergy between the company and internal abilities.
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IV. PRODUCT AND PROCESS DESIGN DESIGN REVIEW
Design for Six Sigma (Continued) There are many product development processes to choose from. Rosenau (1996) suggests that the former “relay race” process (passing the product from marketing to engineering to manufacturing and back through the loop) is obsolete. Multi-functional team activities involving all departments are necessary for effectiveness and speed to market. The process is comprised of 2 parts: a “fuzzy front end” (idea generation and sorting) and new product development.
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IV. PRODUCT AND PROCESS DESIGN DESIGN REVIEW
Design for Six Sigma (Continued) The complete NPD process includes 5 activities:
C Concept study: A study is needed to uncover unknowns about the market, the technology, or the manufacturing process. C Feasibility investigations: There is a need to determine the limitations of the concept. Find out if the unknowns are resolvable. C Development of the new product: This is the start of the NPD process. This includes the specifications, needs of the customer, target markets, and determination of key stage gates. C Maintenance: These are the post delivery activities associated with product development. C Continuous learning: Project status reports and evaluations are needed to permit learning.
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IV. PRODUCT AND PROCESS DESIGN DESIGN REVIEW
Design for Six Sigma (Continued) A stage gate process is used by many companies to screen and pass projects as they progress through development stages. The gate is a management review of the particular stage in question. It is at the various gates that management should make the “kill” decision. Too many projects are allowed to live beyond their useful lives and clog the system.
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IV. PRODUCT AND PROCESS DESIGN DESIGN REVIEW
Design for Six Sigma (Continued) In the area of new product management, Crawford (1997) and Cooper (1993) describe some commonly accepted new product terms: 1. New-to-the-world products: These are inventions, and discoveries like camera phones, and laser printers. 2. New category entries: These are company products that are new to the company. 3. Additions to product lines: These are extensions of the organization’s existing product line. 4. Product improvements: better.
Current products made
5. Repositionings: Products that are retargeted for a brooder use. 6. Cost reductions: New products are designed to replace existing products, but at a lower cost.
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IV. PRODUCT AND PROCESS DESIGN DESIGN REVIEW
Design for Six Sigma (Continued) Treffs (2001) presents a four step design model:
C Identify: Use team charter, voice of customer, QFD, FMEA, and benchmarking C Design: Emphasize CTQs, identify functional requirements, develop alternatives, evaluate and select C Optimize: Use process capability information, a statistical tolerancing approach, robust design, and various six sigma tools C Validate: Test and validate the design
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IV. PRODUCT AND PROCESS DESIGN DESIGN REVIEW
Design for Six Sigma (Continued) Simon (2000) provides a 5 step DMADV process for six sigma design. The DMADV method for the creation of a new product consists of the following steps:
C Define: needs
Define the project goals and customer
C Measure: Measure and determine customer needs and specifications C Analyze: Determine the process options C Design: Develop the details for producing to meet the customers’ needs C Verify: Verify and validate the design
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IV. PRODUCT AND PROCESS DESIGN DESIGN REVIEW
Design for Six Sigma (Continued) The design engineer will select a design process. A typical design process is depicted from Cross (1994): Need
Analysis of Problem
Statement of Problem
Conceptual Design
Selected Schemes
Embodiment of Schemes
Detailing
Working Drawings, etc
The French Design Model The designer will capture the needs, provide analysis, and produce a statement of the problem. The conceptual design will generate a variety of solutions to the problem. This brings together the elements of engineering, science, practical knowledge, production methods, and practices. The detailing step consolidates and coordinates the fine points of producing a product. The use of six sigma tools and techniques must be introduced in a well-thought-out manner at various phases of the project.
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IV. PRODUCT AND PROCESS DESIGN DESIGN REVIEW
Design Using QFD Quality function deployment is a tool that is sometimes referred to as the “voice of the customer,” or as the “house of quality.” By describing the product in the language of the engineer, along the top of the house of quality, the design team lists those engineering characteristics that are likely to affect one or more of the customer attributes. Hauser (1988) states, “by comparing weighted characteristics to actual component costs, creative design teams set priorities for improving components.” It is important to focus on customer satisfaction values when considering engineering characteristics. Increasing one engineering characteristic may have a negative impact on another engineering characteristic.
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IV. PRODUCT AND PROCESS DESIGN DESIGN REVIEW
Design Using QFD (Continued) The house of quality’s distinctive roof matrix helps engineers specify various engineering features that have to be improved collaterally,” (Hauser, 1988). The foundation of the house contains the benchmarking or target values. The values indicate “how much” for each of the measures. The right-hand wall of the house in indicates the customer competitive assessment, and other factors affecting the customer. The competition comparison shows graphically the relative weights. The elements which are included in the house are customized to the particular product or service being described. When reviewing a completed house, the easiest method is to look at each area separately.
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IV. PRODUCT AND PROCESS DESIGN DESIGN REVIEW
Design Using QFD (Continued)
An Expanded Example of QFD
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IV. PRODUCT AND PROCESS DESIGN DESIGN REVIEW
Design Using QFD (Continued) After setting the primary design characteristics, Hauser (1988) suggests using the “hows” from the house of quality as the “whats” of another house that depicts detailed product design. This process is repeated with a process planning house and then production planning house. In this way, the voice of the customer is carried through from design to manufacturing.
Eng ineering characteristics
Parts characteristics
Key process oper atio ns
Prod uction requ irements
House of qua lity
Parts deployment
Process pla nning
Production pla nning
Linked House of Quality Example
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IV. PRODUCT AND PROCESS DESIGN DESIGN REVIEW
A Robust Design Example In 1953, a mid-size Japanese tile manufacturing company was having a serious problem with their $2m kiln. The problem was extreme variation in tile dimensions. The stacked tiles were baked inside a tunnel kiln as shown below. Tiles on the outside of the stack tended to have a different dimension and exhibited more variation than those on the inside of the stack.
Figure 4.1 A Schematic of a Tile Tunnel Kiln The cause of variation was readily understandable. There was an uneven temperature profile inside the kiln. To correct the cause, the company would have to redesign the kiln. This company's budget didn't allow for such costly action, but the kiln was creating a tremendous financial loss.
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IV. PRODUCT AND PROCESS DESIGN DESIGN REVIEW
A Robust Design Example (Continued) Although temperature was an important factor, it was treated as a noise factor. This meant that temperature was a necessary evil and all other factors would be varied to see if the dimensional variation could be made insensitive to temperature. People having knowledge about the process were brought together. They identified seven major controllable factors which they thought could affect the tile dimension. After testing the seven factors over specified levels using an orthogonal design, the experimenters discovered that limestone content was the most significant factor. It was found that by increasing the limestone content from 1% to 2% with slightly better levels for other factors, the percent warpage could be reduced from 30% to less than 1%. Limestone was the cheapest material in the tile mix. Moreover, they found through the experimentation that they could use a smaller amount of amalgamate (the most expensive material) without adversely affecting the tile dimension. This is a classic example of improving quality, reducing cost, and drastically reducing the number of defectives at the same time.
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IV. PRODUCT AND PROCESS DESIGN DESIGN REVIEW
Robust Design The United States has coined the term “Taguchi Methods” to describe Dr. Taguchi’s system of robustness for the evaluation and improvement of the product development. Robust design processes are one of the more important developments in design processes in recent years. This process can produce extremely reliable designs both during manufacture and in use. Robust design uses the concept of parameter control to place the design in a position where random “noise” does not cause failure.
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IV. PRODUCT AND PROCESS DESIGN DESIGN REVIEW
Robust Design (Continued) The diagram below describes the process of robust design. Noise Factors
Signal Factor
Products/Procedures
Response
Control Factors
The concept is that a product or process is controlled by a number of factors to produce the desired response. The signal factor is the signal used for the intended response. The success of obtaining the response is dependent on control factors and noise factors.
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IV. PRODUCT AND PROCESS DESIGN DESIGN REVIEW
Robust Design (Continued) Control factors are those controllable by the designer.
parameters
that
are
Control factors are sometimes separated into those which add no cost to the product or process and those that do add cost. Since factors that add cost are frequently associated with selection of the tolerance of the components, these are called tolerance factors. Factors that don’t add cost are simply control factors. Noise factors are parameters or events that are not controllable by the designer. These are generally random, in that only the mean and variance can be predicted. Noise factors in furnace design might be:
C Line voltage variations C Outside temperature C Parallax errors in dial setting The function of the designer is to select control factors so that the impact of noise factors on the response are minimized while maximizing the response to signal factors. This adjustment of factors is best done using SDE.
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IV. PRODUCT AND PROCESS DESIGN DESIGN REVIEW
Robust Design (Continued) Phadke (1989) describes some key robust design principles:
C Concept design: Concept design is the selection of the process or product architecture based on technology, cost, customer, or other important considerations. This step depends heavily on the abilities and creativity of the designer. C Parameter design: During the parameter design stage the design is established using the lowest cost components and manufacturing techniques. The response is then optimized for control and minimized for noise. C Tolerance design: If the design doesn’t meet requirements, the designer must consider more expensive components or processes that reduce the tolerances. The tolerances are reduced until the design requirements are met.
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IV. PRODUCT AND PROCESS DESIGN DESIGN REVIEW
Concept Design In the development of a new product, the product planning department must determine the functions required. The designer will have a set of requirements that a new product must possess. The designer will develop various concepts, embodiments, or systems that will satisfy the customer’s requirements. All possible alternative systems should be considered. The criteria for selection of a design will be based on the quality level and development costs, that will enable the product to survive in the highly competitive marketplace. The product design must be “functionally robust,” which implies that it must withstand variation in input conditions and still achieve desired performance capabilities. The designer has two objectives:
C Develop a product that can perform the desired functions and be robust under various operating or exposure conditions C Have the product manufactured at the lowest possible cost The nominal values and tolerance parameters of the new system must be determined.
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IV. PRODUCT AND PROCESS DESIGN DESIGN REVIEW
Parameter Design Parameter designs improve the functional robustness of the process so that the desired dimensions or quality characteristics are obtained. The process is considered functionally robust if it produces the desired part for a wide variety of part dimensions. The steps to obtain this robustness would be: 1. Determine the signal factors and the uncontrollable noise factors and their ranges. 2. Choose as many controllable factors as possible, select levels for these factors, and assign these levels to an appropriate SDE. Controllable factors can be adjusted to improve the functional robustness of the process.
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IV. PRODUCT AND PROCESS DESIGN DESIGN REVIEW
Parameter Design (Continued) 3. Calculate S/N ratios from the experimental data. 1 ⎛ s - Ve ⎞ η = S/N = -10 log10 ⎜ β ⎟ r ⎝ VN ⎠
4. Determine the optimal conditions for the process. The optimal conditions are derived from the experimental data. The maximum average S/N of each level of controllable factors will be used for the optimal settings. Additional experiments will be conducted for verification of the settings. 5. Conduct actual production runs.
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IV. PRODUCT AND PROCESS DESIGN DESIGN REVIEW
Signal-to-Noise Ratios A signal-to-noise ratio (S/N) is used to evaluate system performance. In assessing the result of experiments, the S/N ratio is calculated at each design point. The combinations of the design variables that maximize the S/N ratio are selected for consideration as product or process parameter settings. There are 3 cases of S/N ratios: Case 1: S/N ratio for “smaller-is-better”: ⎛ ∑ yi2 ⎞ η = S/N = -10 log10 ⎜ ⎟ ⎝ n ⎠
Where: S/N = -10 log(mean-squared response). This value would be used for minimizing the wear, shrinkage, deterioration, etc. of a product or process. Case 2: S/N ratio for “larger-is-better”: 1 ⎛ ∑ ⎜ y2 i η = S/N = -10 log10 ⎜ ⎜ n ⎜ ⎝
⎞ ⎟ ⎟ ⎟ ⎟ ⎠
Where: S/N = -10log(mean-squared of the reciprocal response).
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IV. PRODUCT AND PROCESS DESIGN DESIGN REVIEW
Signal-to-Noise Ratios (Continued) Suppose a plot of S/N ratio looks like the following for one of the factors in a three level experiment:
S/N ratio (dB)
Levels of the Controllable Factor In the above figure, the input (controllable) factor should be chosen between the medium and high levels, since input variation will cause little output variation. S/N ratios for Case 2 will seek the highest values for items like strength, life, fuel efficiency, etc.
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Signal-to-Noise Ratios (Continued) Case 3: S/N ratio for “nominal-is-best”: 2 2 ⎛ mean ⎞ ⎛y ⎞ η = S/N = 10 log10 ⎜ ⎟ = 10 log10 ⎜ S2 ⎟ ⎝ variance ⎠ ⎝ ⎠
This S/N ratio is applicable for dimensions, clearances, weights, viscosities, etc.
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IV. PRODUCT AND PROCESS DESIGN DESIGN REVIEW
Tolerance Design The tolerances for all system components must be determined. This includes the types of materials used. In tolerance design, there is a balance between a given quality level and cost of the design. The measurement criteria is quality losses. Quality losses are estimated by the functional deviation of the products from their target values plus the cost due to the malfunction of these products. Tolerances are usually established by using engineering experience, considering the uncertainty of design and production factors. Taguchi states that a safety factor of 4 is typically used in the United States. This safety factor will vary across industry. The defense and communications sectors may require much larger values. The shipping specifications for a product characteristic is said to be on a higher-level in relation to the subsystem and parts.
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IV. PRODUCT AND PROCESS DESIGN DESIGN REVIEW
Tolerance Design (Continued) The functional limit )0 must be determined by methods like experimentation and testing. Taguchi (1993) uses a LD50 point as a guide to establish the upper and lower functional limits. The LD50 point is where the product will fail 50% of the time. The formulas for tolerance specifications, the functional limit, and safety factors are as follows: Tolerance Specification =
Functional Limit:
Commonly
Ai =
Δ 0i φi Δ =
Function Limit Safety Limit
(i = 1, 2) Δ0 φ
The economical safety factor N is determined as follows: φ=
Loss when exceeding functional limit = Loss when exceeding tolerance specifications
A0 A
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IV. PRODUCT AND PROCESS DESIGN DESIGN REVIEW
Taguchi’s Quality Imperatives The following is a paraphrase of Taguchi’s robust design principles:
C Robustness is a function of product design. The manufacturing process and on-line quality control cannot do much to change that. Quality losses are a loss to society. C Robust products have a strong signal with low internal noise. The design change of increasing the signal-to-noise ratio will improve the robustness of the product. C For new products, use planned experiments varying values, stresses, and conditions to seek out the parameter targets. Orthogonal arrays are recommended. C To build robust products, use customer-use conditions. C Tolerances are set before going to manufacturing. The quality loss function can be measured.
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IV. PRODUCT AND PROCESS DESIGN DESIGN REVIEW
Taguchi’s Quality Imperatives (Cont’d) C Products that barely meet the standard are only slightly better than products that fail the specifications. The aim should be the target value. C The factory must manufacture products that are consistent. Reduced variation is needed for consistency. C Reducing product failure in the field will reduce the number of defectives in the factory. Part variation reduction decreases system variation. C Proposals for capital equipment for on-line quality efforts should have the average quality loss (quality loss function) added to the proposal. The use of engineering techniques using robust design will improve customer satisfaction, reduce costs, and shorten the development time.
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IV. PRODUCT AND PROCESS DESIGN DESIGN REVIEW
Design for X (DFX) Design for X (DFX) is defined as a knowledge-based approach for designing products to have as many desirable characteristics as possible. These include: quality, reliability, serviceability, safety, user friendliness, etc. This approach goes beyond the traditional quality aspects of function, features, and appearance of the item. AT&T Bell Laboratories coined the term DFX to describe the process of designing a product. The DFX toolbox has continued to grow in number from its inception 15 years ago to include hundreds of tools today (Huang, 1997). The user can be overwhelmed by the choices available. A set methodology would aid in the following ways:
C C C C
Understanding how DFX works Aiding in the selection of a tool Speeding learning of DFX tools Providing a platform for multiple DFX tools
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IV. PRODUCT AND PROCESS DESIGN DESIGN REVIEW
Design for X (DFX) The following material is based principally on the work of Watson (1998): 1. Design guidelines: DFX methods are usually presented as rules of thumb which provides broad design rules and strategies. The design rule to increase assembly efficiency requires a reduction in the part count and part types. The strategy would be to verify that each part is needed. 2. DFX analysis tools: Each DFX tool involves some analytical procedure that measures the effectiveness of the selected tool. A DFA (design for assembly) procedure would address the handling time, insertion time, total assembly time, number of parts, and the assembly efficiency. Each tool should have some method of verifying its effectiveness. 3. Determine DFX tool structure: A technique may require other calculations before being considered complete. An independent tool will not depend on the output of another tool.
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IV. PRODUCT AND PROCESS DESIGN DESIGN REVIEW
Design for X (Continued) 4. Tool effectiveness and context: Each tool can be evaluated for usefulness by the user. The tool may be evaluated based on accuracy of analysis, reliability characteristics and/or integrity of the information generated. 5. The focus of activity and the development process: Use of the DFX tools will be of benefit if the product development process is understood by the design team. Understanding the process activities will help determine when a particular tool can be used. 6. Mapping tool focus by level: The mapping of a tool by level implies that DFX analysis can be complex. Several levels of analysis may be involved with one individual tool. The structure may dictate the feasibility of tool use.
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IV. PRODUCT AND PROCESS DESIGN DESIGN REVIEW
DFX Characteristics The following characteristics and attributes should be considered by DFX projects: (Bralla, 1999) Function and performance: These factors are vital for the product. Safety: Design for safety requires the elimination of potential failure prone elements that could occur in the operation and use of the product. Quality: The three characteristics of quality, reliability, and durability are required and are often grouped together in this category. Reliability: A reliable design has already anticipated all that can go wrong with the product, using the laws of probability to predict product failure. Techniques such as FMEA and derating of parts are considered. Parallel critical component systems may be used.
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IV. PRODUCT AND PROCESS DESIGN DESIGN REVIEW
DFX Characteristics (Continued) Testability: The performance attributes must be easily measured. Manufacturability: The concept of design for manufacturability (DFM), includes testability, and shipability. A design must simplify the manufacture of a product through a reduced number of parts and manufacturing operations. Assembly (design for assembly, DFA): DFA means simplifying the product so that fewer parts are involved, making the product easier to assemble. Environment: The objective is minimal pollution during manufacture, use, and disposal. This could be defined as design for the environment (DFE). Serviceability (maintainability and repairability): A product should be returned to operation and use easily after a failure. This is sometimes directly linked to maintainability.
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IV. PRODUCT AND PROCESS DESIGN DESIGN REVIEW
DFX Characteristics (Continued) Maintainability: The product must perform satisfactorily throughout its intended life with minimal expenses. The best approach is to ensure the reliability of components. User friendliness or ergonomics: Because of human factors, engineering must match the product to the user. Appearance (aesthetics): Attractiveness or “eye appeal” is especially necessary for consumer products. Packaging: The best package for the product must be considered. The size and physical characteristics of the product are important. Automated packaging methods are desirable. Features: Features are the accessories, options, and attachments available for a product. Time to market: The ability to have shorter cycle times in the launch design of a product is desirable.
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IV. PRODUCT AND PROCESS DESIGN TECHNICAL DRAWINGS
Introduction to Blueprints People who design parts and equipment must communicate their ideas to other people. For this reason, it is important to include all necessary information on the drawings used to fabricate the item in question. The information must be presented to minimize misunderstanding. Blueprints must contain a lot of information. All this information takes space. Using “technical shorthand” helps keep this space to a minimum. One example is the use of standard abbreviations. Another is the use of drawing conventions. To read blueprints, the conventions and information locations must be understood. Working drawings are of two different kinds, detail drawings (drawings of individual parts) and assembly drawings (showing how the parts fit together). Assembly drawings also include a parts list, which identifies all the pieces needed to build the item.
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IV. PRODUCT AND PROCESS DESIGN TECHNICAL DRAWINGS
Blueprint Information There are numerous variations of blueprint formats. The example below is representative of most drawing conventions.
A Blank Drafting Sheet
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Blueprint Information The first place to look for information on a drawing is in the title block, located in the lower right-hand corner of the sheet. Although there is some variation among title blocks used by different organizations, certain information is basic. The following paragraphs describe the information one will almost always find in a title block. The numbers before the descriptions refer to the numbers in the previous Figure.
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Blueprint Information (Continued) (1)
Company name. The space above the title is reserved for the company address (by city and state) of the designing or manufacturing firm.
(2)
Title of drawing. This box identifies the part or assembly illustrated.
(3)
Scale. The relationship between the size of the image and the size of the actual object is called the scale of the drawing. Some parts are either too big or too small to show conveniently at full size. The designer has the choice of drawing a mechanical part either full size, or larger or smaller than actual size. When the drawing is larger or smaller than full size, the designer states the scale. Slightly different conventions have been established by the different groups of people who make drawings.
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IV. PRODUCT AND PROCESS DESIGN TECHNICAL DRAWINGS
Blueprint Information (Continued) (4)
Drawing size. This section gives a letter designation for the overall size of the sheet on which the drawing has been made. The following table lists the standard sizes with their corresponding designations. Letter
Width
Height
A B C D E F J R
8.5 11 17 22 34 28 36 48
11 17 22 34 44 40 any any
Standard Blueprint Sizes
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Blueprint Information (Continued) (5)
Drawing number. The drawing number is the basic identification assigned to the drawing, which usually becomes the number of the part itself. This number is also used to file the drawings, making it easier to locate them.
(6)
Sheet number. This space is used to designate how many sheets were used to complete the drawing, and which one of the series this particular drawing happens to be.
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Blueprint Information (Continued) (7)
Approvals block. This is sometimes referred to as the “sign-off block.” This area provides space for the signatures or initials of the persons involved in drafting, checking and approving the drawing. Each person signs the document and fills in the date on the appropriate line when his/her portion of the work was finished or approved.
(8)
Material block. This block specifies what the part is made of - for example, the exact type of steel to be used. This space might also designate the size of the raw stock to be used.
(9)
Tolerance block. Nothing can be to the exact size specified on a drawing. Normal machining and manufacturing processes allow for slight deviations. Many times, the amount of allowed deviation is critical to the proper operation of the part.
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Blueprint Information (Continued) (10) Finish block. This space gives information on how the part is to be finished. That is, will it be buffed, plated, painted, anodized, etc. Added to this requirement might be the type of heat treatment to be applied after the part has been machined. (11) Parts list. (Used only on assembly drawings.) This space is usually positioned right above the title block. Individual component parts, their part numbers and the quantity required for each unit are listed. This list is built from the bottom up. (12) Revision block. The revision block is a separate block positioned in the upper right-hand corner of the drawing. It is used to note any changes that have been made to the drawing after its final approval. It is placed in a prominent position.
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Blueprint Information (Continued) (13) Detail drawing. A detail drawing is intended to provide all the information needed to make a specific part. See the figure below.
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Orthographic Projections A basic problem that must be faced when constructing a drawing is that objects are three-dimensional. That is, they have height, width and depth. A drawing has only two dimensions-height and width. Designers solve this problem by using perspective. Perspective is a way of drawing things as the eye sees them. The Figure below shows perspective.
Vanishing Point Horizontal Line
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Orthographic Projections (Continued) Designers have also developed a way to avoid distortion and draw the surfaces of blocks in their true size and shape. The method used is called orthographic projection. An orthographic projection is actually a right-angle projection that eliminates the distortions in shape and size caused by perspective. It does so by ignoring the fact that things farther from the eye appear smaller.
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Orthographic Projections (Continued)
An Orthographic Projection An orthographic projection shows an object from different views. For example, the figure above shows a notched block inside an imaginary, transparent box. The shape of the block is projected out to each side of the box. The projection on each side shows the true size and shape of the block as seen from that direction.
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IV. PRODUCT AND PROCESS DESIGN TECHNICAL DRAWINGS
Blueprint Lines Notes on detail drawings convey many kinds of information. Specific notes are tied by leaders directly to specific features. The table below, shows common drafting lines. Note that the weight and pattern of the lines indicate special significance. thick lines Object lines - Illustrate all visible edges of the object drawn
medium lines
thin lines
Cutting plane lines - Show where a section has been taken. Arrows indicate the direction in which section is seen in accompanying cutaway view. Hidden lines - Show hidden features of the object. Centerlines - Locate centers of round features (thin lines interrupted by short dashes). Extension lines - Extend from object to dimension lines. Dimension lines - Show dimension.
extent of a
Leaders - Like dimension lines, but usually has a note at the outer end. Phantom lines - Show position(s) of a part of an object that moves.
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IV. PRODUCT AND PROCESS DESIGN TECHNICAL DRAWINGS
Blueprint Lines (Continued) One unique characteristic of detail drawings, as opposed to assembly drawings, is the inclusion of dimension lines. Every measurable dimension is shown. Other lines on a blueprint include break lines as illustrated below: Type
Short Break Line
Long Break Line
Cylindrical Break Line
Cutting Plane Line Section Lines
Examples
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IV. PRODUCT AND PROCESS DESIGN TECHNICAL DRAWINGS
Tolerances Since variation exists in all manufacturing processes, it is customary to designate the permissible tolerance on blue print drawings. Listed below are examples of tolerances. Type
1. Title block tolerance
Illustration x.xxx = ± 0.002" x.xx = ± 0.01"
2. Bilateral tolerance Variation is permitted in both directions from a specified tolerance.
1.000" ± 0.002"
3. Unilateral tolerance Variation is permitted in one direction from a specified tolerance.
+ 0.004" 1.000" - 0.000"
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IV. PRODUCT AND PROCESS DESIGN TECHNICAL DRAWINGS
Tolerances (Continued) Type
4. Limit tolerance A tolerance which shows the high and low limits of a dimension.
5. Single limit tolerance A tolerance specifying a maximum or minimum limit only.
6. Positional tolerancing A feature frame shows the exact location and tolerance (allowable variation from the exact location).
Illustration 1.002" 0.998"
1.002" Max.
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IV. PRODUCT AND PROCESS DESIGN TECHNICAL DRAWINGS
Statistical Assignment of Tolerances The assignment of tolerances involves many factors including the sigma safety level required. There is an exercise on IV - 43 which shows that the standard deviation of an assembly equals the square root of the summation of all component part variances.
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Allowances and Fits Listed below are some major points regarding the relationship between mating parts. Term
Illustration 1.000" 0.998" 1.004" 1.002"
Clearance Fit When two mating parts can be assembled easily (positive allowance), as shown.
Hole
Shaft
1.000" 0.998" 0.997" 0.995"
Interference Fit When two mating parts must be forced together.
Shaft
Hole
1.000" 0.998" 1.001" 0.999"
Transition Fit This fit can be clearance or interference depending upon the actual sizes of the parts.
Shaft
Hole
1.000" 1.000"
Line To Line Fit Shaft
A fit where both parts are the same size (considered an interference fit).
Hole
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Dimensioning A designer must described the dimensions of features in order to control their locations. Some options can permit undesirable tolerance build up.
Parallel Dimensioning Parallel dimensioning consists of several dimensions originating from a projection line. This technique is also called baseline dimensioning. Parallel
Running
Parallel and Superimposed Running Dimensioning Superimposed running dimensions simplify parallel dimensioning in order to reduce drawing space. The dimensions can appear above or below the arrows.
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Chain Dimensioning Chain dimensioning should only be used if the function of the part will not be affected by the accumulation of tolerances. In the Figure below, if A equals 2.000 ± 0.005, B equals 1.000 ± 0.005 and C equals 1.000 ± 0.005, the total part dimension would be 4.000 ± 0.015. Chain
A
B
C
Illustration of Chain Dimensioning
Other Dimensioning Options In some complex parts, combined parallel and chain dimensioning options may be used. In the case of nonlinear hole locations, dimensioning by coordinates (with or without an accompanying table) may be desirable.
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IV. PRODUCT AND PROCESS DESIGN TECHNICAL DRAWINGS
Screw Thread Specifications Listed below is a description of a screw thread drawing specifications. Nominal size
English Thread per inch
Metric
Thread series Thread class
Metric Major diameter
Internal or external Additional data
1/2
16
UNC
3A
LH
Pitch
M
9.0 x 1.25
The definitions for common screw thread specifications are listed on Primer pages V - 46/47.
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IV. PRODUCT AND PROCESS DESIGN TECHNICAL DRAWINGS
Screw Thread Nomenclature Pictured in the figure below are the various parts of a common thread profile. Major diameter Pitch
Width
Pitch diameter Minor diameter
Axis
Depth Root
Thread angle
Crest
The definitions for the most important screw thread parts are listed on Primer page V-47.
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Surface Texture Components Symbol
Description Basic surface finish symbol Surface produced by any means Material removed by machining No material removal permitted Meaning
Lay is parallel to the line Lay is perpendicular to the line
X
Lay is angular in both directions
M
Lay is multidirectional
C
Lay is circular
R
Lay is radial a = roughness value Ra in micrometers b = production method, treatment, etc. c = roughness cutoff in millimeters d = directional lay key e = minimum material removal in mm
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Geometric Dimensioning and Tolerancing Characteristics and Symbols Type
Characteristic
Flatness Straightness Form
Circularity Cylindricity
Profile Profile of a line Profile of a surface Parallelism Orientation Runout
Angularity Perpendicularity Circular runout Total runout Position
Location
Symmetry Concentricity
ANSI Y14.5 M 1982
ASME Y14.5 M 1994
ISO 7083 1994
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Other Symbols and Terms Symbol Description
ANSI Y14.5 M 1982
ASME Y14.5 M 1994
ISO 7083 1994
MMC LMC RFS PTZ Tangent Plane
None
Diameter Basic Dimension Reference Dimension
(100)
(100)
(100)
Datum Feature Between Datum Target
None
None
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Feature Control Frames with Symbols Example 1
Example 2
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Datum Planes When three datums are specified, reference is made to the primary, secondary and tertiary datums. The following rules apply:
C Primary datum. This is the supporting datum that must be contacted at the three highest points on the surface. C Secondary datum. This is an aligning datum that must be contacted at the two highest points on the surface. C Tertiary datum. This is a stopping datum that must be contacted at the highest point on the surface.
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Virtual Condition The virtual condition (virtual size) of any dimension depends upon its size, form and location (position). Consider the following example: 0.260" 0.250"
Shaft
0.272" 0.262"
Hole
Assume that the hole size is true and parallel at a dimension of 0.263". The shaft measures 0.260" maximum O.D. The two parts should, therefore, mate properly with a clearance fit. However, if the shaft is bent, making its virtual size a maximum of 0.265", then the two parts will not mate.
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Virtual Condition (Continued) Examples of violations of dimensional virtual condition are: Size: Form: Position:
Oversize shaft, undersized hole Tapered keyway, crooked shaft, bent pin The feature is out of location
Material Conditions The ANSI terms for maximum material condition and least material condition are and respectively. The definitions are: MMC
The condition of a dimension where the most material allowed (by the tolerance) is still there (the maximum weight).
LMC
The condition of a dimension where the most material to be removed (by the tolerance) has been (the least weight).
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Material Conditions (Continued) MMC is the largest shaft and the smallest hole. LMC is the smallest shaft and the largest hole. Consider the following example: 0.260" 0.250"
Shaft
0.272" 0.262"
Hole
The MMC of the hole is 0.262". The MMC of the shaft is 0.260". The clearance is 0.002".
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Full Indicator Movement Many dimensions are designated as FIM, FIR or TIR. The abbreviations stand for: Full indicator movement, full indicator reading, total indicator reading, respectively. Consider the Figure below. The feature control frame indicates that surface B is to be parallel to surface A within 0.004" FIM. .004
A
B SURFACE
PART
SURFACE PLATE
A SURFACE
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Bonus Tolerancing Bonus tolerance applications can exist when maximum or least material conditions are used. The concept is that when mating parts are manufactured for assembly there may be conditions where each individual part may be slightly further away from its ideal location and still work. Review the Figure below.
Hole
Pin
Non-Symmetrical Part Mating
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Bonus Tolerancing Example Consider an example using MMC. In the Figure below, assume the centerline of the hole to be exactly 1.000 from both datums. 1.000 B .305 .295
1.000
Ø .005 M
A B C
A
The original tolerance is 0.005 for a MMC of 0.295. Assume that the hole were actually produced at 0.301. The following would then be true: Original tolerance 0.005 + Bonus tolerance 0.006 (0.301 - 0.295) Total tolerance 0.011 There is now more tolerance available for clearance between the pin and hole.
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IV. PRODUCT AND PROCESS DESIGN TECHNICAL DRAWINGS
Blueprint Definitions Actual Size
The actual size is a measured size of a feature.
Allowance
The intentional difference between the maximum material limits of mating parts.
ASME Y14.5M-1994
The authoritative document governing the practice of geometric dimensioning and tolerancing in the U.S.
ASME Y14.5M “Rule #1”
The amount of variation in size and geometric form of a feature. The boundary between the maximum (MMC) and least (LMC) material condition.
ASME Y14.5M “Rule #2”
All RFS notations must apply to all individual geometric tolerances and/or datum reference, when no material condition applies.
Basic Size
Any size from which tolerance limits may be derived.
Bilateral Tolerance
A bilateral tolerance permits variation in both directions from a specified dimension.
Circular Runout
The control requirement of circular elements of a surface during a full revolution about a datum center or axis.
Circularity
The condition whereby all points on a surface of revolution (cylinder, cone, sphere) are equidistant or within a specified tolerance from a common center or axis.
Clearance Fit
A clearance fit has size limits such that a clearance will always occur when mating parts are assembled.
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IV. PRODUCT AND PROCESS DESIGN TECHNICAL DRAWINGS
Blueprint Definitions (Continued) Datum
The origin from which the location or geometric characteristics of other part features of a part are established. It is a theoretically exact point, plane or axis.
Datum Feature
An actual feature of a part used to establish a datum.
Datum Feature Symbol
A symbol containing a datum reference letter in a rectangular box.
A
or
A
Datum Line
A line which provides a reference for functional, or measurement purposes.
Datum Plane
A theoretically exact plane established by the outside or contacting points of a feature or by a simulated datum plane such as a surface plate.
Datum Reference
A datum feature as referenced or specified on a drawing.
Datum Reference Frame
The reference frame consisting of three mutually established perpendicular datum planes which provide a complete dimensional orientation for the design features of concern.
Datum Target
A specified point, line, axis or plane (identified on the drawing with a datum target symbol) used to establish a datum.
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IV. PRODUCT AND PROCESS DESIGN TECHNICAL DRAWINGS
Blueprint Definitions (Continued) Feature
A general term used to identify a distinct portion of a part, such as a surface, pin, hole, slot, shaft, etc.
A feature control frame is a compartmentalized box Feature Control Frame containing the geometric characteristic symbol and the corresponding tolerance. .003
Feature of Size
A feature such as a hole, shaft, pin, slot, etc. which has an axis, centerline or center plane when related to or described by geometric tolerances.
Fit
The general term which indicates the amount of tightness or looseness which results from a specified combination of tolerances in the design of mating parts. Fits are of four general types: clearance, interference, transition, and line.
Form Tolerance
A statement of the permissible variation of a feature from a desired actual value. Form tolerance refers to flatness, straightness, circularity, and cylindricity.
Full Indicator Movement (FIM)
The total movement observed on an indicator in contact with a part feature surface during one full revolution about a datum axis. FIM has replaced the terms full indicator reading (FIR) and total indicator reading (TIR) as a standard reference.
Geometric Tolerance
A general term indicating the category of tolerances used to control form, orientation, profile, runout and location on a drawing.
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IV. PRODUCT AND PROCESS DESIGN TECHNICAL DRAWINGS
Blueprint Definitions (Continued) Least Material Condition (LMC)
The condition whereby a feature of size contains the least amount of material, within the slated limits of size. An example is the largest permitted hole size and smallest permitted shaft size. LMC is identified by the symbol .
Limits of Size
The specified maximum and minimum sizes of any feature.
Location Tolerance
A tolerance which states how far an actual feature may vary from an ideal location. These tolerances refer to geometric characteristics containing position and concentricity.
Maximum Material Condition (MMC)
The condition whereby a feature of size contains the maximum amount of material within the stated limits of size. An example is the minimum permitted hole diameter and maximum permitted shaft diameter. MMC is identified by the symbol
Modifier
A modifier is a material condition symbol such as maximum material condition (MMC) , regardless of feature size (RFS) and least material condition (LMC) .
Nominal Size
The nominal size is a stated dimension used for the purpose of general identification ( 2.050,1.310, 0.050).
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IV. PRODUCT AND PROCESS DESIGN TECHNICAL DRAWINGS
Blueprint Definitions (Continued) Parallelism
The condition whereby a surface, line, or axis is equidistant along its length to all points of a datum plane or axis.
Position Tolerance
A zone within which the center or axis of a feature is permitted to vary from a true or exact position.
Profile of a Line
The tolerance (unilateral or bilateral) within which the elements of a line must lie.
Profile of a Surface
The tolerance (unilateral or bilateral) within which the elements of a surface must lie.
Projected Tolerance Zone
A tolerance zone which applies to a feature (such as a hole) into which another feature (such as a pin) is to be inserted. The projected tolerance zone extends from the surface of one part along the functional length of a second mating part to assure proper assembly.
Reference Dimension
A provided dimension used for information purposes only.
Runout
Runout is the permissible error (or control tolerance) of a controlled feature surface during a full rotation (360°) about a datum axis. A runout tolerance may be circular or total.
Symmetry
The condition whereby the median point of all opposing features are correspondingly positioned around the axis or center plane of a datum feature.
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IV. PRODUCT AND PROCESS DESIGN TECHNICAL DRAWINGS
Blueprint Definitions (Continued) Tolerance Zone
The total measured value within which all elements of a surface or axis must fall.
Virtual Condition
The boundary of a feature, that represents the collective effects of size, form and location, considered in determining the fit or clearance between mating parts or features. It represents the most extreme condition of assembly.
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IV. PRODUCT AND PROCESS DESIGN DESIGN VERIFICATION
Design Verification ISO 9001:2000 requires that design and developments be in a form that enables verification against inputs. Designs must be approved before release. Furthermore, design and development outputs should:
C Meet input requirements C Provide adequate information for manufacture and service C Reference product acceptance criteria C Specify any characteristics essential for safe and proper use ISO/TS 16949:2002 requires additionally design outputs.
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IV. PRODUCT AND PROCESS DESIGN DESIGN VERIFICATION
Design Verification (Continued) Verification is confirmation by examination and evaluation of objective evidence that a specific design specification has been met. Validation is confirmation by examination and evaluation of objective evidence that a specific intention has been met. The difference between these two activities entails who does them and the nature of the acceptance criterion.
C Verification is conducted by engineering to determine if the material, component, module, subsystem or system meets the design specifications. C Validation is conducted by the customer (end-user) to see if the product meets their needs. The (internal and external) customer validates the product against their indicated quality characteristics.
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IV. PRODUCT AND PROCESS DESIGN DESIGN VERIFICATION
Design Verification (Continued) Customer Requirements
Verification is done by engineering to design specifications at each stage.
System Specifications Subsystem Specifications Module Specifications Component/Material Specifications Verification
Validation
Component or Material Module Subsystem System Product
Validation is done by the customer to accept the product’s fitness of use, usually when the product is complete.
Verification and Validation Relationships
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IV. PRODUCT AND PROCESS DESIGN DESIGN VERIFICATION
Design Verification (Continued) Several different qualification methods can be used for product verification and validation. One obvious qualification method is to use product testing to determine if the product meets the criteria set forth in the design specification. This tends to be the most common and straight forward method. Another qualification method is product testing using a third-party such as a nationally recognized testing laboratory. It is common for household and electrical products to have safety qualification testing conducted by Underwriters Laboratories.
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IV. PRODUCT AND PROCESS DESIGN RELIABILITY AND MAINTAINABILITY / INTRODUCTION
Reliability and Maintainability Reliability and Maintainability is presented in the following topic areas:
C C C C C
Introduction Preventive maintenance Reliability and maintainability indices Bathtub curve Safety and hazard assessment tools
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IV. PRODUCT AND PROCESS DESIGN R & M / PREVENTIVE MAINTENANCE
Reliability Introduction With an increase in the technical complexity of products, and the advent of world-wide competition, there has been growing concern about product reliability. Simply stated, reliability is the assurance that the product will perform as intended. Product durability implies that the product will last for a long time. Reliability is the probability that a product will perform its intended function satisfactorily for a pre-determined period of time in a given environment. Note that there are four key elements in this definition. One might state that the reliability of an electric motor to operate a water pump in a 35 ° to 100 °F ambient temperature environment for five years is 0.95.
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IV. PRODUCT AND PROCESS DESIGN R & M / PREVENTIVE MAINTENANCE
Preventive Maintenance In general, most pieces of equipment, machinery, or systems are under some sort of preventive maintenance program. When an item or system experiences a breakdown or failure, the item is normally repaired. Individual parts may be replaced in the system, but the bigger system is maintained. In the operation of a plant, equipment and systems fail unexpectedly. The repair of these types of failures is considered corrective maintenance items. Corrective maintenance cannot be planned, but can be determined by reliability. The mean time to repair (MTTR) is applicable for such items. If an item cannot be repaired upon failure, it is characterized by a mean time to failure (MTTF).
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IV. PRODUCT AND PROCESS DESIGN R & M / PREVENTIVE MAINTENANCE
Preventive Maintenance (Continued) The time to repair has three elements to it: 1. Preparation time: Locating people, traveling to the site, obtaining tools, parts, and instruments. 2. Active maintenance time: Studying the charts, performing the repair, and verifying the repair. This can be specified as the mean active maintenance time (MAMT). 3. Delay time: The wait time involved in such activities as locating charts, waiting at the store’s counter, waiting on production to clear the area, and awaiting personnel to verify repairs. Preventive maintenance (PM) has the function of the prevention of failures via planned or scheduled efforts.
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IV. PRODUCT AND PROCESS DESIGN R & M / PREVENTIVE MAINTENANCE
Preventive Maintenance (Continued) Ireson (1996) defines the maintenance concerns as:
C C C C C C C C C C
The mission profile Availability and/or reliability requirements Maintenance worker constraints Weight and volume restrictions Spare parts policy Periodic testing Scheduled maintenance Geographic nature of the system The levels of specialized maintenance required Planned types of support equipment
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IV. PRODUCT AND PROCESS DESIGN R & M / PREVENTIVE MAINTENANCE
Preventive Maintenance (Continued) To optimize maintenance costs and operating costs, it is necessary to gather information and data for the maintained part. The information would include: 1. The time-to-failure distribution parameters for the main failure modes 2. The effects of the failure modes 3. The cost of failure 4. The cost of scheduled replacement 5. The effect of maintenance on reliability 6. The increase in defects before failure 7. The cost of inspection or test (O’Connor, 1996)
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IV. PRODUCT AND PROCESS DESIGN R & M / PREVENTIVE MAINTENANCE
Preventive Maintenance (Continued) The knowledge of various hazard rates are meaningful in that:
C Given a decreasing hazard rate, it is best to not replace the part. C Given a constant hazard rate, part replacement does not reduce failure rates. C Given an increasing hazard rate, scheduled replacement reduces failure rates. C Given an almost failure-free, but increasing hazard rate, scheduled replacement will provide a near zero failure rate.
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IV. PRODUCT AND PROCESS DESIGN R & M / PREVENTIVE MAINTENANCE
Preventive Maintenance (Continued) The collection of information on replaced or maintained parts will provide useful information. The knowledge of various hazard rates are meaningful:
Decreasing hazard rate, it is best to not replace the part. Scheduled maintenance will return the part to the top of the curve.
Constant hazard rate, part replacement will result in the same probability of failure as before.
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IV. PRODUCT AND PROCESS DESIGN R & M / PREVENTIVE MAINTENANCE
Preventive Maintenance (Continued)
Increasing hazard rate. Scheduled replacement of a part will reduce the probability of failures.
Increasing hazard rate with near failure free life. Scheduled maintenance will ensure near failure free probability.
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IV. PRODUCT AND PROCESS DESIGN R & M / INDICES
Reliability and Maintainability Indices Availability
A measure of the degree to which an item is in an operable and committable state at the start of a mission when the mission is called for at an unknown (random) time.
Dependability A measure of the degree to which an item is operable and capable of performing its required function at any (random) time during a specified mission profile, given item availability at the start of the mission. Failure mode and effects analysis (FMEA)
A procedure by which each potential failure mode in a system is analyzed to determine the results or effects thereof on the system, and to classify each potential failure mode according to its severity.
Failure rate (8)
The total number of failures within an item population, divided by the total number of life units expended by that population, during a particular measurement interval under stated conditions.
IV-70 (454)
© QUALITY COUNCIL OF INDIANA CQE 2006
IV. PRODUCT AND PROCESS DESIGN R & M / INDICES
Failure Rate and MTBF For exponential data, the failure rate of a product can be calculated from test data using the formula: Failure Rate = λ =
Number of items failed Total operating hours
For exponential data, the mean time between failures can be calculated from test data using the formula: MTBF = θ =
Total operating hours Number of items failed
There is an obvious relationship between failure rate and MTBF: Failure rate =
1 MTBF
or λ =
1 θ
Various sources denote mean time between failures (MTBF) as either μ or θ. When a product is repairable, MTBF is used. If not, MTTF is used.
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IV. PRODUCT AND PROCESS DESIGN R & M / INDICES
Failure Rate and MTBF (Continued) Example: If seven items are tested for 50 hours each, and one item fails at 20, 38 and 42 hours respectively, what is the failure rate of the item? Let: x = 3, n = 7, t n = 50, t 1 = 20, t 2 = 38, t 3 = 42 λ=
x n
∑t
i
+ ( n - x ) ( tn )
i=1
λ=
3 20 hr + 38 hr + 42 hr + ( 7 - 3 ) ( 50 hr )
λ = 0.01/hr
What is the MTBF? MTBF = θ =
1 1 = = 100 hr λ 0.01 hr
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IV. PRODUCT AND PROCESS DESIGN R & M / INDICES
Series System Reliability In a series system, the total reliability of the system is dependent on each individual component working. The reliability of this type of system is the product of all of the individual component reliabilities. Example: Determine the series system reliability.
Formula:
Answer:
Rseries = R1 x R2 x R3 = 0.90 x 0.95 x 0.94 = 0.80
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IV. PRODUCT AND PROCESS DESIGN R & M / INDICES
Parallel System Reliability In a parallel system, the reliability of the system is calculated by subtracting the product of the unreliabilities from 1. Example: Determine the parallel system reliability.
Formula:
Answer:
U1 = 1 - R1 = 0.10 U2 = 1 - R2 = 0.05 U3 = 1 - R3 = 0.06 Rparallel = 1 - (U1 x U2 x U3) = 1 - (0.10 x 0.05 x 0.06) = 1 - (0.0003) Rparallel = 0.9997
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IV. PRODUCT AND PROCESS DESIGN R & M / INDICES
Combination Systems The important thing to remember in a combined system is to solve the reliability of the parallel system first, then use it in series to solve the series system reliability. Example: Determine the reliability of the combination system below. R2 = 0.9 Input
R1 = 0.95
R4 = 0.99
Output
R3 = 0.9
Formula: R2,3 parallel = 1 - U2 x U 3 = 1 - (0.10 x 0.10) = 1 - 0.01 = 0.99 Rsystem Answer:
= R1 x R2,3 x R4 = 0.95 x 0.99 x 0.99 = 0.93
From the calculations above, it should be clear that the parallel design offers a greater assurance of performance.
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IV. PRODUCT AND PROCESS DESIGN R & M / INDICES
Other Systems There are a large number of system modeling formats, which are probably too complex for the CQE exam. They include:
C C C C C C
Active redundancy systems Standby parallel systems Shared load systems Bayes’ theorem applications Boolean truth table methods Tie and cut set methods
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IV. PRODUCT AND PROCESS DESIGN R & M / INDICES
Exponential Distribution The exponential distribution shown below is commonly used for predicting the reliability of items in the constant rate failure period.
R(t)
t
The reliability for the exponential distribution is: R t = e - λt
or R t = e
-
t θ
-
or R t = e
t μ
Where: Rt = Probability of failure-free operation for a time period t = Specified period of failure-free operation : = 2 = Mean time between failures (MTBF) 8 = Failure rate (the reciprocal of :) e = Natural logarithm base = 2.71828 ...
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IV. PRODUCT AND PROCESS DESIGN R & M / INDICES
Exponential Distribution (Continued) The hazard rate for the exponential is: f (t) λ e - λt h(t) = = - λt = λ R (t) e
The hazard rate is unchanging. Another way that this is stated is that the exponential distribution has a constant failure rate. The exponential properties:
distribution
has
the
following
C The mean and standard deviation have the same value. C Approximately 63.21% of the area under the curve falls below the mean.
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IV. PRODUCT AND PROCESS DESIGN R & M / INDICES
Exponential Distribution (Continued) Example: An item has an exponential failure rate and a MTBF of 500 hours. What is the reliability at 400 hours? 1 1 = = 0.002 failures / hr MTBF 500 hr R ( t ) = e - λt λ=
R ( 400 ) = e- (0.002/hr)(400 hr) R ( 400 ) = 0.449
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IV. PRODUCT AND PROCESS DESIGN R & M / INDICES
Weibull Distribution The Weibull distribution consists of many distributional shapes rather than a single unique shape as in many distributions. The shape of the distribution is mainly a function of the shape parameter $. Several different curve shapes are shown in the Figure below. All curves have the same scale parameter, 0.
$ < 1 Infant mortality $ = 1 Useful life $ > 1 Wearout
There are two common versions of the Weibull distribution used in reliability. The two parameter Weibull and three parameter Weibull. The difference is that the three parameter Weibull distribution has a location parameter
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IV. PRODUCT AND PROCESS DESIGN R & M / INDICES
Weibull Distribution (Continued) For the three parameter Weibull distribution: β -1
β ⎛ t-γ ⎞ ⎛ t-γ ⎞ f (t) = ⎜ exp⎜ η ⎟ η ⎝ η ⎟⎠ ⎝ ⎠
β
for t ≥ γ
Where: $ is the shape parameter 0 is the scale parameter ( is the non-zero location parameter Note the scale parameter is the point where 63.21% of values fall below this parameter. When $ is 1.0, the Weibull function reduces to the exponential and when $ is about 3.5 (and 0 = 1 and ( = 0), the Weibull closely approximates the normal distribution.
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IV. PRODUCT AND PROCESS DESIGN R & M / INDICES
System Effectiveness In many cases, individual items are assembled into subsystems and then into systems. As systems become more complex, the probability of individual items failing becomes greater. It becomes important in many instances that the failure. System effectiveness, then, is a combination of several issues brought together to determine if a system has a high likelihood of achieving the mission at hand. The three major components of a system’s effectiveness are availability, dependability, and capability.
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IV. PRODUCT AND PROCESS DESIGN R & M / INDICES
System Effectiveness (Continued) System effectiveness: A measure of the degree to which an item or system can be expected to achieve a set of specific mission requirements, and which may be expressed as a function of availability, dependability and capability. SE = Availability x Dependability x Capability* The definitions of the three components are: Availability: A measure of the degree to which an item or system is in the operable and committable state at the start of the mission. Dependability: A measure of the item or system operating condition. It may be stated as the probability that an item will (a) enter or occupy any one of its required operational modes during a specified mission, and (b) perform the functions associated with those modes. Capability: A measure of the ability of an item or system to achieve mission objectives given the conditions during the mission.
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IV. PRODUCT AND PROCESS DESIGN R & M / INDICES
Maintainability Maintainability: The measure of the ability of an item to be retained or restored to a specified condition when maintenance is performed by personnel having specified skill levels, using prescribed procedures and resources, at each prescribed level of maintenance and repair. The maintenance action rate is a key component of maintainability. If an item fails, how long does it take to get back into service? The maintenance action rate is often prescribed by contract and is defined as: Maintenance action rate: The reciprocal of the mean time between maintenance actions or 1/MTBMA.
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IV. PRODUCT AND PROCESS DESIGN R & M / INDICES
Availability Availability: A measure of the degree to which an item is in the operable and committable state at the start of a mission, when the mission is called for at an unknown (random) time. The three common measures of availability are: 1. Inherent availability (Ai): This is the ideal state for analyzing availability. The only considerations are the MTBF (reliability) and the MTTR (maintainability). This measure does not take into account the time for preventive maintenance and assumes repair begins immediately upon failure of the system. The measure for inherent (potential) availability (Ai) is: Ai =
MTBF MTBF + MTTR
Note: MTTR stands for mean time to repair.
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IV. PRODUCT AND PROCESS DESIGN R & M / INDICES
Availability (Continued) 2. Operational availability (Ao): This is what generally occurs in practice and takes into account that the maintenance response is not instantaneous. The measure of operational (actual) availability Ao is: Ao =
MTBMA MTBMA + MDT
Where: MTBMA is the mean time between maintenance actions both preventive and corrective and MDT is mean down time. 3. Achieved availability (AA): Achieved availability is somewhat more realistic in that it takes preventive and corrective maintenance. The assumption is no loss of time waiting for the maintenance action to begin. The measure for achieved (final) availability (AA) is: AA =
MTBMA MTBMA + MMT
Where: MTBMA is the mean time between maintenance actions both preventive and corrective and MMT is the mean maintenance action time MMT =
Fc Mct + Fp Mpt Fc + Fp
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IV. PRODUCT AND PROCESS DESIGN R & M / BATHTUB CURVE
Bathtub Curve The three general types of failures observed for complex products are illustrated with the life-history or “bathtub” curve. It should be noted that many electrical products do not follow this model. Infant mortality. These failures are generally the result of components that do not meet specifications or workmanship that is not up to standard. These are not design related issues, but quality related issues. The infant mortality period is noted by a decreasing failure rate. The Weibull distribution is commonly used to determine when the infant mortality period is over. Constant failure rate. Once the failures due to components and workmanship are eliminated, the constant failure rate period is entered. This is also called the random failure rate period. One can predict the probability of a failure in a certain interval, but not a specific failure at a specific time. The constant failure rate period is the most common time frame for making reliability predictions. The exponential distribution is utilized.
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IV. PRODUCT AND PROCESS DESIGN R & M / BATHTUB CURVE
Bathtub Curve (Continued) Wearout period. As components begin to fatigue or wear out, one begins to observe failures at an increasing rate. As time goes on, failures occur more and more frequently to a point where it may no longer be practical to continue operating the system. Several distributions may be appropriate to model the wearout period. The normal and log normal distributions are often used.
An Illustrative Life - History Curve
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IV. PRODUCT AND PROCESS DESIGN R & M / BATHTUB CURVE
Distribution of Time Between Failures Along with concern for high failures during the infant mortality period, customers must be concerned with the length of time that a product will run without failure. This measurement concerns the second stage of the bathtub curve known variously as the normal, chance, or random failure period. Often this failure rate is constant with the time between failures distributed exponentially as shown below:
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IV. PRODUCT AND PROCESS DESIGN R & M / HAZARD ASSESSMENT TOOLS
FMECA A FMECA provides the design engineer, reliability engineer, and others with a systematic technique to analyze a system, subsystem, or item, for all potential or possible failure modes. This method then places a probability that the failure mode will actually occur and what effect this failure has on the rest of the system. The criticality portion of this method allows one to place a value or rating on the criticality of the failure effect on the entire system. A FMEA or FMECA (in some cases there is little, if any, difference) is a detailed analysis of a system down to the component level. Once all of the items are classified as to the failure mode, effect of failure, and probability that failure will occur, they are rated as to their severity via an index called an RPN (risk priority number). Once all components or items have been analyzed and assigned an RPN value, it is common to work from the highest RPN value down.
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IV. PRODUCT AND PROCESS DESIGN R & M / HAZARD ASSESSMENT TOOLS
FMECA Process Steps 1. FMEA Number: assigned number 2. The part number, name, description 3. Design responsibility: 4. Person responsible for FMEA preparation 5. Date the FMEA was prepared and revision level 6. Subsystem part number 7. Component function 8. Potential failure mode 9. The potential effect of failure 10. The potential cause of failure 11. What current controls to prevent the failure?
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IV. PRODUCT AND PROCESS DESIGN R & M / HAZARD ASSESSMENT TOOLS
FMECA Process Steps (Continued) Risk Assessment and RPN The next major step is to weigh the risks associated with the current component, effect, and cause with the controls that are currently in place. 12. P is the probability this failure mode will occur. Values for this index generally range from 1 to 10, with 1 being virtually no chance, and 10 being near certainty of occurrence. 13. S is the severity of the effect of the failure on the rest of the system if the failure occurs. These values are often indexed from 1 to 10. A value of 1 means the user will be unlikely to notice, with a 10 meaning that the safety of the user is in jeopardy. 14. D is a measure of the effectiveness of the current controls (in place) to identify the potential weakness or failure prior to release to production. This index may also range from 1 to 10. A value of 1 means this will certainly be caught, whereas a value of 10 indicates the design weakness would most certainly make it to final production without detection.
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IV. PRODUCT AND PROCESS DESIGN R & M / HAZARD ASSESSMENT TOOLS
FMECA Process Steps (Continued) 15. RPN. The risk priority number is the product of the indices from the previous three columns. RPN = PASAD 16. The actions then are based upon what items either have the highest RPN and/or where the major safety issues are. 17. There is a column for actions to be taken to reduce the risk, a column for who is responsible and finally a column for the revised RPN, once corrective action is implemented. In summary, the FMECA provides a disciplined approach for the engineering team to evaluate designs to ensure that all the possible failure modes have been taken into consideration.
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IV. PRODUCT AND PROCESS DESIGN R & M / HAZARD ASSESSMENT TOOLS
System FMECA Part No./Name: Project: Other Departments: Subsystem Name: Suppliers Involved: Design Responsibility:
37XT11-Lock Mech. Re-design Shop Service, etc. Quill Clamping Mechanisms Wilton and others Bob Dovich
P = Probability S = Seriousness D = Likelihood RPN = Risk Priority Number
PART FUNCTION POTENTIAL POTENTIAL CURRENT RISK POTENTIAL CONTROLS ASSESSMENT NUMBER FAILURE EFFECT(S) CAUSE(S) OF NAME MODE(S) OF FAILURE FAILURE P S D RPN WILTON POWER LOCK
CLAMP
LEAK
HOUSEKEEPING
ACCEPT SUPPLIER'S 2 4 3 INFO
24
LOSES MACHINING SELECTED CLAMPING PARTS INADEQUATE ENG. 2 4 4 FORCE OVERSIZE SIZE POWER STANDARD (SHIFTING) LOCK
32
WEAR
FMEA No. 43 Final Design Deadline: Prepared By: Reviewed By: FMEA Date:
RECOMMENDED CORRECTIVE ACTION(S)
ACTION(S) REVISED RISK RESPONSIBLE TAKEN ASSESSMENT DEPT OR INDIVIDUAL P S D RPN
DISCUSS WITH SUPPLIER
PERFORM LOAD TESTS
MATERIALS & WORKMANSHIP
STD. Q.C.
1 4 2
8
OVER PRESSURE
NONE
2 4 2
16
REVIEW NEED FOR SYSTEM TO PREVENT OVERPRESSURIZATION
8
REVIEW PRESSURE DELIVERED IN FIELD AND ACTUAL NEED
PUMP SIZING
Dec. 1, 2006 RCD BLW Nov. 20, 2006 Rev.
NONE
ENG. 1 4 2 STANDARD
An Illustrative FMECA Note that the above FMECA breakdown uses two probability components: The probability that the failure mode will occur (P) and the probability of detection prior to release (D).
© QUALITY COUNCIL OF INDIANA CQE 2006
IV-83 (478)
IV. PRODUCT AND PROCESS DESIGN R & M / HAZARD ASSESSMENT TOOLS
Risk Assessment Risk assessment is the combination of the probability of an event or failure and the consequence(s) of that event or failure to a system’s operators, users, or its environment. The analysis of risk of failure normally utilizes two measures of failure:
C Severity of failure C Probability of failure
© QUALITY COUNCIL OF INDIANA CQE 2006
IV-84 (479)
IV. PRODUCT AND PROCESS DESIGN R & M / HAZARD ASSESSMENT TOOLS
Risk Assessment (Continued) The severity of failure is generally defined by the hazard severity categories from MIL-STD-1629 (1980). These are shown in Table below. Classification I
Description
Catastrophic A failure that may cause death or mission loss
II
Critical
A failure that may cause severe injury or major system damage
III
Marginal
A failure that may cause minor injury or degradation in mission performance
IV
Minor
A failure that does not cause injury or system damage but may result in system failure and unscheduled maintenance
Hazard Severity Categories
© QUALITY COUNCIL OF INDIANA CQE 2006
IV-84 (480)
IV. PRODUCT AND PROCESS DESIGN R & M / HAZARD ASSESSMENT TOOLS
Risk Assessment (Continued) Another example, from Ireson (1996) uses a severity index based on a scale from 1 to 10. Rank 1
Criteria It is unreasonable to expect that the minor nature of this failure will degrade the performance of the system.
2-3
Minor nature of failure will cause slight annoyance to the customer. Customer may notice a slight deterioration of the system performance.
4-6
Moderate failure will cause customer dissatisfaction. Customer will notice some system performance deterioration.
7-8
High degree of customer dissatisfaction and inoperation of the system. Does not involve safety or noncompliance to government regulations.
9 - 10
Very high severity ranking in terms of safety-related failures and nonconformance to regulations and standards. Commercial Severity Index (Scale 1 - 10)
© QUALITY COUNCIL OF INDIANA CQE 2006
IV-85 (481)
IV. PRODUCT AND PROCESS DESIGN R & M / HAZARD ASSESSMENT TOOLS
Risk Assessment (Continued) The hazard classification or severity index is generated for each component or subsystem by the reliability analyst. This classification is based on the expected results of the failure of the component or subsystem. The probability of failure may also be ranked. A common ranking of failure probabilities is shown in below. Failure Description Probability Level
Probability
A
High likelihood of occurrence
>10-1
B
Probable occurrence
10-1 to 10-2
C
Occasionally occurs
10-2 to 10-3
D
Remote probability
10-3 to 10-6
E
Highly unlikely
<10-6
A Common Failure Probability Ranking
© QUALITY COUNCIL OF INDIANA CQE 2006
IV-85 (482)
IV. PRODUCT AND PROCESS DESIGN R & M / HAZARD ASSESSMENT TOOLS
Risk Assessment (Continued) A number of systems are used to combine the probability of failure and the hazard category. These systems are based on accepting a degree of risk of occurrence with respect to the severity of the hazard. For instance, the table below shows one type of risk assessment matrix. Hazard Category
Allowable Failure Probability Level
I Catastrophic
E (Unlikely)
II Critical
E (Unlikely)
III Marginal
D (Remote)
IV Minor
C (Occasional)
Example Risk Assessment Matrix * Frequently, catastrophic failure modes have additional safety measures, such as redundant components or frequent inspections during service, etc. Note that no hazard category has an allowable failure probability of “frequent” or “probable.”
© QUALITY COUNCIL OF INDIANA CQE 2006
IV-86 (483)
IV. PRODUCT AND PROCESS DESIGN R & M / HAZARD ASSESSMENT TOOLS
Fault Tree Analysis Fault tree analysis (FTA) is a systematic, deductive methodology for defining a single, specific, undesirable event, and determining all possible reasons (failures) that could cause that event to occur. The FTA is an easier and faster method of analysis compared to FMECA because it focuses on those system failures that can cause a catastrophic “top” event. FMECA progresses sequentially through all possible system failure modes, regardless of their severity. When properly applied, a FTA is extremely useful during the initial product design phase. Other potential uses of FTA include:
C C C C C C C C
Functional analysis of highly complex systems Evaluation of subsystem events on the top event Evaluation of safety requirements Evaluation of system reliability Identification of design defects and safety hazards Evaluation of potential corrective actions Maintenance and troubleshooting simplification Logical elimination of causes
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IV-86 (484)
IV. PRODUCT AND PROCESS DESIGN R & M / HAZARD ASSESSMENT TOOLS
Fault Tree Analysis FTA is preferred over FMECA/FMEA when:
C C C C C C C
The safety of personnel is paramount A small number of “top events” can be identified A functional profile is of critical importance There is a high potential for error failure The primary concern is a quantified risk evaluation Product functionality is highly complex The product is not repairable once initiated
FMECA/FMEA is preferred over FTA when:
C C C C
Top events cannot be explicitly defined Multiple successful profiles are feasible The identification of all failure modes is important Product functionally has little human intervention (Reliability Toolkit, 1993)
© QUALITY COUNCIL OF INDIANA CQE 2006
IV-87 (485)
IV. PRODUCT AND PROCESS DESIGN R & M / HAZARD ASSESSMENT TOOLS
FTA Event Symbols There are numerous symbols used in FTA, and these are broken down into two main categories; event symbols and gate symbols as shown below: or
Top event: Contains a description of a system-level fault or undesired event. Basic event: Usually the lowest level of event fault that one wishes to study. It is used as an input to a logic gate. Undeveloped event: This is a fault at the lowest level of examination which is not expanded upon. The undeveloped event is used as an input to a logic gate. It may be developed later.
© QUALITY COUNCIL OF INDIANA CQE 2006
IV-87 (486)
IV. PRODUCT AND PROCESS DESIGN R & M / HAZARD ASSESSMENT TOOLS
FTA Event Symbols (Continued) Input event: Contains what would be an input fault into the system. The input fault can be an internal system fault or a condition from a source that is external to the system.
Fault event: Contains a description of a lower-level fault. It can receive inputs from or provide outputs to a logic gate.
Transfer function: A connection between two or more sections of a fault tree or to signify a location on a separate sheet of the same tree.
© QUALITY COUNCIL OF INDIANA CQE 2006
IV-88 (487)
IV. PRODUCT AND PROCESS DESIGN R & M / HAZARD ASSESSMENT TOOLS
Logic (Gate) Symbols
“and” gate (series)
The output event occurs only if all the input events occur simultaneously.
“or” gate (parallel)
The output event occurs if any one of the input events occur.
Priority “and” gate
The output event occurs if, and only if, all of the input events occur in the order from left to right.
© QUALITY COUNCIL OF INDIANA CQE 2006
IV-88 (488)
IV. PRODUCT AND PROCESS DESIGN R & M / HAZARD ASSESSMENT TOOLS
Logic (Gate) Symbols (Continued)
Exclusive “or” gate
The output occurs if one, but not both, of the input events occur.
m out of n The output event occurs if m (voting) gate of n input events occur. n inputs
© QUALITY COUNCIL OF INDIANA CQE 2006
IV-89 (489)
IV. PRODUCT AND PROCESS DESIGN R & M / HAZARD ASSESSMENT TOOLS
Fault Tree Analysis Example Fault tree analysis begins at the system level, assuming that failure occurs. For instance, consider the probabilities for a home computer failing to work as shown in below: COMPUTER FAILS TO WORK
OR
0.0001 CALCULATED
HARD DRIVE 0.001
AND
CD ROM DRIVE D
CD ROM DRIVE E
0.010
0.010
CPU 0.015
KEYBOARD
MONITOR
0.020
0.015
© QUALITY COUNCIL OF INDIANA CQE 2006
IV-89 (490)
IV. PRODUCT AND PROCESS DESIGN R & M / HAZARD ASSESSMENT TOOLS
FTA Example (Continued) The fault tree is analyzed using the failures, instead of the successes. In the above case, the computer fails to operate if CD ROM drive D and drive E fail, or the hard drive fails, or the CPU fails, or the keyboard fails, or the monitor fails. Since “and” gates multiply and “or” gates add, the probability of the home computer not working can be computed.
:system = 1 - (0.9999)(0.999)(0.985)(0.98)(0.985) :system = 1 - 0.9498 :system = 0.0502 The probability of a failure is 5.02%
© QUALITY COUNCIL OF INDIANA CQE 2006
IV-90 (491)
IV. PRODUCT AND PROCESS DESIGN R & M / HAZARD ASSESSMENT TOOLS
Success Tree Analysis Success tree analysis begins at the system level and assumes a successful system operation. Unlike the fault tree in which the top event is undesirable, the success tree top event is a desirable goal. For instance, consider the probability of success for a home computer operating as shown below. COMPUTER WILL OPERATE
AND
0.9999 CALCULATED
HARD DRIVE
CPU
0.999
0.985
KEYBOARD 0.980
MONITOR 0.985
OR
CD ROM DRIVE D 0.990
CD ROM DRIVE E 0.990
The probability of the home computer working can be computed. Rsystem = (0.9999)(0.999)(0.985)(0.980)(0.985) Rsystem = 0.9498
© QUALITY COUNCIL OF INDIANA CQE 2006
IV-91 (492)
IV. PRODUCT AND PROCESS DESIGN R & M / HAZARD ASSESSMENT TOOLS
Product Safety and Liability A company is liable for its products. The idea that the consumer accepts all the risk as presented in the legal phrase “caveat emptor” (let the buyer beware) is no longer valid. A company has the responsibility to make good on any loss or damage incurred by the user of its product. This is defined by the word liability. Many liability lawsuits are won when the supplier shows deliberate, glaring indifference for user safety. Companies with product safety programs generally need not worry about this type of case because they can normally demonstrate deliberate efforts to protect the user. Unfortunately, blatant user indifference is not the only user safety consideration. Many concepts of law take into account a degree of reasonableness. That is, the standards by which issues are judged are based upon reasonable expectations, safeguards, or user responsibility. However, the present liability standards are moving ever closer to absolute liability. Absolute liability generally absolves the user of fault and places any and all safety responsibilities upon the designer, manufacturer, distributor, or store.
© QUALITY COUNCIL OF INDIANA CQE 2006
IV-91 (493)
IV. PRODUCT AND PROCESS DESIGN R & M / HAZARD ASSESSMENT TOOLS
Product Safety and Liability (Continued) The majority of activities involved in a product safety program take place before a product is placed in the user’s hands. A human factors analysis is one tool used to uncover risk and safety issues associated with the user’s operation of products. The user focus helps reveal many of these post-sale issues before products are released to the customers. However, once a product is in the hands of users, new misuses, risks, user negligence, or additional hazard exposures may become apparent. Often users seek liability damages because a product creates a risk that the company could not predict during the design and manufacturing efforts. These lawsuits are successful because the company has the responsibility to warn users about uncovered post-sale hazards. Without the post-sale monitoring process, the company cannot become aware of new hazards.
© QUALITY COUNCIL OF INDIANA CQE 2006
IV-92 (494)
IV. PRODUCT AND PROCESS DESIGN R & M / HAZARD ASSESSMENT TOOLS
Product Safety and Liability (Continued) One product liability lawsuit can ruin a company. For this reason, many companies involve external or internal legal professionals, along with product safety professionals throughout the product development process. Presented below are some milestone liability and product safety regulations. Topic Traffic safety legislation
Regulations
C C
Consumer Product Safety Act (1972)
C C
Food and Drug, many different acts
C C C C
Directed at the vehicle. The NHTSA instituted passenger restraints (1966) Other laws directed at the motorist and the environment Directed at a wide range of consumer products Granted powers to the Consumer Product Safety Commission Pure Food and Drug Act (1906) Medical Good Manufacturing Practices (1978) Medical Risk (1990) Medical Quality System Regulation (QSR) Covering Manufacturing and Design (1996)
© QUALITY COUNCIL OF INDIANA CQE 2006
IV-92 (495)
IV. PRODUCT AND PROCESS DESIGN R & M / HAZARD ASSESSMENT TOOLS
Product Safety and Liability (Continued) Since products can impact human health and safety, design errors can lead to large personal injury claims. Strategies for dealing with this type of liability include:
C Paying attention to reliability and quality in product development and testing C Releasing products that are well-tested and meet requirements C Establishing mechanisms for immediately notifying customers of any hazards C Arranging a quick replacement of defective units, when a critical problem is found C Selecting a product liability insurance policy that includes provisions for defense of judgments C Negotiating end-user agreements that have a limitation on all damages C Including legal counsel in contract negotiations to be sure the company has adequate protection
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IV-93 (496)
IV. PRODUCT AND PROCESS DESIGN R & M / HAZARD ASSESSMENT TOOLS
Programs to Improve Product Safety C Top management: C C C C C C
Commits to make and sell only safe products Mandates formal design reviews Establishes guidelines for product traceability Establishes claim defense guidelines Establishes safety performance guidelines Ensures compliance via audits
C Supplemental organization product safety structure: C A product safety committee C Safety engineers C Outside experts for advice and audits C Other key product safety responsibility centers include: C C C C C
Product design Manufacturing Quality control Marketing Field service
organizational
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IV-94 (497)
IV. PRODUCT AND PROCESS DESIGN R & M / HAZARD ASSESSMENT TOOLS
Safety Factor A design engineer concerned with mechanical loading devices must consider the safety factor and margin of safety. These are defined as: S a fe ty F a c to r = S .F . =
μx μy
MOS =
μx - μy μy
Where :x = average strength and :y = average stress Example: An aircraft component is being designed with an average material strength of 60,000 psi. The expected stress is 32,000 psi. What is the safety factor? What is the margin of safety? S.F. = MOS =
μx 60,000 psi = = 1.875 = 187.5% 32,000 psi μy μx - μy μy
=
60,000 psi - 32,000 psi = 0.875 32,000 psi
© QUALITY COUNCIL OF INDIANA CQE 2006
IV-94 (498)
IV. PRODUCT AND PROCESS DESIGN R & M / HAZARD ASSESSMENT TOOLS
Stress-Strength Interference In the most basic terms, an item fails when the applied stress exceeds the strength of the item. In general, designers design for a nominal part strength and anticipated applied stress. The variability about the stress and strength nominals is also important. In the Figure below, the distribution curves for stress and strength are far enough apart that there is little probability that a high stress level would interfere with an item that is on the low end of the strength distribution.
© QUALITY COUNCIL OF INDIANA CQE 2006
IV-95 (499)
IV. PRODUCT AND PROCESS DESIGN R & M / HAZARD ASSESSMENT TOOLS
Stress-Strength Interference (Continued) In the Figure below, the proximity and variability of the means for stress and strength indicate an increased likelihood of failure which is represented by the overlapping shaded area.
Stress - Strength Overlap When the stress distribution and strength distribution are independent of each other, the following relationships apply: μ x-y = μ x - μ y
σ x-y = ( σ 2x + σ 2y )
1/2
© QUALITY COUNCIL OF INDIANA CQE 2006
IV-95 (500)
IV. PRODUCT AND PROCESS DESIGN R & M / HAZARD ASSESSMENT TOOLS
Stress-Strength Interference (Continued) To calculate the probability of a failure from stressstrength interference, the standard normal distribution and Z tables are utilized. Z=
μx - μy
(σ
2 x
+ σ 2x )
1/2
Example: If the stress distribution has a mean stress of 1,500 lb with a standard deviation of 20 lb and the unit is designed to handle 1,600 lb with a standard deviation of 30 lb Calculate Z to get the probability of failure:
Z=
μx - μy
(σ
2 x
+ σx ) 2
1/2
=
1600 lb - 1500 lb
( ( 30 lb )
2
+ ( 20 lb )
2
)
1/2
= 2.77
From a standard normal distribution, the area above a Z value of 2.77 (2.77 standard deviations) is 0.0028. The probability of failure is 0.28%.
© QUALITY COUNCIL OF INDIANA CQE 2006
IV-99 (501)
IV. PRODUCT AND PROCESS DESIGN QUESTIONS 4.2. A technique whereby various product features are graded as to relative importance is called: a. b. c. d.
Classification of defects Quality engineering Classification of characteristics Feature grading
4.4. Which of the following activities normally occurs after the final completion of a product design? a. b. c. d.
Verification Validation Apportionment Prototype conversion
4.7. For complex electronic systems, the major contributor to repair time is generally: a. b. c. d.
Diagnosis Disassembly/reassembly Remove/replace Final checkout
Answers: 4.2. c, 4.4. b, 4.7. a
© QUALITY COUNCIL OF INDIANA CQE 2006
IV-100 (502)
IV. PRODUCT AND PROCESS DESIGN QUESTIONS 4.14. Maintenance reduces the probability of failure when: a. b. c. d.
The hazard rate is constant The hazard rate is decreasing The hazard rate is increasing The hazard rate is unknown
4.16. In robust design, a factor that can cause unknown variability, or an error in the response factor, is considered a: a. b. c. d.
Signal factor Control factor Noise factor Response factor
4.18. In the failure rate model shown below, the part of the curve identified as A represents:
a. b. c. d.
The bathtub curve Random and independent failures fitting a Poisson model The debugging period for complex equipment The wear out period
Answers: 4.14. c, 4.16. c, 4.18. c
© QUALITY COUNCIL OF INDIANA CQE 2006
IV-101 (503)
IV. PRODUCT AND PROCESS DESIGN QUESTIONS 4.21. Failure modes and effects analysis involves what activity? a. The determination of the probability of failure in a specified period of time b. The expected number of failures in a given time interval c. The study of failure to determine how a product fails and what causes the failure d. A study of the probability of success in a given time period 4.22. The symbol a. b. c. d.
means:
Welds placed here Position Total runout Geometric tolerance
4.27. Maintainability is: a. The probability of a system being restored to functional operation within a given period of time b. Can be improved only by a state of the art improvement c. Probability of survival of a system for a given period of time d. Maintaining a machine in satisfactory working condition
Answers: 4.21. c, 4.22. c, 4.27. a
© QUALITY COUNCIL OF INDIANA CQE 2006
IV-102 (504)
IV. PRODUCT AND PROCESS DESIGN QUESTIONS 4.30. For a shaft with a specification of 1.000" ± 0.005", what is the MMC? a. b. c. d.
1.000" maximum 0.995" minimum 1.000" ± 0.005" 1.005" maximum
4.31. Reliability, maintainability, and product safety improvements are most often economically accomplished during which of the following phases? a. b. c. d.
Design and development Prototype test Production Field operation
4.35. The principal purpose of robust design techniques is to: a. b. c. d.
Make the product less sensitive to noise effects Use the tools of experimental design Reduce the sources of variation Improve manufacturing quality
Answers: 4.30. d, 4.31. a, 4.35. a
© QUALITY COUNCIL OF INDIANA CQE 2006
IV-103 (505)
IV. PRODUCT AND PROCESS DESIGN QUESTIONS 4.44. The risk priority number is used when: a. b. c. d.
Auditing safety hazards Predicting reliability Constructing a fault tree Completing a FMECA
4.45. A design review is conducted for the purpose of: a. b. c. d.
Verifying the details of all the drawings Verifying the accuracy of all the specifications Verifying workmanship quality of the drawings Verifying the completeness and accuracy of the overall design package
4.48. Specifying a tolerance by +0.000" -0.001", is known as: a. b. c. d.
Bilateral tolerancing Limit dimensioning Manufacturing limits Unilateral tolerancing
Answers: 4.44. d, 4.45. d, 4.48. d
© QUALITY COUNCIL OF INDIANA CQE 2006
IV-104 (506)
IV. PRODUCT AND PROCESS DESIGN QUESTIONS 4.53. If the average repair time for a system is 3 hours and the MTBMA is 122 hours, what is the operational availability? a. 0.975 b. 0.976
c. 0.982 d. 0.997
4.56. Criminal liability involving injury cases may be invoked in all of the following areas, EXCEPT: a. b. c. d.
Negligence Fraud Mountebank Knowingly violating a law
4.60. The qualification of a sophisticated product would entail: a. b. c. d.
Neither verification nor validation Verification, but not validation Both verification and validation Validation, but not verification
Answers: 4.53. b, 4.56. c, 4.60. c
© QUALITY COUNCIL OF INDIANA CQE 2006
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V. PRODUCT AND PROCESS CONTROL
OPPORTUNITIES ARE USUALLY DISGUISED AS HARD WORK, SO MOST PEOPLE DON’T RECOGNIZE THEM. ANN LANDERS
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V. PRODUCT AND PROCESS CONTROL TERMS
Product and Process Control Product and Process Control is presented in the following topic areas:
C Terms C Tools
C Material control C Acceptance sampling
Key Product and Process Control Terms Control plan: A written document of the activities controlling the process or product. Qualification process: A process of demonstrating that a product or process is capable of fulfilling a stated specification. Quality characteristic: A characteristic of a process or product which defines the quality of the process or product. Quality plan: A document with specific quality practices, resources, and sequences of activities to ensure that customer requirements, needs, and expectations are met.
© QUALITY COUNCIL OF INDIANA CQE 2006
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V. PRODUCT AND PROCESS CONTROL TERMS
Key Control Terms (Continued) Rework:The action taken on a nonconforming item so that it will fulfill the originally specified requirements. Special characteristic: A customer-identified product or process characteristic. Specification: Documented, detailed requirements with which a product or service must conform to. Traceability: The ability to trace the history, application, or location of a product, and in some cases, service, by means of recorded identifications. Validation: Confirmation by examination and provision of objective evidence that the particular requirements for a specific intended use are met. Verification: Confirmation by examination and provision of objective evidence that specified requirements have been met.
© QUALITY COUNCIL OF INDIANA CQE 2006
V-3 (510)
V. PRODUCT AND PROCESS CONTROL TERMS
Process Capability Process capability is a measure of the inherent uniformity of the process and the ability to direct the process to a defined target. It is often necessary to compare the process variation with the specification tolerances to judge the suitability of the process.
Quality Planning Documents Quality planning documents are designed for repetitive use. Customarily, they are included in the quality manual and detailed in quality procedures and work instructions. This documentation provides an organized methodology for their perpetual use.
© QUALITY COUNCIL OF INDIANA CQE 2006
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V. PRODUCT AND PROCESS CONTROL TOOLS
Written Procedures A procedure is a document that specifies the way to perform an activity. For most operations, a procedure can be created in advance by the appropriate individual(s). Some procedures may be developed by the quality department for use by other operating departments. Generally, these departments provide input.
Work Instructions Procedures describe the process at a general level, while work instructions provide details and a step-bystep sequence of activities. Controlled copies of work instructions are kept in the area where the activities are performed. Some discretion is required in writing work instructions, so that the level of detail included is appropriate for the background, experience, and skills of the personnel that would typically be using them.
© QUALITY COUNCIL OF INDIANA CQE 2006
V-4 (512)
V. PRODUCT AND PROCESS CONTROL TOOLS
Process Controls Production operations, which directly affect quality, are identified and planned to ensure that they are carried out under controlled conditions. Controlled conditions include the following:
C The prior approval of processes and equipment C Documented procedures defining the manner of production C The use of suitable production and servicing equipment, in an appropriate working environment C Compliance with reference standards, codes, quality plans, and documented procedures C The monitoring and control of suitable process and product characteristics C Workmanship criteria, stated in the clearest practical manner, must be provided C The suitable maintenance of equipment to ensure continued process capability
© QUALITY COUNCIL OF INDIANA CQE 2006
V-5 (513)
V. PRODUCT AND PROCESS CONTROL TOOLS
Product and Process Control Methods Determining product and process control methods is often called the development of a quality plan. Quality planning employs the coordination of company resources to meet customer requirements. The first necessity is to identify all the key internal and external customer requirements. One should remember to include all of the critical product and process characteristics uncovered throughout the complete design process. The second step is to identify the manufacturing process flow and the manufacturing support processes. The third step is to identify the quality tools that a company will use to control the processes.
© QUALITY COUNCIL OF INDIANA CQE 2006
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V. PRODUCT AND PROCESS CONTROL TOOLS
Product and Process Control (Cont’d) Requirements
Support Processes
Quality Tools
Outside diameter
Receiving inspection
Part work instructions
Finishing
Subassembly
Inspection instructions
Packing
System assemble
Process work instruction
Length
Final test
Quality procedures
Material
Shipping
Purchase order data
Safety tests
Purchasing
SPC charts
Labeling
Outside processing
Test fixtures
Identification
Training
Routing sheets
Examples of Product & Process Control Detail
© QUALITY COUNCIL OF INDIANA CQE 2006
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V. PRODUCT AND PROCESS CONTROL TOOLS
Product and Process Control (Cont’d) After the customer requirements, processes, and quality tools have been identified, a control plan can be detailed. First, one takes a customer requirement, then decides which process step and which quality tool should be used to satisfy the requirement. Some examples are:
C The outside diameter is checked at subassembly using a part work instruction. C The packing is completed at shipping using a process work instruction. C The material is controlled by purchasing using purchase order data, requiring a certificate of analysis, and at receiving inspection using a part work instruction. C The length is checked at final inspection using an inspection report. C A safety test is performed by an outside processor using the appropriate purchase order data.
© QUALITY COUNCIL OF INDIANA CQE 2006
V-7 (516)
V. PRODUCT AND PROCESS CONTROL TOOLS
Control Plans A control plan is a document describing the critical to quality characteristics of a part or process. Through this system of monitoring and control, customer requirements will be met, and the product or process variation will be reduced. Each part or process must have a control plan. A group of common parts using a common process can be covered by a single control plan.
© QUALITY COUNCIL OF INDIANA CQE 2006
V-7 (517)
V. PRODUCT AND PROCESS CONTROL TOOLS
Control Plans (Continued) For the automotive sector, ISO/TS 16949:2002 and the Advanced Product Quality Planning APQP (2000) identify three control plan phases:
C Prototype C Pre-launch C Production A prototype control plan is used in the early development stages when the part or process is being defined or configured. A pre-launch control plan is used after the prototype phase is completed, and before full production is approved. A production control plan is used for the full production of a part. It contains all of the line items for a full control plan.
© QUALITY COUNCIL OF INDIANA CQE 2006
V-7 (518)
V. PRODUCT AND PROCESS CONTROL TOOLS
Control Plans (Continued) Often, an improvement team will undertake a project to improve quality, costs, efficiencies, etc. A project control phase is then necessary in order to sustain the project gains. The control plan must truly be a “living document” (APQP, 2000) for it to remain effective. A responsible person must be placed in charge of the control plan. This ensures successful monitoring and updating. The project leader may or may not be a suitable person for the role, as he/she may be replaced or transferred to a different position. A better selection would be the “process owner.” The current process owner can be listed on the control plan, but in reality it is a functional role that is to be passed on to the next individual in that same organizational position. If the control plan is not maintained, the benefits of the project could be slowly lost.
© QUALITY COUNCIL OF INDIANA CQE 2006
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V. PRODUCT AND PROCESS CONTROL TOOLS
Control Plans (Continued) A blank control plan, a description of the line items in the control plan, and a filled in example control plan are illustrated in the Primer. Customer requirements may dictate the exact form of the control plan. Often, there is some flexibility in the construction of the forms. Control Plan (Sample) Control Plan for: Control number:
Team members:
Page: Original date:
Illustrative Blank Control Plan
Reaction plan
Control method
Person Responsible for measurement
Initial Cpk
Sample Frequency
Sample size
Gage Capability
Revision date:
Measurement gage technique
Specifications
S p e c i a l
Key output variable
Key Input variable (X)
Subprocess step
Part/ Process
Contact person (typically process owner):
© QUALITY COUNCIL OF INDIANA CQE 2006
V-9 (520)
V. PRODUCT AND PROCESS CONTROL TOOLS
Description of Control Plan Line Items 1. Control plan: Provide a title for the control plan. The control plan will often be placed into another document, such as an instruction or database. 2. Control number: Provide a reference number. 3. Team members: If a cross-functional team is involved, provide the member’s names. 4. Contact person: This could be the person in charge of the project. However, the name and function of the process owner are more important. 5. Page: Provide page numbers if required. control plans may contain 20 pages.
Some
6. Original date: Indicate the original date of issue. 7. Revision date: Provide the latest revision date of the control plan. 8. Part/ process: List the part number or the process flow being charted. 9. Subprocess step: Indicate the subprocess step.
© QUALITY COUNCIL OF INDIANA CQE 2006
V-9 (521)
V. PRODUCT AND PROCESS CONTROL TOOLS
Control Plan Line Items (Continued) 10. Key input variable (X): Note the key input variable, when appropriate. On any line item, only the X or Y variable is filled out, not both. This indicates which item is being monitored. 11. Key output variable (Y): Note the key input variable, when appropriate. 12. Special characteristics note: Indicate if a special characteristic is to be monitored and controlled. 13. Specifications: For manufacturing applications, the engineering specifications should be controlled. For other applications, use the specification limits and target values. 14. Measurement gage technique: The gage or measurement technique should be described. 15. Gage capability: Provide the capability of the measurement system. Instruments may need uncertainty determinations. The MSA manual lists:
C Under 10% error as acceptable C 10% to 30% error may be acceptable C Over 30% error is not acceptable
© QUALITY COUNCIL OF INDIANA CQE 2006
V-10 (522)
V. PRODUCT AND PROCESS CONTROL TOOLS
Control Plan Line Items (Continued) 16. Sample size: subgroup.
Provide the sample size for each
17. Sample frequency: List how often the inspection or monitoring of the part or process is required. 18. Initial Cpk: This provides an indication of process capability. 19. Person responsible for measurement: Indicate who will make and record the measurement. 20. Control method: Note how this X or Y variable will be controlled. Examples include control charts, checklists, inspections, measurements, etc. 21. Reaction plan: Describe what will happen if the variable goes out of control.
© QUALITY COUNCIL OF INDIANA CQE 2006
V-11 (523)
V. PRODUCT AND PROCESS CONTROL TOOLS
Illustrative Control Plan Control Plan (Example) Control Plan for: CQE Primer Team members: Glenn, Wes, Tim, Bob, Odis, Bill
Page: 1 of 1 Original date: March 16, 2006
Heavy duty slant D
visual
binder print
cool gray 4
20% of black
binder print
PMS 492 (Red)
Pantone color
binder width
3.13" +/- 0.03"
steel ruler
binder height
11.63" +/- 0.03"
steel ruler
Receive ring Primer binders metal
NA
10%
10%
6%
6%
5 lot
5 lot
5 lot
5 lot
5 lot
Reaction plan
Control method
Person responsible for measurement
Initial Cpk
Sample size
Gage capability
Revision date: August 15, 2006
Measurement/ gage technique
Specifications
characteristic Special note
Key output variable (Y)
Key Input variable (X)
Subprocess step
Part/ Process
Contact person (typically Process Owner): Bill
Sample frequency
Control number: CQE-001
NA clerk
Notify Bill contact checklist supplier
1.5 clerk
Notify Bill contact checklist supplier
1.5 clerk
Notify Bill contact checklist supplier
1.7 clerk
Notify Bill contact checklist supplier
1.7 clerk
Notify Bill contact checklist supplier
Control Plan for Receiving Primer Binders In the example above, only the key input column is controlled.
© QUALITY COUNCIL OF INDIANA CQE 2006
V-11 (524)
V. PRODUCT AND PROCESS CONTROL TOOLS
Illustrative Control Plan (Continued) Control plan construction is often led by the leader in charge of the improvement project. The team is usually cross-functional with individuals from different areas, including the process owner. The control plan must show compliance and control before project closure. A successful control plan will remain a living document to ensure that the benefits of the project will be fully realized.
© QUALITY COUNCIL OF INDIANA CQE 2006
V-12 (525)
V. PRODUCT AND PROCESS CONTROL MATERIAL CONTROL / MATERIAL IDENTIFICATION
Material Control Material Control is presented in the following topic areas:
C C C C
Material identification, status, and traceability Material segregation Classification of defects Material review board (MRB)
Material Identification and Traceability ISO 9001:2000 and ISO/TS 16949:2002 both require material identification by a suitable means from receipt through all stages of production, delivery, and installation. In order for the next operation to be successful, there must be assurances that the right inputs are used. This is accomplished by matching the material identification with the requirements on the process control documents.
© QUALITY COUNCIL OF INDIANA CQE 2006
V-12 (526)
V. PRODUCT AND PROCESS CONTROL MATERIAL CONTROL / MATERIAL IDENTIFICATION
Material Identification As material (or product) moves through the manufacturing processes, its current status must be known. In many instances, control marking, inspection stamps, and symbols, tags, cards, or labels are necessary. Material status documents include information about:
C C C C C
Material identification Which process(es) the material has completed Which inspection(s) the material has completed Where the material is going next Additionally, determine if it is in the right place
© QUALITY COUNCIL OF INDIANA CQE 2006
V-12 (527)
V. PRODUCT AND PROCESS CONTROL MATERIAL CONTROL / MATERIAL IDENTIFICATION
Material Traceability Traceability is an ability to trace the history, and application, or location of an item using records. Traceability records would show:
C C C C
The inputs into the product The test or production activities performed The lot, batch, or unit identification Where the item is or where it was used
The purpose of traceability records is to demonstrate product conformance. If sometime after the product ships its conformance is questioned, the records, traceable to the product, would be the evidence of conformance. Traceability records also show where the product went in case the product must be recalled.
© QUALITY COUNCIL OF INDIANA CQE 2006
V-13 (528)
V. PRODUCT AND PROCESS CONTROL MATERIAL CONTROL / MATERIAL IDENTIFICATION
Part Identification Part identification normally refers to the following three major areas:
C Control marking by the supplier, manufacturing department, or quality assurance as required by drawing or inspection routing specifications. These stamps and symbols may be used to verify the performance and/or acceptance of special inspections, fabrication operations, or tests. These stamps may or may not be given a serial number.
© QUALITY COUNCIL OF INDIANA CQE 2006
V-13 (529)
V. PRODUCT AND PROCESS CONTROL MATERIAL CONTROL / MATERIAL IDENTIFICATION
Part Identification (Continued) C The use of inspection stamps and symbols to indicate inspection status and acceptability. Examples include: C Incoming acceptance stamp: An inspector’s acceptance stamp is applied to each part accepted as conforming to drawing or specification requirements. C In-process acceptance stamp: Same as above, except the inspection is in-process and each manufactured part has been actually inspected and found to conform to requirements. C Sample piece identification stamp: A symbol is applied to each sample piece selected to determine final acceptance based on sampling techniques. C Nonconforming material stamp: Any nonconforming parts shall be identified with the inspector’s personal discrepant part stamp.
© QUALITY COUNCIL OF INDIANA CQE 2006
V-13 (530)
V. PRODUCT AND PROCESS CONTROL MATERIAL CONTROL / MATERIAL IDENTIFICATION
Part Identification (Continued) C Items not requiring individual identification: Stamping may be impractical due to physical limitations or detrimental impact on quality requirements. In these cases, an inspection tag, card or label may be attached to a container to indicate the status. The quality department is traditionally responsible for centralized stamp control and administration. This activity includes the responsibility to obtain, stock, issue, and maintain records of all inspection stamps and their identifying serial numbers.
© QUALITY COUNCIL OF INDIANA CQE 2006
V-14 (531)
V. PRODUCT AND PROCESS CONTROL MATERIAL CONTROL / MATERIAL SEGREGATION
Material Segregation When nonconforming items or lots exist, these products should immediately be identified and segregated from good material. Often the nonconforming material is identified with a “hold” status. All nonconforming items should be subjected for review by the designated parties (MRB) to determine if the product can be used “as is”, repaired, reworked, or scrapped. Disposition of nonconforming material should be made as soon as practicable. Decisions to “pass” a segregated product should be accompanied by the appropriate concession, waiver, explanation, etc., and signed by the appropriate authority. All steps of dealing with a nonconforming product should be documented. Depending upon the severity of the nonconformity, a variety of company functions may be assigned to assist with the evaluation, investigation, analysis, and resolution of the problem.
© QUALITY COUNCIL OF INDIANA CQE 2006
V-14 (532)
V. PRODUCT AND PROCESS CONTROL MATERIAL CONTROL / MATERIAL SEGREGATION
Control of Nonconforming Material ISO 9001:2000 states that an organization shall ensure that product which does not conform to product requirements be identified and controlled to prevent its unintended use or delivery. Controls, responsibilities, and authorities for dealing with nonconforming product shall be defined in a documented procedure. An organization shall deal with nonconforming product in one or more of the following ways:
C Taking action to eliminate the nonconformity C Authorizing its use, release, or acceptance under concession by a relevant authority (or customer) C Taking action to preclude its intended use Records of the nature of the nonconformity, and any subsequent action shall be maintained.
© QUALITY COUNCIL OF INDIANA CQE 2006
V-15 (533)
V. PRODUCT AND PROCESS CONTROL MATERIAL CONTROL / MATERIAL SEGREGATION
Control of NC Material (Continued) Additionally, ISO/TS 16949 (2002) requires that:
C Product with unidentified or suspect status be classified as nonconforming C Instructions for rework and reinspection be accessible and utilized C Customers be informed promptly if nonconforming product has been shipped C A customer waiver, concession, or deviation permit be obtained C Any product shipped on a deviation authorization be properly identified C Records for maintained
any
authorized
C Upon authorization expiration, requirements must be met
deviations
the
be
original
© QUALITY COUNCIL OF INDIANA CQE 2006
V-15 (534)
V. PRODUCT AND PROCESS CONTROL MATERIAL CONTROL / MATERIAL SEGREGATION
Control of NC Material (Continued) ISO 9001:2000 states that internal procedures shall control nonconforming product so that it is prevented from inadvertent use or installation. A flow chart could be developed to reveal the following key process steps to control nonconforming material:
C C C C C
The nonconformance is discovered The nonconforming material is segregated The nonconformance is documented A MRB determines disposition Possible dispositions include: C Scrap the part C Accept the part for use as is C Rework the part C The actual disposition is made C The product is returned to normal flow C The paperwork is cleared
© QUALITY COUNCIL OF INDIANA CQE 2006
V-16 (535)
V. PRODUCT AND PROCESS CONTROL MATERIAL CONTROL / MATERIAL SEGREGATION
Nonconforming Material Flow Chart Production or inspection discovers nc product
Product is held in special holding area
Inspection creates a deviation report (DR) to document condition
Quality supervisor reviews product
Deviation report noted with action
Rework product
No
MRB product
Rework successful
Scrap product
MRB makes disposition
Identify as scrap
Yes Use “as is”
Repair product
Scrap product
Send to scrap disposal area
Return product to flow
Return to production for repair
Follow scrap instructions
Clear DR and file
Close DR
File in DR quality records
Yes
Repair successful
No
© QUALITY COUNCIL OF INDIANA CQE 2006
V-17 (536)
V. PRODUCT AND PROCESS CONTROL MATERIAL CONTROL / MATERIAL SEGREGATION
Nonconforming Material Procedure Nonconforming material procedures could vary substantially, dependent upon the product supplied by a company. The key elements for a hypothetical nonconforming material procedure are detailed below:
C Nonconforming purchased materials are addressed: C Receiving inspection identifies any incoming nonconforming material and moves it to a reviewing area. C In the review area, inspection personnel may call upon a quality assurance supervisor and a purchasing representative to make a preliminary review. Several decisions are possible: C C C C C
Referral to the MRB Returned to the supplier for rework or scrap Scrapped internally (after supplier notification) Salvage repair, requiring MRB authorization Accepted for further processing. This generally involves very minor nonconformancies.
© QUALITY COUNCIL OF INDIANA CQE 2006
V-17 (537)
V. PRODUCT AND PROCESS CONTROL MATERIAL CONTROL / MATERIAL SEGREGATION
NC Material Procedure (Continued) C Suppliers are often required to take actions similar to those mentioned above. C Nonconforming fabricated materials are addressed: C Any nonconforming product found during internal in-process inspection is identified and removed from the normal process flow in such a way as to avoid inadvertent return to production. C In the review area inspectors may call upon quality assurance supervisors to make a preliminary review. Actions may include: C Referral to the MRB C Scrapping the material C Reworking the material, requiring reinspection
© QUALITY COUNCIL OF INDIANA CQE 2006
V-18 (538)
V. PRODUCT AND PROCESS CONTROL MATERIAL CONTROL / MATERIAL SEGREGATION
Nonconforming Material Definitions Critical defect: A defect that could cause hazardous or unsafe conditions for individuals using or maintaining the product. A defect that could prevent the product from performing its intended function. Defect: Any material, part, or component that fails to meet specified requirements. Deviation: The planned departure from requirements prior to the initial manufacture of an item. A particular design requirement, a specific number of units or specific period or time and will be identified upon shipment. Deviation permit: Written authorization given in advance of manufacture to deviate from specified requirements for a given number of units or for a specific period of time. Equivalent item: An item that is interchangeable and equal to or better than the item called for in a specification.
© QUALITY COUNCIL OF INDIANA CQE 2006
V-18 (539)
V. PRODUCT AND PROCESS CONTROL MATERIAL CONTROL / MATERIAL SEGREGATION
Nonconforming Material Definitions Major defect: A serious defect, but less severe than a critical defect, that is likely to result in failure or substantially reduce the usability of an item for its intended purpose. Material review board (MRB): A formal multidisciplinary panel established to perform material review. This panel reviews, evaluates, and either fixes, or disposes of, specific nonconforming materials or services. Important supportive responsibilities include the initiation and achievement of corrective action. Minor defect: A defect not likely to reduce the usability of the item for its intended purpose. Nonconformance: A departure from the requirements specified in the contract, specification, drawing, or other product description.
© QUALITY COUNCIL OF INDIANA CQE 2006
V-19 (540)
V. PRODUCT AND PROCESS CONTROL MATERIAL CONTROL / MATERIAL SEGREGATION
NC Material Definitions (Continued) Preliminary review: The review and disposition of nonconforming material, by quality assurance supervisors, as it is initially discovered at the applicable inspection area prior to referral to the material review board. Recertification: A process for retesting or reevaluating material with an expired shelf life to determine if the shelf life can be extended. Reject: A defective or nonconforming item which is unsuitable for use as offered. A product or service which is not accepted because it fails to meet the requirement criteria. Repair: The subjection of nonconforming material to an approved process designed to reduce but not completely eliminate the nonconformance. The purpose of repair is to bring nonconforming material into an acceptable condition. Rework: The reprocessing of nonconforming material to make it conform to the contract requirements.
© QUALITY COUNCIL OF INDIANA CQE 2006
V-19 (541)
V. PRODUCT AND PROCESS CONTROL MATERIAL CONTROL / MATERIAL SEGREGATION
NC Material Definitions (Continued) Salvage repair process: A technique, of possible recurrent use, for repairing a nonconformance when it has been demonstrated that the technique, when properly applied, will result in an adequate and cost effective method for dispositioning the nonconformance. Scrap: Nonconforming material that is not usable for its intended purpose or cannot be economically reworked or repaired. Suspended: Material not acceptable due to lack of corrective action. Use “as is” material: Material that is found to be nonconforming in a minor way but suitable for its intended purpose and acceptable to the customer. Waiver: Written permission to accept for use a completed, but nonconforming, item either “as is,” or upon completion of rework for a specified number of units or period of time.
© QUALITY COUNCIL OF INDIANA CQE 2006
V-20 (542)
V. PRODUCT AND PROCESS CONTROL MATERIAL CONTROL / CLASSIFICATION OF DEFECTS
Classification of Defects Quality defects are not equal in their effect on the useability of the final product or service. Some defects are of critical importance; while others are of minor importance. The more important the characteristic, the greater the effort should be to detect and correct it. Many companies utilize a formal system of seriousness classification which:
C Establishes the classification levels (3 or 4) C Defines each defect level for inspection purposes
© QUALITY COUNCIL OF INDIANA CQE 2006
V-20 (543)
V. PRODUCT AND PROCESS CONTROL MATERIAL CONTROL / CLASSIFICATION OF DEFECTS
Classification of Defects (Continued) The inspection department then classifies each defect into its proper level. Often the classifications are given a numeric weight. Listed below is an example from Benbow (2003): Category
Description
Critical
May lead directly to severe injury or catastrophic economic loss
Serious
May lead to injury or significant economic loss
Major
May cause major problems during normal use and reduce the usability of the product
Minor
May cause minor problems during normal use
© QUALITY COUNCIL OF INDIANA CQE 2006
V-20 (544)
V. PRODUCT AND PROCESS CONTROL MATERIAL CONTROL / CLASSIFICATION OF DEFECTS
An illustration of automotive defect seriousness classifications follows: Class
Nature
Critical Defects which are critical to personal safety or are essential to proper vehicle operation
Examples Poor heat treatment of motor mounts or steering parts, inoperative brakes, etc. Glove box will not open, body rust, cruise control inoperative, etc.
Major
Defects which might affect the general function of essential vehicle parts or appearance
Minor
Minor paint runs, Defects which affect the functions of minor misaligned decals, a parts or not essential loose door panel, etc. appearance
The major category may be subdivided into types A and B, with type A being more severe.
© QUALITY COUNCIL OF INDIANA CQE 2006
V-21 (545)
V. PRODUCT AND PROCESS CONTROL MATERIAL CONTROL / MATERIAL REVIEW BOARD
Material Review Board (MRB) The membership, responsibilities, and supporting activities of a material review board are presented below in outline format.
C Membership: C Includes representatives from the quality assurance and engineering departments. C In many instances, customer representatives, planning, and manufacturing departments are included. C Membership may be on a rotating basis. C The experience and qualifications of MRB members are kept on file in the material review office and should be sufficient to pass an external customer audit or inquiry.
© QUALITY COUNCIL OF INDIANA CQE 2006
V-21 (546)
V. PRODUCT AND PROCESS CONTROL MATERIAL CONTROL / MATERIAL REVIEW BOARD
MRB (Continued) C Responsibilities: C The principal responsibility of the material review board is to determine the disposition of nonconforming materials. C The material review board, in many cases, is responsible for the initiation and follow-up of corrective action requests. In some cases, this responsibility may be referred to a corrective action board (CAB). C The MRB is further responsible for providing meaningful and timely feedback to all key management and manufacturing functions. C The material review board often has the authority to take the following actions: C C C C C
Rework or repair of the product Use the product “as is” Reject or scrap the product Require additional inspection tests Initiate a corrective action request
© QUALITY COUNCIL OF INDIANA CQE 2006
V-22 (547)
V. PRODUCT AND PROCESS CONTROL MATERIAL CONTROL / MATERIAL REVIEW BOARD
MRB (Continued) C Supportive Activities: C A material review area must be set aside for use in holding and accounting for materials awaiting MRB action. C For a contracted item, the MRB must often receive concurrence from the customer. This includes a signature and date. C A quality assurance representative is usually responsible for providing a full description of materials awaiting MRB action. C The MRB’s quality assurance representative is usually responsible for the initiation of a material review report (MRR) form which can include: C C C C C C C C C C
MRR number Discrepant part name and number The contract, or work order identification The department where detected The PO number (customer supplied product) The quantity of units rejected The location of the held items Any pertinent part drawing information A description of the nonconformance An explanation of the probable cause
© QUALITY COUNCIL OF INDIANA CQE 2006
V-22 (548)
V. PRODUCT AND PROCESS CONTROL MATERIAL CONTROL / MATERIAL REVIEW BOARD
MRB (Continued) C The MRB’s quality department representative is generally responsible for the generation of a MRR log sheet (or report) which captures the preceding items and further details: C More information on the nature of the discrepancy C The final disposition of the nonconformity C An identification of those responsible for corrective action C A due date for those actions
© QUALITY COUNCIL OF INDIANA CQE 2006
V-23 (549)
V. PRODUCT AND PROCESS CONTROL MATERIAL CONTROL / MATERIAL REVIEW BOARD
MRB (Continued) C The MRB’s quality department representative may also be responsible for: C Attaching appropriate drawings discrepant material documents
to
the
C Transmitting a request for any necessary testing, inspection, or analysis C When applicable, the MRB requests and processes requests for deviations, and waivers. C In the case of age-sensitive materials that have exceeded expiration dates, a recertification may be requested by the MRB.
© QUALITY COUNCIL OF INDIANA CQE 2006
V-23 (550)
V. PRODUCT AND PROCESS CONTROL MATERIAL CONTROL / MATERIAL REVIEW BOARD
MRB (Continued) C The MRB, or quality representative, can be responsible for the transport of any nonconforming materials and documentation to an appropriate location for disposition. C After an appropriate time interval, verification of the authorized disposition should be made, with the verifier recording appropriate findings. C The follow-up on corrective action is a key system component and may be handled in a variety of venues: the MRB, a management steering committee, or a CAB. In every case, there should be a management review of the process.
© QUALITY COUNCIL OF INDIANA CQE 2006
V-24 (551)
V. PRODUCT AND PROCESS CONTROL ACCEPTANCE SAMPLING / SAMPLING CONCEPTS
Acceptance Sampling Acceptance Sampling is presented in the following topic areas:
C Sampling concepts C Sampling standards and plans C Sample integrity
Sampling Concepts Sampling refers to the evaluation of a portion of a population (lot, batch, etc.) for the purpose of obtaining useful information about it. Acceptance sampling deals with the evaluation of either incoming or outgoing vendor product. Normally an accept/reject decision for an entire lot is made based upon the results of a sample. The advantage of sampling is economics. However, no form of inspection or sampling should be used as a substitute for process control.
© QUALITY COUNCIL OF INDIANA CQE 2006
V-24 (552)
V. PRODUCT AND PROCESS CONTROL ACCEPTANCE SAMPLING / SAMPLING CONCEPTS
Sampling Advantages C C C C C C C
Checks on the adequacy of process control The inspection labor force can be smaller There is less handling damage to the product The product is disposed of in shorter time An inspector will be less bored Generates fewer errors than 100% inspection Lot rejection dramatizes the need for correction
Sampling is most useful when:
C C C C
Inspection damages the product The per unit inspection costs are high The results of passing a defective unit are low There are large amounts of product to be inspected
© QUALITY COUNCIL OF INDIANA CQE 2006
V-25 (553)
V. PRODUCT AND PROCESS CONTROL ACCEPTANCE SAMPLING / SAMPLING CONCEPTS
Sampling Disadvantages C There is a risk of rejecting good product C Administration costs are often high C Less information is obtained versus inspection
Sampling Precautions C C C C C C C C C C C C C C C C
Sampling provides no estimate of lot quality. Rejected product may be fit for use. There is no single “representative sample.” Without statistics, sampling costs can be high Without statistics little information is known. Sample size is more important than lot %. Only random samples are statistically valid. Sample plan misuse of can be costly. Any AQL allows defectives. No sample plan eliminates defectives. Sample access does not guarantee randomness. Stratified samples are sometimes very informative. Sampling often places focus in the wrong place. The supplier should provide evidence of quality. Sampling plans derive from process knowledge. Process control is better than sampling.
© QUALITY COUNCIL OF INDIANA CQE 2006
V-26 (554)
V. PRODUCT AND PROCESS CONTROL ACCEPTANCE SAMPLING / SAMPLING CONCEPTS
Sampling and Inspection Types Types of sampling and inspection are presented below: Type
Function
Description
Detail or 100% inspection
Sorts good pieces Distinguishes from bad pieces good pieces from bad pieces
Acceptance sampling
Distinguishes good lots from bad lots
Classifies lots as to acceptability
Incoming inspection
Distinguishes good lots from bad lots
Is performed on incoming material
Process inspection
Distinguishes good lots from bad lots
Is done between departments of the same company
Final inspection
Distinguishes good lots from bad lots
Is done by the producer prior to shipment
© QUALITY COUNCIL OF INDIANA CQE 2006
V-26 (555)
V. PRODUCT AND PROCESS CONTROL ACCEPTANCE SAMPLING / SAMPLING CONCEPTS
Sampling and Inspection Types (Cont’d) Pre-control techniques
Determines if the process is approaching spec. limits
Determines if a change is significant enough to make adjustments
Control sampling
Determines if the process is changing
Control charts indicate if the process is changing
Accuracy inspection
Evaluates the accuracy of inspectors
Measures the effectiveness of inspectors
Product auditing
Evaluates the quality of the product
Assesses the product and process that produced it
Discovery sampling
Evaluates product quality based on an assumed frequency
Provides a specified probability that the sample will contain at least one defect
© QUALITY COUNCIL OF INDIANA CQE 2006
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V. PRODUCT AND PROCESS CONTROL ACCEPTANCE SAMPLING / SAMPLING CONCEPTS
Random Sampling The use of a sampling plan requires randomness in sample selection. Obviously, random sampling requires giving every item an equal chance of being selected for the sample. The sample must be representative of the lot, not just the product that is easy to obtain. Thus, the selection of samples requires some up-front thought and planning.
© QUALITY COUNCIL OF INDIANA CQE 2006
V-27 (557)
V. PRODUCT AND PROCESS CONTROL ACCEPTANCE SAMPLING / SAMPLING CONCEPTS
Common Sampling Tables ANSI/ASQ Z1.4-2003 provides tables of sampling plans for attributes. There are three types of sampling used: 1. Single sampling: Where lots are inspected and the decision to accept or reject is based on one sample 2. Double sampling: Where the decision to accept or reject a lot is based on a maximum of two samples 3. Multiple sampling: Where the decision to accept or reject the lot is based on a maximum of seven samples ANSI/ASQ Z1.9-2003 provides tables of sampling plans for variables. Dodge-Romig Tables are attribute plans used for effective inspection if the the process average is known.
© QUALITY COUNCIL OF INDIANA CQE 2006
V-27 (558)
V. PRODUCT AND PROCESS CONTROL ACCEPTANCE SAMPLING / SAMPLING CONCEPTS
Variables Versus Attribute Sampling Variables sampling plans should be used when the measurement of a few items is less expensive than the counting of many items, and the population approximates a normal distribution. ANSI/ASQ Z1.42003 (attributes) and ANSI/ASQ Z1.9 -2003 (variables) provide OC curves which allow switching between the two plans where possible. The following two plans have comparable OC curves: Attribute plan n = 125 c= 3
Variables plan n = 19 k = 1.908
© QUALITY COUNCIL OF INDIANA CQE 2006
V-28 (559)
V. PRODUCT AND PROCESS CONTROL ACCEPTANCE SAMPLING / SAMPLING CONCEPTS
Fixed Sampling Taking a fixed sample size from a lot or batch only works if the lot or batch size remains relatively constant. This will be illustrated later with a set of OC curves from 10% sample size plans. The only advantage is that a fixed sample size in inspection is easy to remember. Fixed, small sample sizes are more widely used in auditing.
Stratified Sampling Stratified samples are sometimes more informative than homogeneous samples. When analyzing inventory, one would not want to put $25,000 motors in the same strata with 2¢ screws. Additionally, one might be interested in determining the amount of pallet damage in a storage area. There might be a need to sample more row ends, row corners or bottom pallets in preference to top pallets in the middle.
© QUALITY COUNCIL OF INDIANA CQE 2006
V-28 (560)
V. PRODUCT AND PROCESS CONTROL ACCEPTANCE SAMPLING / SAMPLING CONCEPTS
Zero Defect Sampling There is a growing interest in zero acceptance number plans for two reasons: the advent of six sigma methodology and the litigious society that currently exists. Often, companies claim they are producing parts with very low ppm failure rates. This assumption is based on varieties of Cpk determinations. In fact, a company should not make such a claim until they have inspected millions of parts. Plans with zero acceptance numbers have existed for years. A number of these are evident in the ANSI/ASQ Z1.4-2003 tables that follow. However, many of these plans have relatively small sample sizes. Obviously, other plans with nonzero acceptance numbers and larger sample sizes will better discriminate between quality levels.
© QUALITY COUNCIL OF INDIANA CQE 2006
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V. PRODUCT AND PROCESS CONTROL ACCEPTANCE SAMPLING / SAMPLING CONCEPTS
Continuous Sampling The most widely used continuous sampling plan is the original — the Dodge CSP-1 plan. It is carried out on a stream of product, with production units inspected in order of production. A flow chart follows: Start Inspect i successive units
No defective
Defective found Replace unit with good unit
Random selection fraction f unit
Defective found
No defective
Note that the sampling frequency (f), clearance number (i) must be determined in advance.
© QUALITY COUNCIL OF INDIANA CQE 2006
V-30 (562)
V. PRODUCT AND PROCESS CONTROL ACCEPTANCE SAMPLING / SAMPLING CONCEPTS
Sequential Sampling Sequential sampling is the most discriminating of the acceptance sampling plans. It involves making one of three decisions as each sample item is obtained: accept the lot, reject the lot, or continue sampling. One continues sampling until the cumulative number of defectives crosses either the lot reject limit, or the lot accept limit. When a limit is crossed, the lot size limit is reached and a new lot begins. Sequential sampling requires the least average sample size. Sequential plans are often applied where sample economics are critical, and a minimum sample size is required. A sequential plan is more complex and more difficult to administer than other plans. Samples must be obtained one item at a time, and operators require more training.
© QUALITY COUNCIL OF INDIANA CQE 2006
V-30 (563)
V. PRODUCT AND PROCESS CONTROL ACCEPTANCE SAMPLING / SAMPLING CONCEPTS
Other Sampling Considerations A sampling plan should take advantage of known information (process average, process capability, etc.) to minimize total inspection costs. A good plan should be simple to administer and easy for inspectors to understand. The sampling risks (both " and $ risks) should be known, and be compatible with the consumer’s priorities. The quality index chosen (AQL, AOQL, LTPD, LQL, etc.) should reflect the respective needs of both the producer and the customer.
© QUALITY COUNCIL OF INDIANA CQE 2006
V-31 (564)
V. PRODUCT AND PROCESS CONTROL ACCEPTANCE SAMPLING / SAMPLING CONCEPTS
Inspection/Sampling Economics There are many alternatives for evaluating lots:
C C C C C
No inspection Small samples Large samples 100 percent inspection Redundant inspection (> 100 %)
One cost model for attribute plans is considered below:
Where: TC = Total cost A = Overhead cost B = Cost/unit of sampling
nMAX = Max. Sample size C = Cost/unit of inspecting n = Average sample size
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V. PRODUCT AND PROCESS CONTROL ACCEPTANCE SAMPLING / SAMPLING CONCEPTS
Inspection/Sampling Economics (Cont’d) If the percent defective is greater than 5 %, then 100 % inspection should generally be used. If the sample size is assumed to be small compared to the lot size, the break-even point is determined by:
Where:
D = cost if a defective passes C = inspection cost/item
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V-32 (566)
V. PRODUCT AND PROCESS CONTROL ACCEPTANCE SAMPLING / SAMPLING CONCEPTS
The Operating Characteristic Curve Even 100% inspection does not catch all defects. It is estimated that inspectors using conventional equipment will find 85%/90% of all defects. Sampling also involves risks that the sample will not adequately reflect the conditions in the lot. Sampling risks are of two kinds:
C Good product is rejected (the producer or alpha " risk) C Bad product is accepted (the consumer or beta $ risk) The operating characteristics (OC) curve for a sampling plan quantifies these risks. The OC curve is a graph of the percent defective in a batch versus the probability that the sampling plan will accept that batch.
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V. PRODUCT AND PROCESS CONTROL ACCEPTANCE SAMPLING / SAMPLING CONCEPTS
OC Curve (Continued) Shown below is an “ideal” OC curve. Assume that it is desirable to accept all lots 1% defective or less and reject all lots having a quality level greater than 1% defective. All batches with less than 1% defective have a probability of acceptance of 100% (1.0). All lots greater than 1% defective have a probability of acceptance of 0.
Pa
Lot Percent Defective However, no perfect sampling plan exists. There will always be some risk that a “good” product will be rejected or that a “bad” product will be accepted.
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V-33 (568)
V. PRODUCT AND PROCESS CONTROL ACCEPTANCE SAMPLING / SAMPLING CONCEPTS
Sampling Plan Quality Indices Many sampling plans are based on the quality indices below: 1. Acceptance quality limit (AQL): This is defined as the worst tolerable quality level that is still considered satisfactory as a process average. The probability of accepting a lot produced at the AQL should be high. ANSI/ASQ Z1.4-2003 prefers that the phrase “acceptable quality limit “ no longer be used. 2. Rejectable quality level (RQL): This defines unsatisfactory quality. In the Dodge-Romig plans, the term “lot tolerance percent defective (LTPD)” is used instead of RQL. The probability of accepting a RQL lot should be low. In some tables, this is known as the consumer's risk and has been standardized at 0.1. 3. Indifference quality level (IQL): This is a quality level somewhere between the AQL and RQL. It is normally defined as the quality level having probability of acceptance of 0.50. The IQL is rarely used.
© QUALITY COUNCIL OF INDIANA CQE 2006
V. PRODUCT AND PROCESS CONTROL ACCEPTANCE SAMPLING / SAMPLING CONCEPTS
Typical OC Curve
Pa
Lot Percent Defective
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© QUALITY COUNCIL OF INDIANA CQE 2006
V-34 (570)
V. PRODUCT AND PROCESS CONTROL ACCEPTANCE SAMPLING / SAMPLING CONCEPTS
Constructing an OC Curve An OC curve can be developed by determining the probability of acceptance for each of several values of incoming quality. Pa is the probability that the number of defectives in the sample is equal to or less than the sampling plan acceptance number. There are three attribute distributions that can be used to find the probability of acceptance: the hypergeometic, binomial, and the Poisson distribution. When the defective rate is less than 10%, and the sample size is relatively large, the Poisson distribution is preferable because of the ease of table use. The Poisson formula as applied to acceptance sampling is: e -np ( np ) e- μ ( μ ) P (r ) = = r! r! r
r
P(r) = the probability of exactly r defectives in a sample of n. Note that np = :. The above equation can be solved or Appendix Table III can be used. This table gives the probability of r or fewer defectives in a sample of n from a lot having a fraction defective of p.
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V-35 (571)
V. PRODUCT AND PROCESS CONTROL ACCEPTANCE SAMPLING / SAMPLING CONCEPTS
Constructing an OC Curve (Cont’d) Consider the following example: Assume: n =150, c = 3 P
np
P{r#3}
1%
(150)(0.01) = 1.50
0.93
2%
(150)(0.02) = 3.00
0.65
3%
(150)(0.03) = 4.50
0.34
4%
(150)(0.04) = 6.00
0.15
5%
(150)(0.05) = 7.50
0.06
6%
(150)(0.06) = 9.00
0.02
Pa
Lot Percent Defective
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V-36 (572)
V. PRODUCT AND PROCESS CONTROL ACCEPTANCE SAMPLING / SAMPLING CONCEPTS
OC Curve for Changing Sample Size
c is fixed
Pa
Lot Percent Defective
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V-36 (573)
V. PRODUCT AND PROCESS CONTROL ACCEPTANCE SAMPLING / SAMPLING CONCEPTS
OC Curve for Changing c
n = 40 (fixed) Pa
Lot Percent Defective
© QUALITY COUNCIL OF INDIANA CQE 2006
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V. PRODUCT AND PROCESS CONTROL ACCEPTANCE SAMPLING / SAMPLING CONCEPTS
OC Curve for Changing Lot Size
n = 20 fixed c = 0 fixed Pa
Lot Percent Defective
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V. PRODUCT AND PROCESS CONTROL ACCEPTANCE SAMPLING / SAMPLING CONCEPTS
OC Curve for a Fixed Lot Percentage
n = 10% of N
Pa
Lot Percent Defective Note why fixed % sampling plans do not provide the same risks.
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V. PRODUCT AND PROCESS CONTROL ACCEPTANCE SAMPLING / SAMPLING CONCEPTS
Average Outgoing Quality Limit (AOQL) The term AOQL is used in the Dodge-Romig tables and in other sampling plans. The AOQL is equal to the maximum AOQ. The following example should help with the explanation. Assumptions:
C The lot size (N) is relatively constant C There is 100% inspection of rejected lots C All defective material is replaced with good Where: p = % defective Pa = Probability of acceptance AOQ = p C Pa Pa is obtained from the Poisson distribution table.
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V. PRODUCT AND PROCESS CONTROL ACCEPTANCE SAMPLING / SAMPLING CONCEPTS
AOQL (Continued) For the OC Curve (N = 150, c=3) p
np
Pa
p
AOQ %
0.0 0.00 1.000
0.000
0.5 0.75 0.993
0.496
1.0 1.50 0.934
0.934
1.5 2.25 0.809
1.214
2.0 3.00 0.647
1.294
2.5 3.75 0.484
1.209
np
Pa
AOQ %
3.0 4.50 0.342
1.027
3.5 5.25 0.232
0.811
4.0 6.00 0.151
0.605
4.5 6.75 0.096
0.431
5.0 7.50 0.059
0.296
5.5 8.25 0.036
0.197
6.0 9.00 0.021
0.127
1.4 1.3 1.2 1.1 1 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0
Max AOQ = AOQL = 1.294
Decimal Percent
0
1
2
3
4
Incoming Lot Percent Defective
5
6
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V. PRODUCT AND PROCESS CONTROL ACCEPTANCE SAMPLING / SAMPLING CONCEPTS
Sampling Definitions Some basic sampling definitions follow: Acceptance quality limit (AQL)
The quality level that is the worst tolerable process average when a continuing series of lots is submitted for acceptance sampling.
Acceptance number
The maximum number of defective units or defects in a (Ac or C ) sample that will permit acceptance of the inspection lot.
The expected quality of outgoing Average product following the use of an outgoing quality (AOQ) acceptance sampling plan for a given value of incoming product. Average outgoing quality limit (AOQL)
For a given acceptance sampling plan, the maximum AOQ for all possible levels of incoming quality.
Clearance number
As associated with a continuous sampling plan, the number of inspected units of product that must be found acceptable during 100% inspection before the amount of inspection can be changed.
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V. PRODUCT AND PROCESS CONTROL ACCEPTANCE SAMPLING / SAMPLING CONCEPTS
Sampling Definitions (Continued) Consumer's risk ($)
The probability of accepting a bad lot.
Defect
A departure of a quality characteristic from its intended level or state that occurs with a severity sufficient to cause an associated product or service not to satisfy its intended use.
Defective
A unit of product that contains one or more defects at least one of which causes the unit to fail its specifications.
Discrepancy
A failure to meet the specified requirement, supported by evidence.
Inspection
The process of measuring, examining, testing, or otherwise comparing a unit with requirements.
100% Inspection
Inspection in which specified characteristics of each unit of product are examined or tested to determine conformance with requirements.
Inspection by Inspection, whereby either the unit of attributes product is classified simply as conforming or non-conforming, or the number of nonconformities.
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V. PRODUCT AND PROCESS CONTROL ACCEPTANCE SAMPLING / SAMPLING CONCEPTS
Sampling Definitions (Continued) Inspection by Inspection, wherein certain quality variables characteristics are evaluated with respect to a continuous numerical scale. Inspection level
A feature of a sampling scheme relating the size of the sample to that of the lot.
Inspection, normal
Inspection, used when there is no evidence that the quality of the product being submitted is better or poorer than the specified quality level. This is the usual inspection starting point.
Inspection record
Recorded data concerning inspection results.
Inspection, reduced
A feature of a sampling scheme permitting smaller sample sizes than are used in normal inspection.
Inspection, tightened
A feature of a sampling scheme using stricter acceptance criteria than those used in normal inspection.
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V. PRODUCT AND PROCESS CONTROL ACCEPTANCE SAMPLING / SAMPLING CONCEPTS
Sampling Definitions (Continued) Lot percent defective (LPD)
This percentage is estimated by dividing the number of defectives by the sample size and then multiplying by 100. Example: d / n x 100
Lot size (N)
A collection of units of similar product from which a sample is drawn and inspected.
A curve showing, for a given sampling Operating characteristic plan, the probability of accepting a lot as a function of the lot quality. curve Probability of The probability that a lot will be acceptance accepted under a given sampling plan. (Pa) Process average
The average percent of defectives or average number of defects per hundred units of submitted product.
Producer's risk (")
The probability of rejecting a good lot.
Random sampling
The selection of units such a manner that all combinations of units under consideration have an equal chance of being selected.
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V. PRODUCT AND PROCESS CONTROL ACCEPTANCE SAMPLING / SAMPLING CONCEPTS
Sampling Definitions (Continued) Reduced inspection
Inspection under a sampling plan using the same quality level as for normal inspection, but requiring a smaller sample.
Rejection number (Re)
The minimum number of defects or defective units in the sample that will reject the lot or batch.
Sample size (n)
The number of units in a sample.
Sampling errors
In sampling one never knows whether the lot is good or bad. See the decision matrix below: Lot Quality
Called Good The Decision Made
Called Bad
Good
Bad
1-"
$
Producer’s Confidence
Type II Error
"
1- $
Type I Error
Consumer’s Confidence
Sampling Error Matrix
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V. PRODUCT AND PROCESS CONTROL ACCEPTANCE SAMPLING / SAMPLING CONCEPTS
Sampling Definitions (Continued) Sampling, double
Sampling inspection in which the inspection of the first sample of size n1 leads to a decision to accept a lot, not to accept it, or to take a second sample of size n2.
Sampling, multiple
Sampling inspection in which, after each sample is inspected, the decision is made to accept a lot; not to accept it, or to take another sample to reach the decision.
Sampling plan
A statement of the sample size or sizes to be used and the associated acceptance and rejection criteria.
Sampling, sequential
Sampling inspection in which, after each unit is inspected, the decision is made to accept the lot, not to accept it, or to inspect another unit.
Sampling, single
Sampling inspection in which, after each unit is inspected, the decision is made to accept the lot or reject it.
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V. PRODUCT AND PROCESS CONTROL ACCEPTANCE SAMPLING / SAMPLING STANDARDS
Sampling Standards and Plans Sampling plans are of two major types: 1. Attributes plans Defectives: A sample is taken from a lot with each unit classified as acceptable or defective. The number of defectives is then compared to the acceptance number in order to make an accept or reject decision for the lot. Defects: A sample is taken from a lot and the defects are counted. The ratio of defects/100 units is derived. This value is compared to the acceptance number, in order to make an accept or reject decision for the lot. Examples:
ANSI/ASQ Z1.4-2003. Dodge-Romig tables
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V. PRODUCT AND PROCESS CONTROL ACCEPTANCE SAMPLING / SAMPLING STANDARDS
Sampling Standards and Plans (Cont’d) 2. Variables plans A sample is taken and one or more quality characteristic measurements are made on each unit. These measurements are then summarized into simple statistics (such as the sample average or standard deviation) which are compared with a critical value defined in the plan. A decision is then made to accept or reject the lot. Example:
ANSI/ASQ Z1.9-2003
It is not the intent of this text to provide copies of sampling plans. The intent is to illustrate how the major plans are used. There are provisions for switching between the ANSI/ASQ plans to provide corresponding OC curves.
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V. PRODUCT AND PROCESS CONTROL ACCEPTANCE SAMPLING / SAMPLING STANDARDS
Attribute Sampling Plan Summaries Plan
Type
Application
Key Features
ANSI/ASQ Z1.4 MIL-STD-105E
Single, Bad lots are generally double, and rejected, but may be 100% multiple inspected.
Dodge-Romig
Single and double
Rejected lots are 100% Plans for LTPD or AOQL. inspected and bad product is Minimum inspection is required. replaced.
Chain sampling
Single and two-stage
Useful for destructive or costly testing.
Bayesian (discovery) sampling
Generally single
Used when the probability of Relatively small sample sizes are defective lots can be required. estimated.
Sequential sampling Skip-lot plans
Based on an AQL. Minimizes the rejection of good lots. Easy to explain and administer.
Minimizes sample sizes without large rejection risk.
Unit sampling, Used to screen lots; rejected Examines one item at a time. binomial lots are 100% inspected. The ATI is minimal. Single
Useful for high quality levels and when inspection is costly.
Minimizes inspection with protection against quality deterioration.
MIL-STD-1235 MIL-HDBK-107
Continuous Used for continuous single-level production and nondestructive inspection.
Plans limit the average quality in the long run.
MIL-STD-1235 MIL-HDBK-106
Continuous Same as above. multi-level
Plans limit the average quality in the long run.
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V. PRODUCT AND PROCESS CONTROL ACCEPTANCE SAMPLING / SAMPLING STANDARDS
Variable Sampling Plan Summaries Plan
Distribution
Criteria
Key Features
ANSI/ASQ Z1.9 MIL-STD-414
Normal
Acceptance quality limit
Single-sampling variables plan
Normal
Percent defective
Provides sample size and acceptance values for defined risks.
MIL-HDBK-108
Exponential
Mean life
Provides lot evaluation, with and without item replacement.
MIL-STD-690
Exponential
Failure rate
MIL-HDBK-781 MIL-STD-781
Exponential
Mean life
Provides lot evaluation to a specified AQL.
Provides tables for process evaluation. Provides process and lot evaluation.
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V. PRODUCT AND PROCESS CONTROL ACCEPTANCE SAMPLING / SAMPLING STANDARDS
ANSI/ASQ Z1.4 ANSI/ASQ Z1.4-20032 consists of a sample size code letter table and tables describing acceptance and rejection numbers. Operating characteristic (OC) curves applicable to single, double, or multiple plans are provided.
Single Sampling Tables Three numbers are necessary to describe a single sampling plan using these standards. N = lot size
n = sample size
Ac = c = the maximum number of defectives to still be acceptable
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V. PRODUCT AND PROCESS CONTROL ACCEPTANCE SAMPLING / SAMPLING STANDARDS
ANSI/ASQ Z1.4 (Continued) On the next two pages are a ANSI/ASQ Z1.4-20032 code letter index and a single sampling table for normal inspection. Consider a lot size of 570 pieces, AQL = 4% and general inspection level II.
C In the code letter table, the sample code is J. C In the single sampling table, the Ac number is 7 and the Re number is 8 for a sample size n = 80.
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V. PRODUCT AND PROCESS CONTROL ACCEPTANCE SAMPLING / SAMPLING STANDARDS
ANSI/ASQ Z1.4 Practice Exercises Example 5.1: For N = 75, AQL = 1.5%, single sampling, general inspection level II, determine the following: The code letter The rejection number
The acceptance number The sample size
Example 5.2: For N = 75, what are the code letter, acceptance number, rejection number and sample size for an AQL = 4.0%? Assume general inspection level II and single sampling. Answers: 5.1: D*, 0, 1, 8
5.2: E, 1, 2, 13
* Note the up arrow which changes code letter E to D.
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V. PRODUCT AND PROCESS CONTROL ACCEPTANCE SAMPLING / SAMPLING STANDARDS
ANSI/ASQ Z1.4 Code Letters Special Inspection Levels
Lot Size
S-1 S-2 S-3 S-4
General Levels I
II
III
2 9 16
to to to
8 15 25
A A A
A A A
A A B
A A B
A A B
A B C
B C D
26 51 91
to to to
50 90 150
A B B
B B B
B C C
C C D
C C D
D E F
E F G
151 281 501
to to to
280 500 1200
B B C
C C C
D D E
E E F
E F G
G H J
H J K
to 3200 to 10000 to 35000
C C C
D D D
E F F
G G H
H J K
K L M
L M N
1201 3201 10001
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V. PRODUCT AND PROCESS CONTROL ACCEPTANCE SAMPLING / SAMPLING STANDARDS
ANSI/ASQ Z1.4 Single (Normal) Sampling Code letter
Sample size
Acceptable Quality Limits (normal inspection) 0.25
0.40
0.65
1.0
1.5
2.5
4.0
6.5
10
Ac Re
Ac Re
Ac Re
Ac Re
Ac Re
Ac Re
Ac Re
Ac Re
Ac Re
A
2
0
B
3
C
5
D
8
E
13
F
20
G
32
H
50
J
80
K
125
L
200
1
M
315
N
0 0 0 0 0 0 0
1
1
1
1
1
1
1
1
2
1
2
2
3
1
2
2
3
3
4
1
2
2
3
3
4
5
6
7
8
1
2
2
3
3
4
5
6
8 10 11
1
2
2
3
3
4
5
6
7
7
8
10 11 14 15
1
2
2
3
3
4
5
6
7
8 10 11 14 15 21 22
1
2
2
3
3
4
5
6
2
2
3
3
4
5
6
7
8 10 11 14 15 21 22
2
3
3
4
5
6
7
8 10 11 14 15 21 22
500
3
4
5
6
7
8 10 11 14 15 21 22
P
800
5
6
7
8 10 11 14 15 21 22
Q
1250
7
8
10 11 14 15 21 22
R
2000 10 11 14 15 21 22
Ac Re
1
= Use first sampling plan below arrow = Use first sampling plan above arrow =Acceptance number =Rejection number
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V. PRODUCT AND PROCESS CONTROL ACCEPTANCE SAMPLING / SAMPLING STANDARDS
General ANSI/ASQ Z1.4 Inspection Levels The inspection level to be used for any particular requirement is prescribed by the responsible authority. Three inspection levels: I, II, and III are provided for general use. Unless otherwise specified, inspection level II should be used. Inspection level I may be specified when less discrimination is required. Inspection level III may be specified for greater discrimination.
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V. PRODUCT AND PROCESS CONTROL ACCEPTANCE SAMPLING / SAMPLING STANDARDS
Normal, Tightened, and Reduced Inspection Normal inspection: Normal inspection is used at the start of inspection, unless otherwise directed by the responsible authority. Reduced inspection: Under reduced inspection, the plans allow a smaller sample to be taken than under normal inspection. Reduced inspection may be implemented when it is evident that quality is running unusually well. Tightened inspection: Under tightened inspection, the inspection plan requires more stringent acceptance criteria. Such a plan is used when it becomes evident that quality is deteriorating.
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V. PRODUCT AND PROCESS CONTROL ACCEPTANCE SAMPLING / SAMPLING STANDARDS
Special Inspection Levels Four special inspection levels S-1, S-2, S-3, and S-4 are provided. They are used where relatively small sample sizes are necessary and large sampling risks can or must be tolerated. In the designation of inspection levels S-1 to S-4, care must be exercised to avoid AQLs inconsistent with these inspection levels.
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V. PRODUCT AND PROCESS CONTROL ACCEPTANCE SAMPLING / SAMPLING STANDARDS
ANSI/ASQ Z1.4 Switching Procedures Normal ! Tightened: When 2 out of 5 consecutive lots or batches have been rejected on original inspection. Tightened ! Normal: When 5 consecutive lots or batches have been considered acceptable on original inspection. Normal ! Reduced: All of the following must be satisfied:
C The preceding 10 lots or batches have been acceptable. C The total number of defectives from the 10 lots or batches is equal to or less than an applicable number. C Production is at a steady rate. C Reduced inspection is considered desirable by the responsible authority.
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V. PRODUCT AND PROCESS CONTROL ACCEPTANCE SAMPLING / SAMPLING STANDARDS
ANSI/ASQ Z1.4 Switching Procedures (Cont’d) Reduced ! Normal: When any of the following occur:
C A lot or batch is rejected. C Under reduced inspection, the sampling procedure may terminate without acceptance or rejection. The lot is considered acceptable, but then normal inspection is used. C Production becomes irregular or delayed. C Other conditions warrant it.
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V. PRODUCT AND PROCESS CONTROL ACCEPTANCE SAMPLING / SAMPLING STANDARDS
Single, Double, and Multiple Sampling Sampling plans like ANSI/ASQ Z1.4-2003 give a choice among single, double, and multiple sampling. In single sampling plans, a random sample is drawn from the lot. If the number of defectives is less than or equal to the acceptance number, the lot is accepted. In double sampling plans, a smaller initial sample is usually drawn. A decision to accept or reject is reached on the basis of a single sample if the number of defectives is either quite large or quite small. A second sample is then taken if the first one cannot be accepted or rejected. In multiple sampling plans, still smaller samples are taken (seven in ANSI/ASQ Z1.4-2003), continuing as needed, until a decision to accept or reject is made. Double and multiple sampling plans usually mean less inspection but are complicated to administer.
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V. PRODUCT AND PROCESS CONTROL ACCEPTANCE SAMPLING / SAMPLING STANDARDS
Single, Double, and Multiple Sampling (Cont’d) It is possible to select single, double, or multiple sampling schemes with very similar operating characteristic curves as illustrated below using ANSI/ASQ Z1.4-2003 code letter H, with an AQL = 4.0. Plan Type
Sample Number
Sample Size
Total Sample
Ac
Re
Single
1
50
50
5
6
Double
1
32
32
2
5
2
32
64
6
7
1
13
13
#
4
2
13
26
1
5
3
13
39
2
6
4
13
52
3
7
5
13
65
5
8
6
13
78
7
9
7
13
91
9
10
Multiple
Ac = Acceptance number Re = Rejection number # = Acceptance not permitted at this sample size
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V. PRODUCT AND PROCESS CONTROL ACCEPTANCE SAMPLING / SAMPLING STANDARDS
ANSI/ASQ Z1.4 Double Sampling Code Sample Sample Total letter size sample size
Acceptable Quality Limits (normal inspection) 0.25
0.40
0.65
1.0
1.5
2.5
4.0
6.5
Ac Re
Ac Re
Ac Re
Ac Re
Ac Re
Ac Re
Ac Re
Ac Re
A B C D E F G H J K L M N P Q R
First
2
2
Second
2
4
First
3
3
Second
3
6
First
5
5
Second
5
10
First
8
8
Second
8
16
First
13
13
Second
13
26
First
20
20
Second
20
40
0
First
32
32
Second
32
64
First
50
50
0
Second
50
100
1
2
1
2
0
2
0
3 4
1
2
3
0
2
0
3
1
4
1
2
3
4
4
5
0
2
0
3
1
4
2
5
1
2
3
4
4
5
6
7
0
2
0
3
1
4
2
5
3
7
1
2
3
4
4
5
6
7
8
9
2
0
3
1
4
2
5
3
7
5
9
2
3
4
4
5
6
7
8
9
12
13
First
80
80
0
2
0
3
1
4
2
5
3
7
5
9
7
11
Second
80
160
1
2
3
4
4
5
6
7
8
9
12
13
18
19
First
125
125
0
2
0
3
1
4
2
5
3
7
5
9
7
11
11
16
Second
125
250
1
2
3
4
4
5
6
7
8
9
12
13
18
19
26
27
First
200
200
0
3
1
4
2
5
3
7
5
9
7
11
11
16
26
27
Second
200
400
3
4
4
5
6
7
8
9
12
13
18
19
First
315
315
1
4
2
5
3
7
5
9
7
11
11
16
26
27
Second
315
630
4
5
6
7
8
9
12
13
18
19
First
500
500
2
5
3
7
5
9
7
11
11
16
Second
500
1000
6
7
8
9
12
13
18
19
26
27
First
800
800
3
7
5
9
5
9
11
16
26
27
Second
800
1600
8
9
12 13
18
19
First
1250
1250
5
9
7
11
11
16
Second
1250
2500
1
13
18 19
26
27
= Use first sampling plan below arrow. = Use first sampling plan above arrow = Use corresponding single sampling plan
© QUALITY COUNCIL OF INDIANA CQE 2006
V-52 (601)
V. PRODUCT AND PROCESS CONTROL ACCEPTANCE SAMPLING / SAMPLING STANDARDS
Multiple Sampling Plan An example of a multiple sampling plan is shown on V - 52.
© QUALITY COUNCIL OF INDIANA CQE 2006
V-53 (602)
V. PRODUCT AND PROCESS CONTROL ACCEPTANCE SAMPLING / SAMPLING STANDARDS
Dodge-Romig Sampling Tables Dodge-Romig sampling inspection tables (Dodge, 1959) provide four sets of attributes sampling plans corresponding to the desired lot tolerance percent defective (LTPD) or average outgoing quality limit (AOQL).
C Lot tolerance percent defective (LTPD) both single and double sampling C Average outgoing quality limit (AOQL): both single and double Dodge-Romig plans differ from those in ANSI/ASQ Z1.42003 because they assume that all rejected lots are 100% inspected and the defectives are replaced with good product. The tables provide protection against poor quality based on the average long-run quality.
© QUALITY COUNCIL OF INDIANA CQE 2006
V-53 (603)
V. PRODUCT AND PROCESS CONTROL ACCEPTANCE SAMPLING / SAMPLING STANDARDS
Dodge-Romig Tables (Continued) LTPD plans ensure that a lot having poor quality will have a relatively low probability of acceptance. The LTPD values range from 0.5% to 10.0% defective. The AOQL plans ensure that, after all sampling and 100% inspection, the average quality (for many lots) will not exceed the AOQL. The AOQL values range from 0.1% to 10.0%. Each AOQL plan lists the corresponding LTPD (LQL) and vice-versa. The selection of a Dodge-Romig plan requires two items of information: the size of lot to be sampled and the expected process average based on past inspection records and any additional information which may be used to predict the expected quality level.
© QUALITY COUNCIL OF INDIANA CQE 2006
V-54 (604)
V. PRODUCT AND PROCESS CONTROL ACCEPTANCE SAMPLING / SAMPLING STANDARDS
LTPD Sampling Plan There is an LTPD sampling plan shown on V - 54. Actual use of Dodge-Romig is not anticipated on the CQE exam.
© QUALITY COUNCIL OF INDIANA CQE 2006
V-55 (605)
V. PRODUCT AND PROCESS CONTROL ACCEPTANCE SAMPLING / SAMPLING STANDARDS
Dodge-Romig Tables (Continued) Primer page V - 56 shows a typical table of AOQL plans using double sampling. In contrast to the lot tolerance table, this table gives plans which differ considerably as to lot tolerance, but which have the same AOQL, 1%. The corresponding lot tolerances are given. AOQL plans are the Dodge-Romig Tables most frequently used. They are appropriate only when all rejected lots are 100% inspected. The average of the perfect quality of the inspected lots with the poor quality of some accepted lots determines the average outgoing quality limit. Sampling is uneconomical if the average quality submitted is not considerably better than the specified AOQL because of administration expenses.
© QUALITY COUNCIL OF INDIANA CQE 2006
V-55 (606)
V. PRODUCT AND PROCESS CONTROL ACCEPTANCE SAMPLING / SAMPLING STANDARDS
Minimum Inspection per Lot The Dodge-Romig tables are constructed to minimize the average total inspection (ATI) per lot for a given process average. This is perhaps the most important feature of the Dodge-Romig tables. The total number of items inspected is made up of two components: (1) The sample which is inspected for each lot, and (2) The remaining items which must be inspected if the lot fails.
© QUALITY COUNCIL OF INDIANA CQE 2006
V-57 (607)
V. PRODUCT AND PROCESS CONTROL ACCEPTANCE SAMPLING / SAMPLING STANDARDS
Variables Sampling All attribute sampling plans are based on data that can be counted. Each inspected item is classified as either good or bad and an accept/reject decision is made based on a previously selected sampling risk. Variables sampling plans require unit measurements. The sample data is recorded and processed to yield a statistic such as a sample average, range, or standard deviation. These calculated values are then compared to a critical or table value to arrive at a decision on the lot in question. The sample size and critical value are based on the desired sampling risk.
© QUALITY COUNCIL OF INDIANA CQE 2006
V-57 (608)
V. PRODUCT AND PROCESS CONTROL ACCEPTANCE SAMPLING / SAMPLING STANDARDS
ANSI/ASQ Z1.9 Sampling Plans ANSI/ASQ Z1.9-2003 has four sections: Section A: General description of sampling plans Section B: Consists of sampling plans that are used when the variability is unknown, and the standard deviation method is used. Section C: Consists of sampling plans that are used when the variability is unknown, and the range method is used. Section D: Consists of sampling plans that are used when the variability is known. ANSI/ASQ Z1.9-2003 has five inspection levels: S3, S4, I, II, III (When no level is specified, use level II.)
© QUALITY COUNCIL OF INDIANA CQE 2006
V-57 (609)
V. PRODUCT AND PROCESS CONTROL ACCEPTANCE SAMPLING / SAMPLING STANDARDS
ANSI/ASQ Z1.9 Sampling Plans To use ANSI/ASQ Z1.9-2003, follow the sequence below:
C C C C
Choose the level Choose the method (standard deviation or range) Know the AQL Know the lot size
© QUALITY COUNCIL OF INDIANA CQE 2006
V-58 (610)
V. PRODUCT AND PROCESS CONTROL ACCEPTANCE SAMPLING / SAMPLING STANDARDS
Z1.9 AQL Conversion Table An AQL conversion table is required to align with standard AQLs used in ANSI/ASQ Z1.9 tables. ANSI/ASQ Z1.9 AQL Conversion Table For specified AQL values
Use this AQL value
0.109
0.10
0.110 to 0.164
0.15
0.165 to 0.279
0.25
0.280 to 0.439
0.40
0.440 to 0.699
0.65
0.700 to 1.09
1.0
1.10 to 1.64
1.5
1.65 to 2.79
2.5
2.80 to 4.39
4.0
4.40 to 6.99
6.5
7.00 to 10.9
10.0
© QUALITY COUNCIL OF INDIANA CQE 2006
V-58 (611)
V. PRODUCT AND PROCESS CONTROL ACCEPTANCE SAMPLING / SAMPLING STANDARDS
Z1.9 Code Letters The lot size is used to determine an inspection level code. ANSI/ASQ Z1.9 Code Letters Inspection Levels Special General Lot Size 2 to 8 9 to 15 16 to 25 26 to 50 51 to 90 91 to 150 151 to 280 281 to 400 401 to 500 501 to 1,200 1,201 to 3,200 3,201 to 10,000 10,001 to 35,000 35,001 to 150,000 150,001 to 500,000 500,001 and over
S3
S4
I
II
III
B B B B B B B C C D E F G H H H
B B B B B C D E E F G H I J K K
B B B C D E F G G H I J K L M N
B B C D E F G H I J K L M N P P
C D E F G H I J J K L M N P P P
© QUALITY COUNCIL OF INDIANA CQE 2006
V-59 (612)
V. PRODUCT AND PROCESS CONTROL ACCEPTANCE SAMPLING / SAMPLING STANDARDS
Standard Deviation Method-Section B An upper value, QU, or lower value, QL, is calculated for a single specification limit. For double specification limits, both the QU and QL are calculated. The technique used is similar to that of determining a Z value in Section X of this Primer. QU =
U-X s
QL =
X-L s
Where: s = Sample standard deviation U = Upper specification limit X = Sample mean L = Lower specification limit The acceptability criteria is based on a comparison of QU and QL with the acceptability constant k, which is given in a master table. If QU > k or QL > k, the lot meets the acceptability criterion. If QU < k or QL < k, the lot does not meet the acceptability criterion. A plan from ANSI/ASQ Z1.9-2003 Section B, standard deviation method, single specification limit, Form 1,is shown as a Primer example.
© QUALITY COUNCIL OF INDIANA CQE 2006
V-60 (613)
V. PRODUCT AND PROCESS CONTROL ACCEPTANCE SAMPLING / SAMPLING STANDARDS
ANSI/ASQ Z1.9-2003 General Information Detailed use of the Z1.9-2003 standard is not anticipated on the CQE exam. The student should be familiar with the general concepts. Note that the whole process is very similar to capability determinations and Z table usage presented in Primer Section X.
© QUALITY COUNCIL OF INDIANA CQE 2006
V-61 (614)
V. PRODUCT AND PROCESS CONTROL ACCEPTANCE SAMPLING / SAMPLING STANDARDS
Z1.9 Range Method-Section C When using the range method, it is necessary to find R 6, which is the average range of the subgroups. All subgroups consist of five measurements, n = 5. (If there is only one subgroup, R is used.) There are three different severities for inspection: normal, tightened, and reduced. Each of these severities has rules. The severity must be known for the sampling plan to be found. The student is referred to the standard itself for all procedures and calculations. An upper value, QU, or lower value, QL, is calculated for a single specification limit. For double specification limits, both the QU and QL are calculated. The technique used is similar to that of the standard deviation method shown previously, except that the average sample range is used: QU =
U-X R
QL =
X-L R
The acceptability criteria is based on a comparison of QU and QL with the acceptability constant k. If QU > k or QL > k, the lot meets the acceptability criterion.
© QUALITY COUNCIL OF INDIANA CQE 2006
V-61 (615)
V. PRODUCT AND PROCESS CONTROL ACCEPTANCE SAMPLING / SAMPLING STANDARDS
Sample Integrity A sample is a subset from the population used to gather data about the population. This sample is used to gather acceptance data about each lot. The samples should be a random (unbiased) representation of the lot. Since the sample is used to determine the acceptance of a lot, care is taken to ensure that the sample is not contaminated. In some products, such as foods, any unsanitary factor introduced by the sampling process could influence the outcome. Some common influencing factors are:
C Personnel C Instruments C Containers
C Storage areas C Environment conditions C Laboratory conditions
Acceptability results may also become questionable by inappropriate labeling which would void the link between the sample and the lot. Cross contamination between samples must be avoided.
© QUALITY COUNCIL OF INDIANA CQE 2006
V-62 (616)
V. PRODUCT AND PROCESS CONTROL ACCEPTANCE SAMPLING / SAMPLING STANDARDS
Sample Integrity (Continued) The recruitment and selection of sampling and inspection personnel should follow the same sound judgment as with other company positions. The major job functions that impact sample integrity typically include the following:
C C C C C C C
The ability to interpret blueprints, specifications The ability to operate test equipment proficiently The appropriate physical capacity The ability to properly record and analyze data Knowledge of materials and processes Adherence to company policies and procedures The ability to prepare reports and communicate
Some pre-testing may prove beneficial in identifying the presence or absence of necessary skills. Many of the above items can be taught.
© QUALITY COUNCIL OF INDIANA CQE 2006
V-62 (617)
V. PRODUCT AND PROCESS CONTROL ACCEPTANCE SAMPLING / SAMPLING STANDARDS
Sample Integrity (Continued) Many experiments indicate that a typical individual under normal (often interrupted) conditions, will only catch 80%-90% of the defects present in a high volume operation. The attainment of inspection accuracy depends in large measure on advanced planning, the identification of key characteristics, the proper tools, specifications, facilities, etc. However, other sources of human error exist. Examples include: Rounding: The discard of some test accuracy Pencil whipping: This indicates the faking of data Pressure: An individual yielding to delivery needs Flinching: Moving readings inside the specification
© QUALITY COUNCIL OF INDIANA CQE 2006
V-62 (618)
V. PRODUCT AND PROCESS CONTROL ACCEPTANCE SAMPLING / SAMPLING STANDARDS
Sample Integrity (Continued) Unknown errors are unintentional and may be consistent or intermittent: Inadvertent errors: These errors are sporadic in nature and difficult to avoid. Rigidly enforced procedures, automated inspection, or error-proofing may help. Technique errors: These errors are consistently made by some individuals and may indicate lack of training, lack of skill, or lack of capacity. Remedies include: additional training, product magnification, and/or individual replacement.
© QUALITY COUNCIL OF INDIANA CQE 2006
V-65 (619)
V. PRODUCT AND PROCESS CONTROL QUESTIONS 5.1. The primary reason that nonconforming material should be identified and segregated is: a. So that the cause of nonconformity can be determined b. So it cannot be used in production without proper authorization c. To obtain samples of poor workmanship for use in the company's training program d. So that responsibility can be determined and disciplinary action taken 5.2. Using ANSI/ASQC Z1.4 for a lot of 1,000 parts, a general inspection level II, the code letter J, an AQL of 1.0%, and a sample size of 80, what is the accept number? a. 0 b. 1 c. 2 d. 3 5.8. Which of the following is the principal purpose of the MRB? a. Identifying potential suppliers b. Disposing of nonconforming material c. Appraising suppliers d. Detecting nonconforming material
Answers: 5.1. b, 5.2. c, 5.8. b
© QUALITY COUNCIL OF INDIANA CQE 2006
V-66 (620)
V. PRODUCT AND PROCESS CONTROL QUESTIONS 5.12. Two quantities which uniquely determine a single sampling attributes plan are: a. AQL and LTPD b. Sample size and rejection number c. AQL and producer's risk d. LTPD and consumer's risk 5.15. Using visual inspection standards and traditional methods, some 100 defects are located in a large batch of product. What is the best estimate of the total number of defects in the product before inspection? a. 95 - 98 b. 108 - 111 c. 117 - 120 d. 125 - 128 5.21. What is the importance of the reaction plan in a control plan? a. It describes what will happen if a key variable goes out of control b. It indicates that a new team must be formed to react to a problem c. It lists how often the process should be monitored d. It defines the special characteristics to be monitored
Answers: 5.12. b, 5.15. c, 5.21. a
© QUALITY COUNCIL OF INDIANA CQE 2006
V-67 (621)
V. PRODUCT AND PROCESS CONTROL QUESTIONS 5.22. ANSI/ASQ Z1.4 sampling plans allow reduced inspection when four requirements are met. One of these is: a. Inspection level I is specified b. 10 lots have been on normal inspection and none have been rejected c. The process average is less than the AOQL d. The maximum percent defective is less than the AQL 5.27. The most important activity of a material review board (MRB) would normally be: a. Making sure that corrective action is taken to prevent recurrence of the problem b. To provide a segregated area for holding discrepant material pending disposition c. To prepare discrepant material reports for management review d. To accept discrepant material when "commercial" decisions dictate 5.29. In a visual inspection situation, one of the best ways to minimize deterioration of the quality level is to: a. Retrain the inspector frequently b. Have a program of frequent eye exams c. Add variety to the task d. Have a standard to compare against as an element of the operation
Answers: 5.22. b, 5.27. a, 5.29. d
© QUALITY COUNCIL OF INDIANA CQE 2006
V-68 (622)
V. PRODUCT AND PROCESS CONTROL QUESTIONS 5.32. The purpose of a written inspection procedure is to: a. Provide answers to inspection questions b. Let the operator know what the inspector is doing c. Fool-proof the inspection function d. Standardize methods and procedures of inspectors 5.35. A sampling plan that may use up to 4 samples to make a decision to accept or reject is: a. Single sampling b. Double sampling c. Multiple sampling d. Quadruple sampling 5.40. Which of the following elements would NOT be expected on a control plan form? a. Specifications b. Potential causes of failure c. Key input variables d. Key output variables
Answers: 5.32. d, 5.35. c, 5.40. b
© QUALITY COUNCIL OF INDIANA CQE 2006
VI-1 (623)
VI. TESTING & MEASUREMENT
THERE IS THINGS.
MEASURE
IN
ALL
HORACE SATIRES, BOOK I, 35 B.C.
© QUALITY COUNCIL OF INDIANA CQE 2006
VI-2 (624)
VI. TESTING & MEASUREMENT MEASUREMENT TOOLS
Testing and Measurement Testing and Measurement are presented in the following topic areas:
C C C C C C
Measurement tools Testing and measurement definition Destructive tests Nondestructive tests Metrology Measurement system analysis
Measurement Tools At least 30 types of measurement tools are described in the Primer. Destructive and nondestructive tests are described later in this Section.
© QUALITY COUNCIL OF INDIANA CQE 2006
VI-3 (625)
VI. TESTING & MEASUREMENT MEASUREMENT TOOLS
Instrument Selection Listed below applications. Type of Gage
are
some
gage
Accuracy
accuracies
and
Application
Adjustable snap gages
Usually accurate within 10% Measures diameters on a of the tolerance. production basis where an exact measurement is needed.
Air gages
Accuracy depends upon the Used to measure the diameter of gage design. Measurements a bore or hole. However, other of less than 0.000050" are applications are possible. possible.
Automatic sorting gages
Accurate within 0.0001".
Used to sort parts by dimension.
Combination square
Accurate within one degree.
Used to make angular checks.
Coordinate measuring machines
Accuracy depends upon the part. Axis accuracies are within 35 millionths and T.I.R. within 0.000005".
Can be used to measure a variety of characteristics, such as contour, taper, radii, roundness, squareness, etc.
Dial bore gages
Accurate w ithin 0.0001" using great care.
Used to measure bore diameters, tapers, or out-ofroundness.
Dial indicator
Accuracy depends upon the type of indicator. Some measure within 0.0001".
Measures a variety of features such as: flatness, diameter, concentricity, taper, height, etc.
Electronic comparator
Accurate from 0.00001" to Used where the allowable 0.000001". tolerance is 0.0001" or less.
© QUALITY COUNCIL OF INDIANA CQE 2006
VI-4 (626)
VI. TESTING & MEASUREMENT MEASUREMENT TOOLS
Instrument Selection (Continued) Type of Gage
Accuracy
Application
Fixed snap gages
No set accuracy.
Normally used to determine if diameters are within specification.
Flush pin gages
Accuracy of about 0.002".
Used for high volume single purpose applications.
Gage blocks
Accuracy of the gage block Gage blocks are best adapted depends upon the grade. for precision machining and as a Normally the accuracy is comparison master. 0.000008" or better.
Height verniers
Mechanical models measure Used to check dimensional to 0.0001". Some digital tolerances on a surface plate. models attain 0.00005".
Internal and external thread gages
No exact reading. discriminate to a specification limit.
Micrometer (inside)
Mechanical accuracy is Used for checking large hole about 0.001". Some digital diameters. models are accurate to 0.00005".
Micrometer (outside)
Mechanical accuracy is Normally used to check diameter about 0.001". Some digital or thickness. Special models models are accurate to can check thread diameters. 0.00005".
Optical comparator
The accuracy can be within Measures difficult contours and 0.0002". part configurations.
Optical flat
Depending on operator skill, Used only for very precise tool Best used for accurate to a few millionths room work. checking flatness. of an inch.
Plug gages
Accuracy very good for checking the largest or smallest hole diameter.
Will Used for measuring inside and given outside pitch thread diameters.
Checking the diameter of drilled or reamed holes. Will not check for out of roundness.
© QUALITY COUNCIL OF INDIANA CQE 2006
VI-5 (627)
VI. TESTING & MEASUREMENT MEASUREMENT TOOLS
Instrument Selection (Continued) Type of Gage
Accuracy
Application
Precision straight edge
Visual 0.10". With a feeler gage 0.003".
Used to check flatness, waviness or squareness of a face to a reference plane.
Radius & template gages
Accuracy is no better than 0.015".
Used to check small radii, and contours.
Ring gages
Will only discriminate against diameters larger or smaller than the print specification.
Best application is to approximate a mating part in assembly. Will not check for out of roundness.
Split sphere & telescope
No better than 0.0005" using Used for measuring small hole a micrometer graduated in diameters. 0.0001".
Steel ruler or scale
No better than 0.015".
Surface plates
Flatness expected to be no Used to measure the overall better than 0.0005" between flatness of an object. any 2 points.
Tapered parallels
U s i n g a n a c c u r a t e Used to measure bore sizes in micrometer, the accuracy is low volume applications. about 0.0005".
Tool maker's flat
Accuracy is no better than Used with a surface plate and 0.0005" depending upon the gage blocks to measure height. instrument used to measure the height.
Vernier calipers
About 0.001". Some digital Used to check diameters and models are accurate to thickness. 0.00005".
Vernier depth gage
About 0.001". Some digital Used to check depths. models are accurate to 0.00005".
Used to measure heights, depths, diameters, etc.
© QUALITY COUNCIL OF INDIANA CQE 2006
VI-6 (628)
VI. TESTING & MEASUREMENT MEASUREMENT TOOLS
Surface Plates To make a precise dimensional measurement, there must be a reference plane or starting point. The ideal plane for dimensional measurement should be perfectly flat. Surface plates are customarily used with accessories like: a toolmaker's flat, angles, parallels, V blocks and cylindrical gage block stacks. Dimensional measurements are taken from the plate up since the plate is the reference surface. Surface plates must possess the following important characteristics:
C Sufficient strength and rigidity C Sufficient and known accuracy Surface plates maintenance:
C C C C C
require
appropriate
care
and
The surface should be cleaned before use The surface should be covered between uses Work should be distributed to avoid wear Move the test pieces and equipment carefully A surface plate should not become a storage area
© QUALITY COUNCIL OF INDIANA CQE 2006
VI-6 (629)
VI. TESTING & MEASUREMENT MEASUREMENT TOOLS
Surface Plates (Continued) Surface plates are made of cast iron or granite. Both have merits: Cast iron plates:
C C C C
Usually weigh less per square foot of plate area Are not likely to chip or fracture Are acceptable for magnetic fixtures Can provide a degree of wringability
Granite plates:
C C C C C C C
Are noncorrosive Require less maintenance Do not burr or retain soft metals Are cheaper per relative size Have greater thermal stability Have closer flatness tolerances Are nonmagnetic
© QUALITY COUNCIL OF INDIANA CQE 2006
VI-7 (630)
VI. TESTING & MEASUREMENT MEASUREMENT TOOLS
Angle Measurement Tools Angle measurement tools include protractors, sine bars and angle blocks. Note that angles may also be measured using tools described elsewhere in this Section (such as optical comparators, profile projectors and coordinate measuring machines).
© QUALITY COUNCIL OF INDIANA CQE 2006
VI-7 (631)
VI. TESTING & MEASUREMENT MEASUREMENT TOOLS
Universal Bevel Protractor One of the most widely used pieces of equipment to measure angles is the universal bevel protractor. It is a hand held tool used to obtain an angular reading in degrees and minutes of the workpiece. The scale is often magnified for easier reading. The most common errors that occur in the use of the bevel protractor are:
C Misreading of the scale C Improper seating of the protractor base
© QUALITY COUNCIL OF INDIANA CQE 2006
VI-7 (632)
VI. TESTING & MEASUREMENT MEASUREMENT TOOLS
Sine Bar Angle measurements in dimensional standardization are often made using a device known as a sine plate or sine bar. The sine bar is a machined steel bar that has two cylinders spaced at known dimensions on the bar. An angle is generated indirectly by using precision geometry based on gage block stacks to define the height of one leg of a right triangle. The hypotenuse of the triangle is a known, fixed dimension. From these two measurements, the angle of the plate may be calculated. Normally, the desired part angle is known and a calculation is made for the gage block stack. The sine bar is different than the bevel protractor because:
C No direct reading may be obtained C It is used in conjunction with gage blocks
© QUALITY COUNCIL OF INDIANA CQE 2006
VI-8 (633)
VI. TESTING & MEASUREMENT MEASUREMENT TOOLS
Sine Bar (Continued) The sine bar, cylinder and gage block combination creates an angular plane to seat the workpiece. To use a sine bar, one must first know the length of the sine bar. Standard sine bar lengths are 5", 10", and 15". The angle, ", to be checked is determined from the part drawing or other source. The required height of gage blocks is then determined from a sine bar table or calculated using a trigonometric function relationship. In the figure below the sine (sin) of angle " equals the gage stack height divided by the effective sine bar length.
Illustration of a Sine Bar in use
© QUALITY COUNCIL OF INDIANA CQE 2006
VI-9 (634)
VI. TESTING & MEASUREMENT MEASUREMENT TOOLS
Angle Blocks Angle blocks are used for the alignment and measurement of precise angles. They are typically sold in sets, containing several different angles. Stacking of angle blocks is used to create angles other than those of the individual blocks. Note that the angles may be added together to form a new angle, or by inverting one of the blocks, the angles may be subtracted.
Block 2
Block 1
Block 1
Angles are Added
Angles are Subtracted
Stacking of Angle Blocks
© QUALITY COUNCIL OF INDIANA CQE 2006
VI-10 (635)
VI. TESTING & MEASUREMENT MEASUREMENT TOOLS
Variable Gages Variable measuring instruments provide a physical measured dimension. Examples of variable instruments are line rules, vernier calipers, micrometers, depth indicators, runout indicators, etc. Variable information provides a measure of the extent that a product is good or bad, relative to specifications. Variable data is often useful for process capability determination and may be monitored via control charts.
© QUALITY COUNCIL OF INDIANA CQE 2006
VI-10 (636)
VI. TESTING & MEASUREMENT MEASUREMENT TOOLS
The Steel Rule The steel rule is a linear scale which is widely used factory measuring tool for direct length measurement. Steel rules and tapes are available in different degrees of accuracy and are typically graduated on both edges.
A Typical Steel Rule The fine divisions on a steel rule (thirty-seconds on the one above) establish its discrimination. The steel rule typically has discriminations of 1/32, 1/64, or 1/100 of an inch. Obviously, measurements requiring accuracies of 0.01" or finer should be performed with other tools (such as a digital caliper).
© QUALITY COUNCIL OF INDIANA CQE 2006
VI-11 (637)
VI. TESTING & MEASUREMENT MEASUREMENT TOOLS
The Steel Rule (Continued) Shown below are the correct and incorrect methods of measurement.
Incorrect
Correct
© QUALITY COUNCIL OF INDIANA CQE 2006
VI-11 (638)
VI. TESTING & MEASUREMENT MEASUREMENT TOOLS
Hook Rules Steel rules may be purchased with a moveable bar or hook on the zero end which serves in the place of a butt plate. These rulers may be used to measure around rounded, chamfered or beveled part corners. The hook attachment becomes relied upon as a fixed reference. However, by its inherent design, it may loosen or become worn. The hook should be checked often for accuracy.
Steel Rule with Hook Attachment
© QUALITY COUNCIL OF INDIANA CQE 2006
VI-12 (639)
VI. TESTING & MEASUREMENT MEASUREMENT TOOLS
Micrometers Micrometers, or “mics,” are commonly used hand-held measuring devices. Micrometers may be purchased with frame sizes from 0.5 inches to 48 inches. Normally, the spindle gap and design permits a 1" reading span. Thus, a 2" micrometer would allow readings from 1" to 2". Most common “mics” have an accuracy of 0.001". With the addition of a vernier scale, an accuracy of 0.0001" can be obtained. Fairly recent digital micrometers can be read to 50 millionths of an inch. The two primary scales for reading a micrometer are the sleeve scale and the thimble scale. Most micrometers have a 1" “throat.” All conventional micrometers have 40 markings on the barrel consisting of 0.025" each. The 0.100", 0.200", 0.300", etc. markings are highlighted. The thimble is graduated into 25 markings of 0.001" each. Thus, one full revolution of the thimble represents 0.025".
© QUALITY COUNCIL OF INDIANA CQE 2006
VI-12 (640)
VI. TESTING & MEASUREMENT MEASUREMENT TOOLS
Micrometers (Continued) Shown below, are simplified examples of typical micrometer readings.
Micrometer set at 0.245" 0.200" +0.025" +0.020" 0.245"
Micrometer set at 0.167" 0.100" +0.050" +0.017" +0.167"
Two Micrometer Reading Examples
© QUALITY COUNCIL OF INDIANA CQE 2006
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VI. TESTING & MEASUREMENT MEASUREMENT TOOLS
Measuring Pitch Diameter In order to determine the pitch diameter of screw threads by measuring the corresponding over-wire size, the most practical procedure is the use of three wires, actually small hardened steel cylinders, placed in the thread groove, two on one side and one on the opposite side of the screw. The arrangement of the wires, as indicated in the diagram (below), permits the opposite sensing elements of a length-measuring instrument to be brought into simultaneous contact with all three wires.
An Illustration of Three Wire Measurement
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Measuring Pitch Diameter (Continued) The best wire size may be calculated by: w = 0.5p sec " Where: w = wire diameter " = 1/2 the included thread angle p = thread pitch
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Measuring Pitch Diameter (Continued) The formula to calculate the pitch diameter after measurement is: E = M + (0.86603p) - 3W Where: E = M= p= W=
pitch diameter over the wire measurement thread pitch wire size used
Example: Assume that M is 0.360", p is 0.050" and W is 0.030". Calculate the pitch diameter. E E E E
= = = =
M + (0.86603p) - 3W 0.360 + (0.86603 x 0.050) - 3(0.030) 0.360 + 0.0433 - 0.090 0.3133 inch
E is the pitch diameter which must be checked with the tolerance limits on the drawing to determine if the part is acceptable.
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Gage Blocks Near the beginning of the 20th century, Carl Johansson of Sweden, developed steel blocks to an accuracy believed impossible by many others at that time. His objective was to establish a measurement standard that not only would duplicate national standards, but also could be used in any shop. Today gage blocks are used in almost every shop manufacturing a product requiring mechanical inspection. They are used to set a length dimension for a transfer measurement, and for calibration of a number of other tools. ANSI/ASME B89.1.9 (2002), distinguishes three basic gage block forms - rectangular, square and round. The rectangular and square varieties are in much wider usage. Generally, gage blocks are made from high carbon or chromium alloyed steel.
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Gage Blocks (Continued) All gage blocks are manufactured with tight tolerances on flatness, parallelism and surface smoothness. Gage blocks may be purchased in 4 standard grades: Federal Accuracy Grades New Old Designation Designation 0.5 AAA 1 AA 2 A+
Accuracy In Length *
± 0.000001 ± 0.000002 + 0.000004 - 0.000002 3 A&B + 0.000008 - 0.000004 * Applies to gage blocks up to 1". The accuracy tolerance then increases as the gage block size increases. Master blocks are grade 0.5 or 1 Inspection blocks are grade 1 or 2 Working blocks are grade 3
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Gage Blocks (Continued) Gage blocks should always be handled on the nonpolished sides. Blocks should be cleaned prior to stacking with filtered kerosene, benzene or carbon tetrachloride. A soft clean cloth or chamois should be used. A light residual oil film must remain on blocks for wringing purposes. Block stacks are assembled by a wringing process which attaches the blocks by a combination of molecular attraction and the adhesive effect of a very thin oil film. Air between the block boundaries is squeezed out. The sequential steps for the wringing of rectangular blocks is shown below.
Hold Crosswise
Swivel the Pieces
Slip into Position
Finished Stack
Illustration of the Wringing of Gage Blocks
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Wear Blocks For the purpose of stack protection, some gage manufactures provide wear blocks. Typically, these blocks are 0.050 inch or 0.100 inch thick. They are wrung onto each end of the gage stack and must be calculated as part of the stack height. Since wear blocks “wear” they should always be used with the same side out.
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Gage Block Sets Individual gage blocks may be purchased up to 20" in size. Naturally, the length tolerance of the gage blocks increases as the size increases. Typical gage block sets vary from 8 to 81 pieces based upon the needed application. Listed below are the contents of a typical 81 piece set: Ten-thousands blocks
(9) 0.1001, 0.1002 ... 0.1009
One-thousands blocks
(49) 0.101, 0.102 ... 0.149
Fifty-thousands blocks
(19) 0.050, 0.100 ... 0.950
One inch blocks
(4) 1.000, 2.000, 3.000, 4.000
Also included in the set, are two wear blocks that are either 0.050" or 0.100" in thickness.
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Minimum Stacking A minimum number of blocks in a stack lessens the chance of unevenness at the block surfaces. Stack up 2.5834" using a minimum number of blocks: 2.5834 - 0.1004 2.483 - 0.133 2.350 - 0.350 2.000
(use 0.1004" block) (use 0.133" block) (use 0.350" block) (use 2.000" block)
This example requires a minimum of four blocks and does not consider the use of wear blocks.
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Attribute Gages Attribute gages are fixed gages which typically are used to make a go, no-go decision. Examples of attribute instruments are master gages, plug gages, contour gages, thread gages, limit length gages, assembly gages, etc. Attribute data indicates only whether a product is good or bad (in most cases, it is known in what direction the product is good or bad). Attribute gages are quick and easy to use but provide minimal information for production control.
Snap Gages Snap gages are used to check outside dimensions in high volume operations. Snap gages are constructed with a rigid frame and normally contain hardened anvil inserts. These gages may have provisions for a small range of adjustments and can be used to make rapid “go, no-go” decisions.
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Ring Gages Ring gages are used to check external cylindrical dimensions, and may also be used to check tapered, straight, or threaded dimensions. A pair of rings with hardened bushings are generally used. One bushing has a hole of the minimum tolerance and the other has a hole of the maximum tolerance. Ring gages have the disadvantage of accepting out of round work and taper if the largest diameter is within tolerance.
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Ring Gages (Continued) A thread ring gage is used to check male threads. The go ring must enter onto the full length of the threads and the no-go must not exceed three full turns onto the thread to be acceptable. The no-go thread ring is identified by a groove cut into the outside diameter.
A No-go Thread Ring Gage
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Plug Gages Plug gages are generally “go, no-go” gages, and are used to check internal dimensions. The average plug gage is a hardened and precision ground cylinder about an inch long. A set is usually held in a hexagonal holder with the “go” plug on one end and the “no-go” plug on the other end. To make it more readily distinguishable, the “no-go” plug is generally made shorter. The thread plug gage is designed exactly as the plug gage but instead of a smooth cylinder at each end, the ends are threaded. One end is the go member and the other end is the no go member. A threaded plug gage has a feature used to clear chips out of the female threads. This feature is called the chip groove or notch.
A Thread Plug Gage
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Spring Calipers Spring calipers are transfer tools that perform a rough measurement of wide, awkward or difficult to reach part locations. These tools usually provide a measurement accuracy of approximately 1/16 inch. A spring caliper measurement is typically transferred to a steel rule by holding the rule vertically on a flat surface. The caliper ends are placed against the rule for the final readings. See the diagram below.
Inside Calipers
Outside Calipers
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Telescoping Gages Telescoping gages (telescope gages) are a type of transfer gage. They consist of a handle and a T-shaped portion that has a spring loaded cylinder and a fixed cylinder at right angles to the handle. The spring cylinder is compressed and the gage is placed inside a bore or interior surface of a part.
Small Hole Gages Small hole gages or split sphere gages are similar to telescoping gages, but are used for the size range from about 1/8 inch to 1/2 inch. The gage consists of two hemispherical contact surfaces that are spread apart by an adjustable wedge.
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Radius Gages Radius gages come in sets for checking inside and outside radii over the range of about 1/16 inch to 1 inch, or larger. They are made from thin pieces of metal sheet and have the dimension stamped or printed on the side. These gages provide only an attribute measurement since the gage only provides an approximate range for the radius of interest, e.g. between 13/16 and 7/8 inch. Template gages may be custom made for checking more complex surfaces.
Radius Gage with Fixed Radii
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Dial Indicators Dial indicators are mechanical instruments for measuring distance variations. Most dial indicators amplify a contact point reading by use of an internal gear train mechanism. The standard nomenclature for dial indicator components is shown in the diagram below:
Commonly available indicators have discriminations (smallest graduations) from 0.00002" to 0.001" with a wide assortment of measuring ranges.
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Dial Indicators (Continued) Dial indicators are available in a variety of measurement ranges and graduations. Thus, the proper dial must be selected for the length measurement and required discrimination. Dial indicators also come with balanced or continuous dials. Shown below are examples of both.
Continuous Dial With Revolution Counter
Balanced Dial
Contact Tips Contact points are available in a variety of shapes (standard, tapered, button, flat, wide-face, etc.). The tips are made from a number of wear resistant materials (carbide, chrome plated steel, sapphire or diamond).
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Indicator Errors Although dial indicators offer advantages in operational flexibility, there are numerous potential opportunities for mistakes. Some of the more common errors include:
C Loose clamping of the gage. C Reading errors - These errors occur when the indicator face is not viewed at a 90° angle or when the shadow of the needle is mistaken for the needle itself. C Not adjusting for indicator over-travel. C Rounding errors - Generally due to improper dial discrimination or inadequate training. C Over-looking the number of tip revolutions. C Cosine error - Created by misalignment between the work piece and indicator tip. This error could allow both the rejection of an acceptable dimension and the acceptance of a rejectable dimension.
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Digital Indicators Digital indicators use the same principle of operation as is found in dial indicators, however the display is a digital readout. Key advantages of digital indicators over dial indicators are the elimination of the reading errors, indicator over-travel errors, rounding errors, over-looking the number of revolutions and the cosine errors. Many digital tools have an optional interface for connection to a computer or other electronic data collection devices. A yellow faceplate on a dial indicator means that the readings are in metric (SI).
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The Vernier Scale Vernier scales are used on a variety of measuring instruments such as height gages, depth gages, vernier calipers and gear tooth verniers. Except for the digital varieties, readings are made between a vernier plate and beam scales. A vernier scale may have line divisions of 0.025 inch or 0.050 inch. One must identify the “plate” and “bar” components on the instrument. The proper figure is indicated where a line of the plate aligns with a line of the bar. The two numbers are added together to make a composite reading. Shown below is an illustrative example.
Record 1.050" Add 0.019" Final reading 1.069"
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Analog and Digital Displays The measurement scales can be analog or digital. The analog display is defined as one having a continuous range of values. For example, one would visually interpret the time of day (10:20 am) by looking at a traditional watch face with hour and minute hands. The digital watch would not have a clock face, but instead provide a numerical display (10:20 am). Some instruments can incorporate both analog and digital displays.
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Nongraduated and Graduated Scales Various general purpose measuring tools or instruments can be divided into two classes: nongraduated tools and graduated tools. Nongraduated tools or instruments do not have linear or angular graduations on the tool. Examples of these types of tools would be: calipers, dividers, telescope gages, straightedges, squares, surface plates, and sine bars. Graduated tools or instruments have linear or angular graduations. The user can make a direct measurement on the part. Examples of graduated tools would be: rules, slide calipers, vernier calipers, vernier depth calipers, micrometers, protractors, and mechanical indicating gages.
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Electronic Measuring Equipment There are hundreds of types of instruments that can be classified as electronic measuring equipment. Most of these instruments are produced in both analog and digital display formats, although the digital formats are rapidly replacing the analog units, in most cases. Examples of electronic measuring equipment include:
C C C C C C C C C
Voltmeters Ohmeters Ammeters Wattmeters Capacity meters Inductance meters pH meters Load sensors Torque sensors
Obviously this list is not exhaustive. The digital equipment normally has an optional interface for communication with external computers or other data storage and processing equipment.
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Electronic Gaging There are hundreds of types of electronic gaging devices. A summary of three basic electronic tools, the oscilloscope, multimeter, and pyrometer, are described in the Primer.
Oscilloscopes An oscilloscope displays voltage on the vertical axis and time on the horizontal axis. Grid lines in the display show relative values for both the x and y directions. By changing ranges for either voltage or time, signals can be displayed as waveforms over frequencies from direct current (DC) up to MHz range and above, and from mV to 100 V or more.
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Electronic Gaging (Continued) Multimeters A multimeter is an electrical meter that measures several electrical properties including voltage, current, and resistance. Multimeters use multiple scale ranges, within a measurement property, to improve resolution of the readings. The two general types of multimeters are analog and digital.
Pyrometers A pyrometer is an instrument used for measuring high temperatures. The two main types of pyrometers are a thermocouple with a temperature display and an optical pyrometer.
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Laser Designed Gaging The use of lasers are prevalent when the intent of inspection is a very accurate non-contact measurement. The laser beam is transmitted from one side of the gage to a receiver on the opposite side of the gage. Measurement takes place when the beam is broken by an object and the receiver denotes the dimension of the interference to the laser beam. The laser has many uses in gaging. Automated inspection, fixed gaging, and laser micrometers are just a few examples of the many uses of the laser.
Machine Vision Gaging Machine vision gaging is accomplished using some type of light source and an image capture device, such as a video camera. The image is digitized and then processed using a computer. Computer analysis of the image can determine dimensions, angles, areas and perimeters.
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Pneumatic Gages There are two general types of pneumatic amplification gages in use. One type is actuated by varying air pressure and the other by varying air velocity at constant pressure. There are numerous advantages of pneumatic gages. Some of the more important ones are listed below:
C C C C C C
A high level of skill is not required Air gages tend to be self-cleaning The equipment is safe, fast, reliable and accurate The equipment is very versatile Attribute or variable measurements can be made Measurements can be read to millionths of an inch
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Balances and Scales Balances and scales cover the weight range from 1 mg and smaller for laboratory balances to over 100,000 lb capacity truck and crane scales. There are two primary types of balances and scales: those that balance a known mass, sometimes through a lever arm system, against the unknown weight; and those that use a load cell to measure the applied force. Most electronic balances and scales have the optional output capability to interface with a computer.
Whenever balances or scales are moved, they should be recalibrated. When weights, balances and scales are calibrated, it is recommended that they be sent to an accredited calibration laboratory
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Surface Analyzers Surface analyzers include instruments such interferometry and surface roughness testers.
as
Interferometry The greatest possible accuracy and precision are achieved by using light waves as a basis for measurement. A measurement is accomplished by the interaction of light waves that are 180° out of phase. This phenomenon is known as interference.
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Surface Roughness Testers A surface profiler or profilometer is the most common method of measuring surface roughness, although other techniques are available. The profilometer (or profile tracer) uses a stylus or probe to traverse the surface of interest. The average roughness is the total area of the peaks and valleys divided by the evaluation length, it is expressed in :m. Surface finish describes the deviation from the ideal flat surface. This deviation is normally expressed in terms of roughness, lay, and waviness, defined as:
C Roughness represents the size of the finely distributed surface pattern deviations from the smooth surface. C Lay represents the dominant direction of the surface pattern, such as grinding scores. C Waviness represents deviations which are relatively far apart.
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Surface Roughness Testers (Continued) The figure below depicts roughness, lay and waviness on a magnified surface.
Y = Roughness, S = Lay, V = Waviness
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Fingernail Comparator When an approximate indication of the surface roughness is sufficient, a fingernail comparator may be used. A small sheet of metal with a variety of machined areas and finishes is used as the surface roughness standard. A person’s fingernail is run across the standard at the specified roughness, perpendicular to the lay, and then across the part surface for comparison. If the standard “feels” rougher than the part, then the part is considered acceptable.
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Shape and Profile Measurement Shape and profile measurement is done using comparators and roundness testers.
Comparators Mechanical or bench comparators have a dial or digital indicator on a stand with a reference base. The indicator may be adjusted vertically with respect to the base to accommodate various part sizes. Using a standard, such as a gage block, the indicator is zeroed to a known dimension. The part to be inspected is then placed on the base, and the difference from the known dimension is read on the indicator gage. Cylindrical parts can be checked for runout or T.I.R. (total indicator reading) by placing the part on a v-block and rotating the part manually. Pneumatic comparators (commonly called air gages) are often used for tight tolerance measurements.
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Roundness Testers Roundness testers are used for measuring roundness, cylindricity, coaxiality, concentricity, straightness, parallelism, flatness and a number of other features on round and cylindrical parts. These testers utilize a rotating base and a vertical column with a probe extending from the column. The probe may be moved vertically and is held in contact with the part surface while the part is rotated on the support base or turntable. Data from the probe is processed using computer software to create the desired measurements and/or graphic outputs.
Schematic of a Roundness Tester
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Optical Tools Optical tools include such items as comparators, profile projectors, optical flats and microscopes.
Optical Comparators Optical comparators or profile projectors are devices for comparing a part to a form that represents the desired part contour or dimension. The relationship of the form with the part indicates acceptability. A beam of light is directed upon the part to be inspected, and the resulting shadow is magnified by a lens system, and projected upon a viewing screen by a mirror. The figure below shows a schematic of a simple optical comparator.
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Microscopes The term microscope refers to several types of instruments including the following:
C C C C C C C
Compound light microscope Dissection microscope or stereoscope Metallograph Confocal microscope Scanning electron microscope (SEM) Transmission electron microscope (TEM) Scanning probe microscope
Microscopes are used to analyze structures of specimens, determine chemical composition, and measure feature dimensions. Each type of microscope has specific advantages, as well as limitations.
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Optical Flats An optical flat is a highly polished transparent material such as glass - ground into approximately two to four inch diameter cylinders. These cylinders are 3/8 inch to 3/4 inch thick. They are used to measure the flatness of a surface using the principles associated with interferometry. See the diagram below: MONOCHROMATIC LIGHT F
MICROINCHES 34.8
E
D
C
B
OPTICAL FLAT
LIGHT DARK DARK
23.2
A
LIGHT DARK
11.6
LIGHT
AIR WEDGE 1 2 3 HALF - WAVE LENGTHS
PART PART
When the optical flat is placed over the workpiece, a thin sloping air space is created. Monochromatic light rays enter the optical flat and are reflected from the surface of the workpiece. The light rays are reflected from the surface of the workpiece. When the light rays are reflected, interference bands are visible.
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Optical Flats (Continued) The illustration below shows the bands as they might appear through an optical flat.
Flat Surface
Convex Surface
Concave Surface
Warped Surface
The above images may vary considerably based on the amount and type of out of flat condition.
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Digital Vision Systems Advances in computer hardware and digital image capture devices have resulted in tremendous growth in the use of digital vision systems for quality inspection applications. A basic digital vision system has the following components:
C C C C C
Test specimens (S) Reference standards Lighting system (L) Digital image capture devices (D) Computer hardware (C) C User interface, controls, monitor (M) C Networking, data storage, remote data transfer (N) C Analysis software C Sample control system, servo-control (V)
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Digital Vision Systems (Continued) The arrangement of digital vision components is illustrated in the figure below.
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Coordinate Measuring Machines (CMMs) A coordinate measuring machine (CMM) is used for dimensional measurements in three dimensions. The CMM has three basic directions of movement, the X, Y and Z axes. The Z axis is vertical, the X axis is horizontal left to right, and the Y axis is horizontal front to back. In some cases, the X and Y axes are reversed. Some machines also have a W axis, which is rotational. The base of the CMM is a surface plate. Workpieces are placed on the surface plate and a stylus is maneuvered to various contact points to send an electronic signal to a computer that is recording the measurements. A schematic of a CMM is shown below.
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Gage Maintenance and Storage The control of measuring and monitoring devices from ISO 9001 (2000), Section 7.6, is paraphrased below. The organization must identify the measurements to be made, and the measuring and monitoring devices required for product conformity to specified requirements. Measuring and monitoring devices must be used and controlled to ensure that measurement capability is consistent with measurement requirements. Where applicable, measuring and monitoring devices must be calibrated and adjusted prior to use; be safeguarded from adjustments that would invalidate the calibration; be protected from damage and deterioration during handling, maintenance and storage; have calibration results recorded; and have the validity of previous results reassessed if subsequently found to be out of calibration, with corrective action taken. Software used for measuring and monitoring specified requirements must be validated prior to use.
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Gage Maintenance and Storage (Cont’d) The appropriate organizational authority should ask the following questions:
C C C C C C C C C C C C C C
Are the appropriate measurements determined? Will the measurements provide adequate evidence? Are processes determined? Are devices calibrated at specified intervals? Are calibration actions recorded and maintained? Are measuring devices adjusted as necessary? Is the calibration status identified? Are devices safeguarded from invalid adjustments? Are measuring devices protected from damage? Are devices protected during handling? Are nonconforming measurements assessed? Are nonconforming measurements recorded? Is measurement software confirmed? Is the measurement software reconfirmed?
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Gage Maintenance and Storage (Cont’d) Some instruments require storage in a customized case or controlled environment when not in use. Even sturdy hand tools are susceptible to wear and damage. Hardened steel tools require a light film of oil to prevent rusting. Care must be taken in the application of oil since dust particles will cause buildup on the gage's functional surfaces. Tools should be examined frequently for wear on the measuring surfaces.
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VI. TESTING & MEASUREMENT DEFINITIONS
Testing and Measurement Definitions The following definitions are pertinent to understanding and communicating testing and measurement. Accuracy (of measurement)
An unbiased true value which is normally the difference between the average of several measurements and the true value.
Attribute gage
A gage that measures on a good/bad or go/no-go basis.
Bias in measurement
Bias occurs when the actual reading is adversely affected by misalignment, overpressure, the use of an improper starting point, etc.
Brittleness
The property of a metal that allows it to deform very little prior to fracture.
Charpy test
An impact test which measures the toughness of a material by measuring the resistance to fracture in the presence of a notch.
Compressive strength
The maximum amount of resistance to pressing or squeezing type stress before failure.
Creep
The resistance of a material to plastic deformation under a static load.
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Testing & Measurement Definitions (Cont’d) Critical stress
The stress below which the number of fatigue failures is dramatically reduced.
Deformation
The amount a material is stretched or compressed when force is applied.
Differential measurement
The use of a measuring device that transforms actual movement into a known value (a dial indicating gage).
Direct measurement
A standard or tool is applied to the part such that a direct reading can be made.
Discrimination
The ability to distinguish between the divisions on a scale.
Discrimination rule
According to AIAG (1995)3, measurement increments should be no greater than onetenth of the smaller of either the process variability or the specification tolerance.
Ductility
The property of a material that allows it to stretch prior to fracture.
Elastic region
The area of the stress-strain curve in which stress is proportional to strain according to Hooke's law.
Elastic limit
The point in the stress-strain curve in which the strain becomes plastic.
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Testing & Measurement Definitions (Cont’d) Elongation
The extension of material caused by the uniform strain of an external load prior to necking.
Fatigue
Material failure due to repeated strains.
Fatigue strength
The ability of a material to withstand dynamic stress.
Impact strength
A material’s resistance to shock due to toughness which is dependent on strength and ductility.
Malleability
The property that allows a material to be bent and shaped by rolling or hammering.
Measured surface
That surface of a measuring tool that is movable and with which the actual measurement is made.
Measurement deviation
The difference between a measurement and its stated value or intended level.
Measurement error
The difference between a measured value and a true value.
Measurement pressure
A positive, nonexcessive measurement tool force. The most important factor is that the pressure used on the work piece be the same as that used during calibration.
Measurement standard
A standard of measurement that is a recognized and accepted true value.
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Testing & Measurement Definitions (Cont’d) Measuring and test equipment
All devices used to measure, gage, test inspect, diagnose, or otherwise examine materials, supplies and equipment to determine compliance with technical requirements.
Mechanical properties
Properties such as tensile, impact, and compression that indicate how a material will behave when force is applied.
Metrology
The science and practice of measurement.
Parallax error
The error in measurement caused by a reading misalignment. An example is the act of viewing an indicator dial from an improper angle.
Percent elongation
A measure of ductility during a tensile test. The percent a material increases in gage length (after fracture).
Plastic deformation
Deformation of a permanent nature which occurs when a material has been stretched beyond the elastic limit.
Plasticity
The ability of a material to stretch or deform prior to failure.
Pressure
The action of a force per unit area applied to a substance.
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Testing & Measurement Definitions (Cont’d) Primary reference standard
An extremely accurate reference standard that is traceable to a NIST standard.
Quenching
Rapid cooling by water, air, oil, or brine in order to control microstructural changes in the material.
Reference surface
That surface of a measurement tool that is fixed.
Secondary reference standard
A standard that may be used to perform test equipment or working level calibration. They are of a lower level than a primary standard.
Shear strength
The ability of atoms to resist sliding in the crystal lattice.
Shear failure
Occurs when atoms slide past one another in the crystal lattice and cause failure.
Slip
A failure of a material when stress is applied as atoms slide past one another in the crystal lattice.
Slip plane
Weakly bonded planes in the crystal lattice that allow atoms to slide over one another.
Specification limits
Limits that define the conformance boundaries for a product or service.
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Testing & Measurement Definitions (Cont’d) Strain
Deformation of a material due to applied forces. It is the ratio of elongation to the original sample length in tensile testing.
Stress
The ability to withstand an amount of applied force. The amount of load per unit cross-section of force applied.
Stress-strain curve
A method of determining mechanical properties by plotting stress against strain. Values for the elastic limit, proportional limit, yield strength and failure point can be determined.
Tensile strength
Ability of a material to withstand being pulled apart.
Testing
A means of determining the capability of an item to meet specified requirements by subjecting the item to a set of physical, chemical, or environmental conditions.
Transfer tool
A tool or measuring instrument that has no reading scale. This device will make a part measurement and then transfer it to another scale for direct reading.
Variable gage
A gage that is capable of measuring the actual size of a part.
Viscosity
The property of a liquid to offer continuous resistance to flow.
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Testing & Measurement Definitions (Cont’d) Wear
The ability of a material to withstand contact stress and deterioration (scratching, abrasion, corrosion, pitting).
Working standards
Standards that are used to perform equipment calibration. These standards are of a lower (third) level and are usually calibrated to secondary standards.
Yield point
The limiting stress for elastic behavior found on the stress-strain curve.
Yield strength
A calculated point on the stress-strain curve when the yield point is not clearly defined. A 0.2% offset method is used to construct a line parallel to the elastic modulus line.
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VI. TESTING & MEASUREMENT DESTRUCTIVE TESTS
Destructive Testing Destructive testing includes tensile tests, impact tests, shear tests, compression tests, fatigue testing and flammability tests. Leak testing is also reviewed in this element although it can also be considered a nondestructive or functional test, as well.
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Tensile Test Tensile strength is the ability of a metal to withstand a pulling apart tension stress. The tensile test is performed by applying a uniaxial load to a test bar and gradually increasing the load until it breaks. The load is then measured against the elongation using an extensometer. The data may be analyzed using a stressstrain curve. T Y R
P E
0.0002 0.002
STRAIN (IN/IN)
In the diagram above, the elastic limit (E), the proportional limit (P), the highest stress value (T), and the rupture strength (R) are identified.
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Impact Test Impact strength is a material's ability to withstand shock. Tests such as Charpy and Izod use notched samples which are struck with a blow from a calibrated pendulum. The major difference between the two are the way the bar is anchored and the speed in which the pendulum strikes the bar. The Charpy holds the bar horizontally and strikes with a velocity of 17.5 ft/sec. The Izod holds the test bar vertically and has a velocity of 11.5 ft/sec.
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Shear Test Shear strength is the ability to resist a “sliding past” type of action when parallel but slightly off-axis forces are applied. Shear can be applied in either tension or compression.
An Illustration of a Shear Test
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Compression Test Compression is the result of forces pushing toward each other. The compression test is run much like the tensile test. The specimen is placed in a testing machine, a load is applied and the deformation is recorded. A compressive stress-strain curve can be drawn from the data.
A Typical Compression Test Curve
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Fatigue Test Fatigue strength is the ability of material to take repeated loading. There are several types of fatigue testing machines. In all of them, the number of cycles are counted until a failure occurs and the stress used to cause the failure is determined.
A Typical Fatigue Curve
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Flammability Tests The purpose of flammability testing is to determine the rates that items burn when exposed to a specified ignition source, under specified conditions. The resulting flammability ratings are used to accept or reject materials for given applications. Common applications of flammability tests include toys, building materials, textiles used for furniture, clothing, carpets and drapes, and fire safety systems. These tests are also used to determine burn rates where it is desirable to have a flame, such as candles, matches, and heating fuels such as natural gas and kerosene. Flammability tests are conducted at various temperatures, which include the intended use temperature such as ambient conditions. The relative humidity (R.H.) during the test must also be controlled and measured, since the R.H. affects the flame propagation rate. The air velocity must also be measured during testing and some methods require the test to be performed in still-air or draft-free conditions.
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Leak Testing Leak testing is concerned with the escape of liquids, vacuum, or gases from sealed components or systems. Leak testing may be destructive or nondestructive depending upon the purpose of the test. Leak testing saves costs by reducing the number of reworked products, warranty repairs and liability claims. The three most common reasons for performing a leak test are:
C To avoid material loss in chemical or energy areas C To avoid contamination or personnel hazards C To provide component reliability for critical parts
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VI. TESTING & MEASUREMENT DESTRUCTIVE TESTS
Non-Destructive Testing (NDT) NDT is a technique of testing material properties without impairing their future usefulness. Tests like the tensile test, bend test, creep test, voltage breakdown, acid etch, spectroscopic test and gas and liquid chromatography are categorized as destructive tests, since a portion of the material is destroyed during the test. In recent years, engineers and scientists have been successful in applying natural phenomena to nondestructive testing. The use of X-rays, light waves, magnetism and sound waves, are all important NDT techniques. Common among these methods are ultrasonics, radiography, fluoroscopy, microwave, magnetic particle, liquid penetrant, and eddy current. More recently, the development of the laser has led to a new method of NDT (holography).
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Choosing the Most Suitable NDT Method There are numerous material types, defects, applications, and needed product quality levels. Therefore, many factors must be evaluated before deciding upon a particular test method. Some of the important considerations are listed below: Part size Material composition Inspection rate Surface condition Reference standards Accessibility Inspector training Part usage Test recording
Part geometry Material condition Defect location Defect orientation Defect size Acceptance criteria Cost of equipment Safety Test specifications
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Basic NDT Techniques Listed in the table below are some of the most widely used NDT techniques. Technique
Description
Electromagnetic
The test object is magnetized. Magnetic particles are applied to the object surface. Surface or subsurface defects will disrupt the magnetic field and be indicated by the particles.
Image generation
X-rays are passed through a test object which cause some materials to fluoresce. An immediate image of defects is displayed on a screen.
Optical
A clean test surface is covered with a dye penetrant that permeates into surface cracks. A developer is then applied which displays any defects visually.
Radiation
X-rays are imposed on a test object to detect defect size and location.
Thermal
The measurement of temperature and heat-flow variations through a test object will indicate the presence of defects.
Ultrasonic
A sound frequency is introduced to match the part resonant frequency. Part thickness and defect location are determined.
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Nondestructive Testing Comparison Test Type
Application Advantages
Limitations
Eddy Current
Can check material thickness, conductivity, coating thickness and physical pr o p e r t ies. Adaptable to 100 % high speed applications where no probe contact is desired. The costs can be relatively low.
Only useful for conductive materials. Reliable standards and frequent calibration are required. Part thickness and penetration depth can pose problems. Results are normally comparative.
Liquid Penetrant
A simple accurate, inexpensive technique to locate surface defects. The penetrant/developer contrast makes visual inspection easy. Works on nonmetallic and nonmagnetic materials.
Does not work for porous materials. The process requires cleaning operations. Works on surface defects only. Not as fast as eddy current methods.
Magnetic Particle
Can detect surface and subsurface defects in ferromagnetic parts. Portable equipment may be used. This technique is economical.
Used for ferromagnetic parts only. Surfaces must be clean and dry. Magnetism may have to be two directional to find all discontinuities. Parts may require demagnetizing.
Microwave
Used for thickness measurement. Cannot detect subsurface defects in Can also monitor moisture and metals. chemical composition of both liquids and solids.
Ultrasonic
Can locate and determine the relative size and orientation of internal defects. Can measure thicknesses difficult to reach with mechanical methods. Inspection units can be portable.
Complex part geometries present difficulties. Requires skilled operators and good test standards. Coupling materials such as water, glycerine or petroleum jelly must be used.
Useful in detecting internal defects in metals. Some techniques provide a permanent record of defects. Provides continual product movement and rapid decisions.
Relatively high initial costs. Trained technicians are required. Not applicable to extremely thin products. The results may not be immediately known. Inherent safety risks.
Transmission Pulse echo or Resonance X-Ray Fluoroscopy Gamma Ray TVX
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Visual Inspection One of the most frequent inspection operations is the visual examination of products, parts and materials. The color, texture, and appearance of a product gives valuable information if inspected by an alert observer. Lighting and inspector comfort are important factors in visual inspection. In this examination, the human eye is frequently aided by magnifying lenses or other instrumentation. This technique is sometimes called scanning inspection.
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Ultrasonic Testing The application of high frequency vibration to the testing of materials is a widely used and important nondestructive testing method. Ultrasonic waves are generated in a transducer and transmitted through a material which may contain a defect. A portion of the waves will strike any defect present and be reflected or “echoed” back to a receiving unit, which converts them into a “spike” or “blip” on a screen. Refer to the figure below.
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Ultrasonic Testing (Continued) The three basic elements of an ultrasonic test system are:
C A transducer which transmits pulsed waves and then receives their echoes C A test object through which the high frequency waves are transmitted C An electronic system which converts the sound waves into a visual pattern Ultrasonic inspection has been widely used measurement of dimensional thickness. The ultrasonic testing technique is similar to sonar. Sonic energy is transmitted by waves containing alternate, regularly spaced compressions and refractions. Audible human sound is in the 20 to 20,000 Hertz range. For nondestructive testing purposes, the vibration range is from 200,000 to 25,000,000 Hertz. The three fundamental techniques of ultrasonic inspection are called pulse echo, through transmission and resonance.
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Pulse Echo The pulse echo technique utilizes a transducer to both generate and receive high frequency sound waves. The returning echo must travel the same path as the original pulse. The amount of returned energy depends upon the size and orientation of any defect obstruction.
Through Transmission This variation is similar to the pulse echo technique except that matched transducers are utilized. The signal is transmitted from a sending transducer through the part to a receiving transducer.
Resonance Any material has a natural resonant frequency which is proportional to its thickness. In resonance testing, a transducer produces a continuous signal. The frequency of the signal is varied until it exactly matches the resonant frequency of the test material. Resonance testing is frequently used for measuring thickness and detecting large laminar defects.
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Holographic Inspection Holography is a method of photography that involves three-dimensional instead of conventional twodimensional images. A laser beam of coherent light is split to create a hologram. One part of the beam illuminates the object being photographed, while the other is used as a reference beam. Instead of taking a photograph, only interference patterns are recorded. Convergence of the two beams creates a pattern of interference fringes which produces a hologram on film. Acoustical holography is a further adaptation of interference holography. This technique utilizes high frequency sound waves to create a three-dimensional real time image of the internal structure of a test piece.
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VI. TESTING & MEASUREMENT DESTRUCTIVE TESTS
Magnetic Particle Testing Magnetic particle inspection is a nondestructive method of detecting the presence of many types of defects or voids in ferromagnetic metals or alloys. This technique can be used to detect both surface and subsurface defects in any material capable of being magnetized. The first step in magnetic particle testing is to magnetize a part with a high amperage, low voltage electric current. Then fine steel particles are applied to the surface of the test part. These particles will align themselves with the magnetic field and concentrate at places where magnetic flux lines enter or leave the part. The test part is examined for concentrations of magnetic particles which indicate that discontinuities are present. See the figure below:
Flux Lines in a Defective Test Piece
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Magnetic Particle Testing (Continued) There are three common methods in which magnetic lines of force can be introduced into a part. The selected method will depend upon the configuration of the part and the orientation of the defects of interest. The three methods are: 1)
Longitudinal Inside a Coil
2)
Circular Magnetization
3)
Circular Magnetization (Internal Conductor)
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Types of Current Alternating current (AC) magnetizes the surface layer of the material more strongly than the interior region of the part and is used to discover surface discontinuities. Direct current (DC) gives a more uniform field intensity over the entire section. DC provides greater sensitivity for the location of subsurface defects. The rapid shifting of both currents, using some specialized equipment, can permit the detection of most internal and external defects in one operation.
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Types of Particles There are two general categories of magnetic particles (wet or dry), which depend upon the carrying agent used. Either water or oil may be used as a vehicle in the wet method. In the dry method, the particles are typically sprinkled or dusted on. In either case, the particles are made of carefully selected magnetic materials of proper size, shape, and retentivity. They are often dyed to give good contrast with the inspected surface and may be fluorescent for viewing under black light. Wet particles are best suited for the detection of fine surface cracks. When using wet particles the surface of the test piece should be free from oil, grease, sand, loose rust, or loose scale. Degreasing is preferred. Dry particles are more sensitive in detecting subsurface defects and are usually used with portable types of equipment. Reclaiming and reusing dry particles is not recommended. Magnetic particle testing is limited to products made of iron, steel, nickel and cobalt. In some cases, the parts require demagnetization before subsequent operations are performed.
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VI. TESTING & MEASUREMENT DESTRUCTIVE TESTS
Liquid Penetrant Testing Liquid penetrant inspection is a rapid method for detecting open surface defects in both ferrous and nonferrous materials. It may be effectively used on nonporous metallic and nonmetallic materials. Tests have shown that penetrants can enter material cracks as small as 3,000 angstroms. The size of dye molecules used in fluorescent penetrant inspection are so small that there may be no surface cracks too small for modern penetrants to detect. The factors that contribute to the success of liquid penetrant inspection are the ability of a penetrant to carry a dye into a surface defect and the ability of a developer to contrast that defect by capillary attraction. False positive results may sometimes confuse an inspector. Irregular surfaces or insufficient penetrant removal may indicate nonexistent flaws.
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Penetrant Advantages and Limitations Penetrants are much faster and more economical than ultrasonic methods for finding surface discontinuities. Penetrants are not limited by part geometry and are cheaper for mass production applications. Penetrants are more flexible than eddy current techniques and will work on nonmagnetic materials. Penetrants are not successful in locating internal defects. Magnetic particle inspection is superior to penetrants for ferromagnetic materials with open surface defects. Penetrants are not as fast on bars and tubing as eddy current testing.
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Eddy Current Testing Eddy currents involve the directional flow of electrons under the influence of an electromagnetic field. Nondestructive testing applications require the interaction of eddy currents with a test object. This is achieved by:
C Measuring the flow of eddy currents in a material having virtually identical conductivity characteristics as the test piece C Comparing the eddy current flow in the test piece (which may have defects) with that of the standard Eddy currents are permitted to flow in a test object by passing an alternating current through a coil placed near the surface of the test object. Eddy currents will be induced to flow in any part that is an electrical conductor.
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Eddy Current Testing (Continued) The induced flow of electrons produces a secondary electromagnetic field which opposes the primary field produced by the probe coil. This resultant field can be interpreted by electronic instrumentation. See the following diagram:
Defect size, and location cannot be read directly during eddy current testing. This test requires a comparative analysis. Therefore, test conditions must be tightly controlled and reject standards must be developed.
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Eddy Current Advantages/Limitations Advantages include 100 % high speed inspection, no probe contact, portability of equipment and the use of automatic part rejection. Thin film coating and thin wall tubing products are excellent applications. The costs are comparatively low and relatively unskilled operators can be used. Limitations include a maximum depth of penetration (approximately 1/2 inch), the need for reliable standards and the need for frequent calibration. Part cleanliness and test equipment sensitivity are important considerations. The service technicians should be skilled and qualified. Test parts must be able to conduct electricity.
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Radiography Many internal characteristics of materials can be photographed and inspected by the radiographic process. Radiography is based on the fact that gamma and X-rays will pass through materials at different levels and rates. Therefore, either X-rays or gamma rays can be directed through a test object onto a photographic film and the internal characteristics of the part can be reproduced and analyzed. Because of their ability to penetrate materials and disclose subsurface discontinuities, X-rays and gamma rays have been applied to the internal inspection of forgings, castings, welds, etc. for both metallic and nonmetallic products.
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Radiography (Continued) The major steps associated with radiography inspection are:
C C C C C
Making the test piece setup Exposing the test piece to X-rays Processing the film containing the part image Analyzing the radiographic film Making a decision based upon the results
For proper X-ray examination, adequate standards must be established for evaluating the results. A radiograph can show voids, porosity, inclusions, and cracks if they lie in the proper plane and are sufficiently large. However, radiographic defect images are meaningless, unless good comparison standards are used. A standard, acceptable for one application, may be inadequate for another.
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How X-Rays are Produced Typically, X-rays are produced when high speed electrons strike a tungsten target in a vacuum tube. These electrons can then be propelled against a test target producing X-rays.
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Related X-Ray Techniques There have been new developments in the radiographic field of nondestructive testing. Several common recent applications include:
C Fluoroscopy C Gamma Radiography C Televised X-Ray (TVX) All radiographic techniques require trained technicians. In some cases, the results are not immediately known. There are inherent human risks involved in the use of all radiographic techniques.
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Hardness Testing A large number of field and laboratory tests have proven to be useful for material hardness evaluation. Listed below are the most commonly used techniques. Type Brinell File Knoop Mohs
Technique Area of Penetration Appearance of Scratch Area of Penetration Presence of Scratch
Rockwell
Depth of Penetration
Rockwell Superficial
Depth of Penetration
Shore Sonodur Vickers
Height of Bounce Vibration Frequency Area of Penetration
Penetrator 10 mm Ball
Loading 500-3000 kg.
Scale HBW, HBS, BHN
File
Manual
None
25-3600 g
HK
Manual
Units Mohs
60-100150 kg.
Rc
15-3045 kg.
15N, 30T, 45X, etc.
Gravity
Units Shore
N.A.
BHN
25 g to 120 kg
HV, DPH
Pyramidal Diamond 10 Stones Diamond Point or 1/16-1/8 Ball Diamond Point or 1/16-1/8 Ball 40 Grain Weight Vibrating Rod Pyramidal Diamond
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Brinell Hardness Testing The Brinell hardness testing method is primarily used for bulk hardness of heavy sections of softer steels and metals. Compared to other hardness tests the imprint left by the Brinell test is relatively large. This type of deformation is more conducive to testing porous materials such as castings and forgings. Extremely thin samples cannot be tested using this method. Since a large force would be required to make a measurable dent on a very hard surface, the Brinell method generally is restricted to softer metals.
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Rockwell Hardness Testing The most popular and widely used of all the hardness testers is the Rockwell tester. This type of tester uses two loads to perform the actual hardness test. Surface imperfections in samples are eliminated by the use of a preliminary load. This “minor load” is applied before the actual hardness is taken. This makes the readings very accurate when the second load is applied. Rockwell machines may be manual or automatic. The Rockwell hardness value is based on the depth of penetration with the value automatically calculated and directly read off the machine scale. At least three readings should be taken and averaged. The Rockwell method has two key advantages:
C Because of the minor load, surface imperfections have little effect C Because the hardness value can be read directly, error is minimized
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Shore Scleroscope Hardness Testing The Shore Scleroscope is a dynamic hardness test that uses a material’s absorption factor and measures the elastic resistance to penetration. It is unlike the other test methods in that there is no penetration. In the test, a hammer is dropped and the bounce is determined to be directly proportional to the hardness of the material. Some machines are available with a scale follower which records the first bounce on a dial. The advantages of the Shore method are:
C There is negligible indention on the sample surface C A variety of materials and shapes can be tested C The equipment is very portable The major disadvantage to Shore testing is that the sample must be smooth, flat, clean, and horizontal.
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Vickers Hardness Testing The Vickers hardness testing differs from Brinell in the following ways:
C A square-based pyramid is used (not a round ball) C The load or force is less (1 to 120 kg) C The units are HV (previously called DPH) The surface should be as smooth, flat and clean as possible with the test piece placed horizontally on the anvil before testing. The angle of the diamond penetrator should be approximately 136 degrees. The Vickers test does not damage the sample as severely as the Brinell test because of the lighter load. The Vickers test is very sensitive and is considered a surface test. Small areas, very thin samples and hard materials may be tested using this method.
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Knoop Hardness Testing The Knoop is a microhardness testing method used for testing surface hardness of very small or thin samples. A sharp elongated diamond is used as the penetrator with a 7-1 ratio of major to minor diagonals. Surfaces must be very fine ground, flat, and square to the axis of the load. The sample must be very clean as even small dust particles can interfere. Loads may go as low as 25 grams. The Knoop hardness testing method is used for extremely thin materials like coatings, films, and foils. It is basically used for research testing in the research lab.
Sonodur Hardness Testing Method The Sonodur is one of the newer test methods and uses the natural resonant frequency of metal as a basis of measurement. Hardness of a material affects this frequency and therefore can be measured. This method is considered to be very accurate.
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Mohs Hardness Testing The scratch test was probably the first hardness testing method developed. It is very crude and fast and is based on the hardness of ten minerals. In 1824, an Austrian mineralogist by the name of F. Mohs chose ten minerals of varying hardness and developed a comparison scale. The softest mineral on the MOHS scale is talc and the hardest is diamond.
File Hardness Testing File hardness is a version of the scratch testing method where a metal sample is scraped with the edge of a file. If a scratch results, the material is “not file hard” but if there is no mark the material is “file hard.” This is a very easy way for inspectors to determine if the material has been hardness treated.
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Functionality Testing Functionality testing involves a large number of common physical and mechanical applications. Torque and surface tension measurement are discussed in the Primer. Various tension and compression tests are also considered to be functional tests except that loading is not applied until part failure. These tests are usually conducted to confirm that a customer specification or requirement is met. In fact, torque may also be measured to a predetermined value, or to failure of a component.
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Torque Measurement Torque is measured using a torque wrench. There are many types of torque wrenches. Two types most commonly used are the flexible beam type, and the rigid frame type. Torque wrenches may be preset to the desired torque. The wrench will either make a distinct “clicking” sound or “slip” when the desired torque is achieved. Torque measurement is required when the product is held together by nuts and bolts. The torque applied to a fastener is an indication of the tensile preload in the bolt. The wrong torque can result in the assembly failing due to a number of problems. Parts may not be assembled securely enough for the unit to function properly or threads maybe stripped because torque is too high, causing the unit to fail. Torque is described as a force producing rotation about an axis.
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VI. TESTING & MEASUREMENT DESTRUCTIVE TESTS
Torque Measurement (Continued) The formula for torque is: Torque = Force x Distance Example: A force of 2 pounds applied at a distance of 3 feet equals: Torque = Force x Distance Torque = 2 lbf x 3 ft Torque = 6 ft-lbf
Torque may be applied in either the clockwise (CW) direction or counterclockwise direction (CCW). Tightening right-hand threaded fasteners is done by applying a clockwise torque. Loosening of the same fastener is done by applying a counterclockwise torque. When tightening, always follow the manufacturer’s specifications for recommended torque values.
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VI. TESTING & MEASUREMENT DESTRUCTIVE TESTS
Torque Wrench Precautions C Handle torque wrenches carefully C Hold the center of the handle C Apply the force slowly and smoothly C Hold the wrench steady for a short time after reaching the desired torque C Use torque wrenches within 80 percent of their stated range C Beware of false applications of torque, such as a long bolt bottoming out C Keep torque wrenches calibrated against a known standard C If it is necessary to extend a torque wrench, ensure that compensation is made for the change in distance C Ensure that the extension is in line to avoid cosine error
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VI. TESTING & MEASUREMENT NONDESTRUCTIVE TESTS
Tensiometers Tensiometers measure the surface tension of liquids. The surface tension is measured either as a force divided by a length, expressed as mN/m, or a force divided by an area (which is equivalent to a pressure), expressed in bar, millibar (mbar), centibar (cbar), or cm of water pressure. Tensiometers are also used to measure the pressure or matric potential of the soil. This is the force with which water is held in the soil. If the tension of a soil is high or the pressure potential low, plants use more energy to remove water from the soil. Under these conditions, plants may grow at a slower rate. Soil moisture control is very important in many areas of the world.
© QUALITY COUNCIL OF INDIANA CQE 2006
VI-64 (735)
VI. TESTING & MEASUREMENT METROLOGY
Metrology Metrology is the science of measurement. The word metrology derives from two Greek words: matron (meaning measure) and logos (meaning logic). Metrology encompasses the following key elements:
C The establishment of measurement standards that are both internationally accepted and definable C The use of measuring equipment to correlate the extent that product and process data conforms to specification. C The regular calibration of measuring equipment, traceable to established international standards
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VI. TESTING & MEASUREMENT METROLOGY
Units of Measurement There are three major international systems of measurement: the English, the Metric, and the System International D`unites (or SI). The U.S. has effectively retained the English System as a remnant of British colonial influence. The metric and SI systems are decimal-based, the units and their multiples are related to each other by factors of 10. The SI system was established in 1968 and the U.S. officially adopted it in 1975. The transition is occurring very slowly. The final authority for standards rests with the internationally based system of units. Fundamental, supplementary, and derived SI units.
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VI. TESTING & MEASUREMENT METROLOGY
SI System Units Listed below is a summary table of the fundamental and supplement SI units: Quantity Measured
Unit
Symbol
Fundamental Units amount of substance length mass time electric current temperature luminous intensity
mole meter kilogram second ampere kelvin candela
mol m kg s A K cd
Supplementary Units plane angle solid angle
radian steradian
rad sr
The Primer lists a large number of derived SI units.
© QUALITY COUNCIL OF INDIANA CQE 2006
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VI. TESTING & MEASUREMENT METROLOGY
Types of Measurements There are three common types of measurements: direct, indirect, and comparative.
Direct Measurement The direct type of measurement is also termed an absolute measurement. A direct measurement is made via using an instrument (a steel ruler) to determine the length of a steel rod. A measuring instrument is applied to an unknown and a measurement value is read from a scale.
Indirect Measurements Some measurements are made indirectly. That is, the variable of interest is not the one that is actually measured. Angle measurements are often made indirectly by using a sine plate or sine bar.
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VI. TESTING & MEASUREMENT METROLOGY
Types of Measurements (Continued) Comparative (Transfer) Measurements A comparative measurement is made when a gage block of a specified height is compared to a part. Comparative measurements can often obtain great accuracy. The three most commonly used comparative gages are mechanical, pneumatic, and electronic.
Comparative (Differential) Measurement Differential gaging occurs where two sensing devices, in simultaneous contact with the part surface, mutually reference their positions. The measured dimension is the change in position of the sensing devices.
Other Measurements In laboratory situations, zero difference, substitution, ratio, and ratio transfer measurements are used. These techniques are outside the scope of the CQE Exam.
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VI. TESTING & MEASUREMENT METROLOGY
10:1 Rule AIAG (1995) states that measurement increments should be no greater than one-tenth of the smaller of either the process variability or the specification. An instrument must be capable of dividing the process variability or tolerance into ten parts.
Uncertainty The calculation of uncertainty requires a detailed budget which breaks down the variance of measurement error into consistent components, each of which can be separately estimated. The detailed model becomes something like: 2 σM = σE2
instrument
+ σE2
fixture
+ σE2
environment
+ σE2
calibration
+ σE2
sample
+ σE2
analysis
+ξ
Historically, a measurement term called test accuracy ratio (TAR) has been used. TAR is calculated as the ratio of the tolerance of the unit under test divided by the tolerance of the reference standard. In the past, a TAR of 10:1 was considered acceptable. Today, a TAR of 4:1 or 3:1 is much more common.
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VI. TESTING & MEASUREMENT METROLOGY
Unnecessary Accuracy In the real world, unnecessary accuracy is expensive. The two most common examples of loss result from unnecessary tight design tolerances and the use of measuring instruments that are too discriminating. Obviously, a gage with 0.0001" graduations should not be used for a + _ 0.250" tolerance. With the advent of modern electronics and computer technology is not uncommon to obtain a resistor with a Cpk of 40. To be able to measure the variation in the performance of the resistor to one-tenth the process variation could cost a supplier 100,000 times the original cost of the resistor. The current philosophy is to select the most economic means of measurement.
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VI-68 (742)
VI. TESTING & MEASUREMENT METROLOGY
The 10:1 Calibration Rule In some cases, it is possible to calibrate an instrument with a standard that has 10 times more accuracy. These cases are few and far between. ANSI/NCSL Z540-1-1994 states that the accuracy, stability, range and resolution of measurement standards should not exceed 25 % of acceptable tolerance. The advent of true measurement uncertainty and more accurate measuring instruments makes even this ratio hard to maintain.
© QUALITY COUNCIL OF INDIANA CQE 2006
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VI. TESTING & MEASUREMENT METROLOGY
The 10:1 Measurement Rule For heavens sake on an ASQ exam, use the 10: rule. However, the origin of this 10 % “rule of thumb” appears to date back to MIL-STD-120 (1950), which was canceled in 1996. This standard stated that the accuracy of the measuring instrument should be less than 20 % of the tolerance and that instruments with an accuracy of 10 % of the tolerance should be used if available. The only current basis for the 10:1 measurement rule lies with the AIAG MSA (1995). This manual states that a measuring system with less than a 10 % error in the specification spread is acceptable. However, the standard goes on to state that 10 % to 30 % R&R error may be acceptable based upon the importance of the application, cost of the gage, and cost of repairs, etc.
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VI. TESTING & MEASUREMENT METROLOGY
Calibration Calibration is the comparison of a measurement standard or instrument of known accuracy with another standard or instrument to detect, correlate, report or eliminate by adjustment, any variation in the accuracy of the item being compared. The elimination of measurement error is the primary goal of calibration systems.
Calibration Definitions Calibration Control
A documented system for assuring that measuring and test equipment devices and measurement standards are calibrated at appropriate intervals.
Calibration interval
The period of time between calibrations. Intervals can vary depending upon their stability, purpose and degree of usage.
Calibration recall
A system for indicating in advance when measuring and test equipment is next due to be calibrated.
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VI. TESTING & MEASUREMENT METROLOGY
Calibration Definitions (Continued) Certification
Approval given for the use of newly acquired or modified measuring and test equipment devices following a verification and calibration examination.
Standard Interim
A standard used until a permanent standard is established.
Standard Reference
An instrument or device of the high order of accuracy used in a calibration system as a primary reference standard traceable to NIST.
Standard Transfer
An instrument or device in a calibration system used to transfer measurements from the reference standard to a working standard.
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VI. TESTING & MEASUREMENT METROLOGY
Calibration Interval It is generally accepted that the interval of calibration of measuring equipment be based on stability, purpose and degree of usage. Intervals should be shortened if previous calibration records and equipment usage indicate this need. The interval can be lengthened if the results of prior calibrations show that accuracy will not be sacrificed. Measuring and test equipment should be traceable to records that indicate the date of the last calibration, by whom it was calibrated, and when the next calibration is due. Coding is frequently used.
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VI. TESTING & MEASUREMENT METROLOGY
Calibration Standards Any system of measurement must be based on fundamental units that are virtually unchangeable. In all industrialized countries, there exists an equivalent to the United States National Institute of Standards and Technology whose functions include the construction and maintenance of “primary reference standards.” These standards consist of copies of the international kilogram plus measuring systems which are responsive to the definitions of the fundamental units and to the derived units of the SI table.
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VI. TESTING & MEASUREMENT METROLOGY
Calibration Standards (Continued) Linear standards are easy to define and describe if they are divided into functional levels. There are five levels in which linear standards are usually described. Working Level
This level includes gages used at the work center.
Calibration Standards
These are standards to which working level standards are calibrated.
Functional Standards
This level of standards is used only in the metrology laboratory of the company for measuring precision work and calibrating other standards.
Reference Standards
These standards are certified directly to the NIST and are used in lieu of national standards.
This is the final authority of measurement National & International to which all standards are traceable. Standards
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VI. TESTING & MEASUREMENT METROLOGY
Calibration Standards (Continued) Since the continuous use of national standards is neither feasible nor possible, other standards are developed for various levels of functional utilization. National standards are taken as the central authority for measurement accuracy, and all levels of working standards are traceable to this “grand” standard. The downward direction of this traceability is shown as follows: 1. National Institute of Standards and Technology 2. Standards Laboratory 3. Metrology Laboratory 4. Quality Control System (Inspection Department) 5. Work Center
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VI. TESTING & MEASUREMENT METROLOGY
Calibration Functional Responsibilities Listed below are some of the responsibilities normally assigned to calibration personnel: 1. Maintain a record system to assure the initial and periodic calibration of all measuring and test equipment serviced both internally and externally.
2. Assure that the calibration program complies with the established practices and standards. 3. Ensure the traceability of all performed calibrations to known standards. 4. Perform measurements or calibrations, as specified by the company, utilizing known standards. 5. Determine at the time of calibration that the equipment is free of foreign matter that could compromise the calibration. 6. Perform necessary calibrations or functional tests on newly acquired or relocated measurement equipment.
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VI. TESTING & MEASUREMENT METROLOGY
Calibration Functional Responsibilities (Continued) 7. Identify equipment with a proper calibration status. 8. Suspend measuring and test equipment from use when conditions warrant. 9. Obtain corrective action from the responsible organization for any conditions found to be detrimental to the calibration program and system. 10. When requested or when conditions warrant provide personnel for operation of gages, measuring, and test devices for verification of their accuracy. 11. Perform gage studies to determine the suitability of measuring instrumentation for the measurement system. The calibration of measuring instruments is necessary to maintain accuracy, but does not necessarily increase precision. Precision most generally stays constant over the working range of the instrument.
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VI-74 (752)
VI. TESTING & MEASUREMENT MEASUREMENT SYSTEM ANALYSIS
Measurement System Analysis The following are summaries of what must be accomplished to meet measurement system requirements.
C Measuring equipment (devices) - All measuring equipment (company or employee owned) must be identified, controlled, and calibrated. Records of this action must be kept. C Confirmation system - The system by which the measuring equipment is evaluated to meet the required sensitivity, accuracy, and reliability must be defined in written procedures. C Periodic audit and review - The calibration system must be evaluated on a periodic basis by internal audits and by management reviews. C Planning - The actions involved with the entire calibration system must be planned. This planning must consider management system analysis. C Uncertainty of measurement Generally the determination of the uncertainty of measurement involves gage repeatability and reproducibility as well as other statistical methods.
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VI. TESTING & MEASUREMENT MEASUREMENT SYSTEM ANALYSIS
Measurement System Analysis (Cont’d) C Environmental conditions - Gages, measuring equipment, and test equipment will be used, calibrated, and stored (when not in use) in conditions that ensure the stability of the equipment. Laboratories must also control dust, temperature, noise, lighting, and humidity. C Records - Records must be kept on the operations that are used to calibrate measuring and test equipment. The retention time for these records must be specified. A gage status record is required. C Nonconforming measuring equipment - Suitable procedures must be in place to assure that nonconforming measuring equipment is not used. C Confirmation labeling - A labeling system must be in place that shows the unique identification of each measuring device and its status. C Intervals of confirmation - The frequency that each measuring device is recalibrated must be established and documented.
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VI. TESTING & MEASUREMENT MEASUREMENT SYSTEM ANALYSIS
Measurement System Analysis (Cont’d) C Sealing for integrity - Where adjustments may be made that may logically go undetected, sealing of the adjusting devices is required. C Use of outside products and services - Procedures must define controls that will be followed when any outside calibration source or service is used. C Traceability - Calibrations must be traceable to national standards. If no national standard is available, the method of establishing and maintaining the standard must be documented. C Storage and handling - Measuring equipment, when in use, will be handled according to established procedures and in accordance with operator training. When the measuring equipment is not in use, it will be in storage as prescribed by procedures to ensure unwanted use. C Personnel - Documented procedures are required for the qualifications and training of personnel that make measurement or test determinations.
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VI-75 (755)
VI. TESTING & MEASUREMENT MEASUREMENT SYSTEM ANALYSIS
Measurement Error The error of a measuring instrument is the indication of a measuring instrument minus the true value.
F2 ERROR
= F2 MEASUREMENT - F2 TRUE
or F2 MEASUREMENT = F2 TRUE + F2 ERROR The precision of measurement can best be improved through the correction of the causes of variation in the measurement process. However, it is frequently desirable to estimate the confidence interval for the mean of measurements which includes the measurement error variation. The confidence interval for the mean of these measurements is reduced by obtaining multiple readings according to the central limit theorem using the following relationship. σ MEASUREMENT =
σ READINGS n
The formula states that halving the error of measurement requires quadrupling the number of measurements.
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VI. TESTING & MEASUREMENT MEASUREMENT SYSTEM ANALYSIS
Measurement Error (Continued) There are many reasons that a measuring instrument may yield erroneous variation, including the following categories:
C Operator Variation C Operator to Operator Variation C Equipment Variation C Material Variation C Procedural Variation C Software Variation C Laboratory to Laboratory Variation
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VI-77 (757)
VI. TESTING & MEASUREMENT MEASUREMENT SYSTEM ANALYSIS
R&R Terms AIAG MSA (1995) defines five sources of measurement variation that can be determined by gage R&R studies. Reproducibility - The “reliability” of the gage system or similar gage systems to reproduce measurements. Repeatability - The variation in measurements obtained with one instrument, by the same operator, measuring the same characteristic on the same part at or near the same time (virtually the same as precision). Bias - The difference between the observed average of measurements and a reference value. Linearity - The difference in bias (offset) values throughout the expected operating ranges of a gage. Stability - Is the drift or change in bias obtained with a measurement system on the same measurement characteristic over an extended time period. The calibration of measuring instruments is necessary to maintain accuracy (lack of bias), but does not necessarily increase precision (repeatability).
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VI. TESTING & MEASUREMENT MEASUREMENT SYSTEM ANALYSIS
Parameters that Change Slowly Bias or Offset The systematic difference between the measurement results from two different processes attempting to perform the same measurement.
Accuracy Accuracy is the lack of bias between the user’s current measurement process and the same process using an accepted standard as a reference.
Drift or Stability Drift is a change in bias, which means the bias isn’t really constant, just changing on a slower time scale than the measurement.
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VI. TESTING & MEASUREMENT MEASUREMENT SYSTEM ANALYSIS
Parameters that Change Quickly Precision or Noise Precision describes how close in value successive measurement results fall when attempting to repeat the same measurement. Precision is usually visualized as varying rapidly so that successive measurements will capture all aspects of the distribution.
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VI. TESTING & MEASUREMENT MEASUREMENT SYSTEM ANALYSIS
Other Measurement Parameters Repeatability Repeatability is a measure of the ability of a measurement process to get the same answer when has an attempt is made to keep all factors constant, or at least as stable as possible.
Reproducibility Reproducibility is the measure of the ability of a measurement process to get the same answer under conditions of all relevant factors varying normally.
Linearity Linearity is a description of measurement bias indicating how the value of the bias varies over the entire capability range of a measurement system.
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VI. TESTING & MEASUREMENT MEASUREMENT SYSTEM ANALYSIS
Other Measurement Parameters (Cont’d) Sensitivity Sensitivity is a measure of the smallest value of the measured parameter that can be sensed by a measurement system.
Selectivity Selectivity is a measure of the ability of a measurement system to distinguish between and display the difference in two measured results when their measurands actually have two different values.
Resolution Resolution is a measure of the smallest change in the measurand that can be represented by the display mechanism of the measurement system.
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VI. TESTING & MEASUREMENT MEASUREMENT SYSTEM ANALYSIS
Repeatability and Reproducibility There are three widely used methods to quantify measurement error: the range method, the average and range method and the ANOVA method. A brief description of each follows:
Range Method The range method is a simple way to quantify the combined repeatability and reproducibility of a measurement system.
Average and Range Method The average and range method computes the total measurement system variability, and allows the total measurement system variability to be separated into repeatability, reproducibility, and part variation.
Analysis of Variance Method ANOVA is the most accurate method for quantifying repeatability and reproducibility and allows the variability of the interaction between the appraisers and the parts to be determined.
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VI. TESTING & MEASUREMENT MEASUREMENT SYSTEM ANALYSIS
Average and Range Method The average range method partitions variation into repeatability, reproducibility, and process variation. The result of this analysis will:
C Determine repeatability by examining the variation between the individual technicians and within their measurement readings C Determine reproducibility by examining the variation between the average of the individual technicians for all parts measured C Establish process variation by checking the variation between part averages that are averaged among the technicians
VI-81 (764)
© QUALITY COUNCIL OF INDIANA CQE 2006
VI. TESTING & MEASUREMENT MEASUREMENT SYSTEM ANALYSIS
Average and Range Method (Continued) Note that the R&R determination described in this following example is referred to as the “short method.”
Technician
A
Part
1 2 3 4 5
Readings 1st Set
2nd Set
2.0 2.0 1.5 3.0 2.0
1.0 3.0 1.0 3.0 1.5
RA = B
1 2 3 4 5
1.5 2.5 2.0 2.0 1.5
1.5 2.5 1.5 2.5 0.5
RB =
C
1 2 3 4 5
1.0 1.5 2.0 2.5 1.5
1.0 2.5 1.0 3.0 0.5
RC = Grand Ranges and Averages
Within Part R1 1.0 1.0 0.5 0.0 0.5
X1
Within Tech R2
Between Tech
X2
1.5 2.5 1.25 3.0 1.75
1.75
2.0
1.5 2.5 1.75 2.25 1.0
1.50
1.8
1.0 2.0 1.5 2.75 1.0
1.75
1.65
0.567
1.817
1.67
1.817
R1
X1
R2
X2
R3
0.6 0.0 0.0 0.5 0.5 1.0 0.4 0.0 1.0 1.0 0.5 1.0 0.7
R&R Data for Average and Range Method
0.35
R3
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© QUALITY COUNCIL OF INDIANA CQE 2006
VI. TESTING & MEASUREMENT MEASUREMENT SYSTEM ANALYSIS
Average and Range Method (Continued) To proceed further, one must determine several standard deviations using the range formula: σˆ =
R d2
Using 1/d2 table values the calculation for repeatability is:
( )
⎛ 1⎞ σ Repeat = ⎜ ⎟ R 1 = (0.885)(0.567) = 0.502 ⎝ d2 ⎠
Where 1/d2 is based on K = 15 samples and n = 2. From Table 6.40, the ∞ column is used for K and 1/d2 equals 0.885. R1 is the grand average range within parts. The calculation for reproducibility is: ⎛ 1⎞ σ Repro = ⎜ ⎟ ( R 3 ) = (0.524)(0.35) = 0.183 ⎝ d2 ⎠
Where 1/d2 is based on one sample, K = 1, and n = 3. From Table 6.40, 1/d2 equals 0.524. R3 is the range between the average of all measurements taken by each technician.
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VI. TESTING & MEASUREMENT MEASUREMENT SYSTEM ANALYSIS
Average and Range Method (Continued) The total measurement standard deviation is determined by the additive law of variances according to the following formula: σ Meas =
( σ Repeat )
σ Meas =
( 0.502 )
The production determined by:
2
process
2
+ ( σ Repro )
2
+ ( 0.183 ) = 0.534 2
standard
deviation
is
⎛ 1⎞ σ Process = ⎜ ⎟ ( R 2 ) = (0.420)(1.67) = 0.701 ⎝ d2 ⎠
Where 1/d2 is based on three samples, K = 3, and a sample size n = 5. From Table 6.40, 1/d2 equals 0.420. R 2 equals the average range between technicians.
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VI. TESTING & MEASUREMENT MEASUREMENT SYSTEM ANALYSIS
Average and Range Method (Continued) The total observed standard deviation in the example can also be determined by the additive law of variances according to the following formula: σ Observed =
( σ Proc )
2
σ Observed =
( 0.701)
+ ( 0.534 ) = 0.881
2
+ ( σ Meas )
2
2
In this example, the measurement error constitutes a substantial portion of total observed variation (about 37%). The AIAG (2002) method of calculating the percentage of tolerance consumed by the measuring system yields a value of 49% as shown in the Primer.
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VI. TESTING & MEASUREMENT MEASUREMENT SYSTEM ANALYSIS
Analysis of Variance Method The example in the Primer is for five parts, three technicians and two replications. ANOVA TABLE " = 0.05 SS
DF
MS
Fcal
F(")
Var
Adj Var
%
Technician
0.6167
2
0.3083
1.28
3.68
0.0111
0.0111
2.34
Part No.
9.867
4
2.467
10.21
3.06
0.2225
0.2225
46.81
Interaction
1.633
8
0.2041
0.84
2.64
-0.019
0
0
Error
3.625
15
0.2417
0.2417
50.85
Total DF
29
Source
SIGe = 0.4916
Totals
0.4753
100
SIGtot = 0.7368
For this example, repeatability is the error variance and contributes 50.85% of the total variation in the data. Reproducibility is the variation among technicians which contributes 2.34% of the variation in the data. Process variation accounts for 46.81% of the total variation in the data. Hypothesis tests based on the F distribution are used to determine if there are differences between technicians or between processes.
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VI-87 (769)
VI. TESTING & MEASUREMENT MEASUREMENT SYSTEM ANALYSIS
Control Chart Methods In addition to the R&R methods that have been previously discussed, a number of graphical tools (such as control charts) have been useful in screening measurement data for special causes of variation. Some authorities maintain that these graphical presentations should precede any other form of statistical analysis. The average and range data, presented earlier, will be plotted on both unstacked and stacked control charts. the resulting average chart provides an indication of the “usability” of the measurement system. 3
UCL = 2.883
2.5 2
1.817
1.5 1
LCL = 0.751
0.5
STACKED
UNSTACKED
0 TECH A
TECH B
TECH C
PARTS
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VI. TESTING & MEASUREMENT MEASUREMENT SYSTEM ANALYSIS
Control Chart Methods (Continued) By traditional control chart analysis, the average chart looks pretty good. There’s only one “special” event for technician A. However, the area within the control limits represents the measurement sensitivity. Since the group of parts being measured represents the part variation, approximately one half (or more) of the averages should fall outside the control limits. In this case, the data does not show this pattern. This indicates that either the measurement system lacks effective resolution or the samples do not represent the expected process variation. If the samples do represent the anticipated process variation, corrective action must be taken on the measurement system.
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VI. TESTING & MEASUREMENT MEASUREMENT SYSTEM ANALYSIS
Control Chart Methods (Continued) The range chart is used to determine if the measurement process is in control. Even if the measurement error is large, the calculated control limits will adjust for that error. Any special causes should be identified and removed before a measurement study is initiated. Shown below are unstacked and stacked versions of the range chart for the data collected earlier. It should be noted that the data used for this example is limited. 2
UCL = 1.85
UNSTACKED
STACKED
1.5
1 R = 0.567
0.5
LCL = 0
0 TECH A
TECH B
TECH C
PARTS
© QUALITY COUNCIL OF INDIANA CQE 2006
VI-88 (772)
VI. TESTING & MEASUREMENT MEASUREMENT SYSTEM ANALYSIS
Control Chart Methods (Continued) The range chart can be analyzed as follows:
C If all ranges are in control, all technicians are doing the same job. That is, there is statistical control with respect to repeatability. C If one technician is out of control, that individual’s method differs from the others. C If multiple technicians have out of control points, the measurement system is overly sensitive to technique errors and needs improvement. Neither the average or range chart should show patterns in the data relative to the technician or part. Trend analysis must not be used.
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VI. TESTING & MEASUREMENT QUESTIONS 6.1. Precision can best be defined as: a. The ability to target a process to a specified normal value b. The average reading determined after repeated measurements by different operators c. The difference between the repeated measurements on the same item d. The agreement or closeness of measurements on the same item 6.3. A subsurface discontinuity in some purchased steel bar stock is a suspected to be the cause of high failure rates. All of the following nondestructive test (NDT) methods could be used to screen the bar stock, EXCEPT: a. b. c. d.
Magnetic particle testing Liquid penetrant testing Eddy current testing Radiographic testing
6.8. Products should be subjected to tests which are designed to: a. Demonstrate the basic function at a minimum testing cost b. Approximate the conditions to be experienced in the customer's application c. Ensure that specifications are met under laboratory conditions d. Ensure performance under severe environmental conditions
Answers: 6.1. d, 6.3. b, 6.8. b
© QUALITY COUNCIL OF INDIANA CQE 2006
VI-92 (774)
VI. TESTING & MEASUREMENT QUESTIONS 6.11. When specifying the "10:1 calibration principle", one is referring to: a. The ratio of the frequency of calibration of a secondary standard to a primary standard b. The ratio of the frequency of calibration of the instrument to that of the primary standard c. The ratio of the main scale to vernier scale calibration d. The ratio of calibration standard accuracy to calibrated instrument accuracy 6.16. What type of measurement error is caused by drift? a. b. c. d.
Equipment variation Material variation Operator-to-operator variation Laboratory-to-laboratory variation
6.20. Because it takes the least amount of surface preparation, the hardness test most generally used for bulk hardness in foundry work would be the: a. b. c. d.
Vickers Rockwell Knoop Brinell
Answers: 6.11. d, 6.16. a, 6.20. d
© QUALITY COUNCIL OF INDIANA CQE 2006
VI-93 (775)
VI. TESTING & MEASUREMENT QUESTIONS 6.23. Reproducibility in an R & R study would be considered the variability introduced into the measurement system by: a. b. c. d.
The change in instrument differences over the operating range The total measurement system variation The bias differences of different operators The part variation
6.26. The error term in an ANOVA based R & R study is a reflection of: a. b. c. d.
Reproducibility Part variation Mathematical errors Repeatability
6.28. Why would control chart methods be used in screening measurement data before other measurement analysis? a. b. c. d.
They might replace the need for an ANOVA They are more effective than the average and range method They can indicate if the measurement system is adequate They require the collection of less data
Answers: 6.23. c, 6.26. d, 6.28. c
© QUALITY COUNCIL OF INDIANA CQE 2006
VI-94 (776)
VI. TESTING & MEASUREMENT QUESTIONS 6.33. The interaction term in an ANOVA R & R study indicates an interaction between: a. b. c. d.
The technician and measurement error The technician and the part The part and the total variation The repeatability and the reproducibility
6.34. On which of the following would a liquid penetrant be the LEAST successful? a. b. c. d.
Polyurethane foam Plastic Glass Steel
6.39. Identify the factual comment regarding torque wrench usage: a. Most torque wrenches will operate to 120% of stated range b. Holding a torque wrench handle below midpoint may produce a low torque reading c. Torque wrenches cannot be calibrated in a conventional sense d. Applying an extension, without compensation, may result in a low torque reading
Answers: 6.33. b, 6.34. a, 6.39. b
© QUALITY COUNCIL OF INDIANA CQE 2006
VII-1 (777)
VII. QUALITY & MANAGEMENT TOOLS QUALITY CONTROL TOOLS
QUALITY IS NEVER AN ACCIDENT, IT IS ALWAYS THE RESULT OF INTELLIGENT EFFORT. JOHN RUSKIN
© QUALITY COUNCIL OF INDIANA CQE 2006
VII-2 (778)
VII. QUALITY & MANAGEMENT TOOLS QUALITY CONTROL TOOLS
Control and Management Tools Control and Management Tools are presented in the following topic areas:
C Quality control tools C Management and planning tools
Quality Control Tools Quality Control Tools are presented in the following topic areas:
C C C C C C C
Cause-and-effect diagrams Flow charts Check sheets Histograms Control charts Pareto diagrams Scatter diagrams
© QUALITY COUNCIL OF INDIANA CQE 2006
VII-2 (779)
VII. QUALITY & MANAGEMENT TOOLS QUALITY CONTROL TOOLS
Basic Problem Solving Steps The six basic problem solving steps are:
C Identify the problem (Select a problem to work on) C Define the problem (If a problem is large, break it into smaller pieces) C Investigate the problem (Collect data and facts) C Analyze the problem (Find all possible causes and potential solutions) C Solve the problem (Select from the available solutions and implement) C Confirm the results (Was the problem fixed? Was the solution permanent?)
Other problem solving techniques like PDCA and DMAIC can be used.
© QUALITY COUNCIL OF INDIANA CQE 2006
VII-3 (780)
VII. QUALITY & MANAGEMENT TOOLS QUALITY CONTROL TOOLS
Problem Solving Using Control Tools
© QUALITY COUNCIL OF INDIANA CQE 2006
VII-4 (781)
VII. QUALITY & MANAGEMENT TOOLS QUALITY CONTROL TOOLS
Cause-and-Effect Diagrams The relationships between potential causes and resulting problems are often depicted using a causeand-effect diagram which:
C C C C C
Breaks problems down into bite-size pieces Displays many possible causes in a graphic manner Is also called a fishbone, 4-M, or Ishikawa diagram Shows how various causes interact Follows brainstorming rules when generating ideas
A fishbone session is divided into three parts: brainstorming, prioritizing, and development of an action plan. The problem statement is identified and potential causes are brainstormed into a fishbone diagram. Polling is often used to prioritize problem causes. The two or three most probable causes may be used to develop an action plan.
© QUALITY COUNCIL OF INDIANA CQE 2006
VII-4 (782)
VII. QUALITY & MANAGEMENT TOOLS QUALITY CONTROL TOOLS
Cause-and-Effect Diagrams (Continued) Machine
Material
Measurement
Problem Statement
Method
Manpower
Environment
Basic Fishbone 5 - M and E Example
© QUALITY COUNCIL OF INDIANA CQE 2006
VII-5 (783)
VII. QUALITY & MANAGEMENT TOOLS QUALITY CONTROL TOOLS
Cause-and-Effect Diagrams (Continued) M ateria l
M ach in e V ARIAT IO N IN T O L E RAN CE
M an W E AR AN D TE AR
1 . P L ATING 2 . M AT E RIAL T HICK NE SS
1 . W O RN N UM B E RS O N SC AL E KE Y S 2 . C O N TAINE RS B RO KE N
INS UF F IC IE N T TR AIN IN G K EY PU NC H E RR O R S O VE R IS S UE U PD ATE S N O T M AD E P UL L E D W RO NG P AR TS F RO M LO CA TIO N
3 . S CR AP AN D F O R E IG N EL E M E NT S 4 . L E NG TH S
R ED UC E IN CO M ING R EC E IP T E RR O R S F RO M 4 % T O 1% O F T RAN SA CT IO NS S US P EC T PA N T ARE W EIG H TS
AIRF L O W V EN DO R CO UN TS ACC E PT ED
T ARE W EIG H TS N O T O N PAN S
D EB RIS
N O N -S TAN DAR D S AM P L IN G P RO CE DU RE (IN AD EQ UA TE S AM P L E Q U ANT IT Y)
S CAL E C AL IB RA TIO N W R O N G PA RT N UM B E RS F RO M DE PA RT M EN TS
T HR EE D IF F E RE NT S CAL E S
INT ER RU PT IO NS
S CAL E # 2 M O R E AC CU RAT E T HAN S CAL E # 1
M eas urem en t
E n viro nm en t
M eth o d
An Actual Fishbone Example
© QUALITY COUNCIL OF INDIANA CQE 2006
VII-6 (784)
VII. QUALITY & MANAGEMENT TOOLS QUALITY CONTROL TOOLS
Flow Charts A flow chart, or process map, is useful both to people familiar with a process and to those that have a need to understand a process, such as an auditor. A flow chart can depict the sequence of product, containers, paperwork, operator actions or administrative procedures. A flow chart is often the starting point for process improvement. Flow charts are used to identify improvement opportunities as illustrated in the following sequence:
© QUALITY COUNCIL OF INDIANA CQE 2006
VII-6 (785)
VII. QUALITY & MANAGEMENT TOOLS QUALITY CONTROL TOOLS
Process Flow Applications Purchasing: Processing purchase orders, placing actual purchases, vendor contract negotiations Manufacturing: Processing returned goods, handling internal rejections, production processes, training new operators Sales: Making a sales call, taking order information, advertising sequences Administration: Correspondence flow, processing times, correcting mistakes, handling mail, typing letters, hiring employees Maintenance: Work order processing, p.m. scheduling Laboratory: Delivery of samples, testing steps, selection of new equipment, personnel qualification sequence, management of workflow
© QUALITY COUNCIL OF INDIANA CQE 2006
VII-6 (786)
VII. QUALITY & MANAGEMENT TOOLS QUALITY CONTROL TOOLS
Process Mapping There are advantages to depicting a process in a schematic format. The major advantage is the ability to visualize the process being described. Process mapping or flow charting has the benefit of describing a process with symbols, arrows and words without the clutter of sentences. Many companies use process maps to outline new procedures and review old procedures for viability and thoroughness.
© QUALITY COUNCIL OF INDIANA CQE 2006
VII-7 (787)
VII. QUALITY & MANAGEMENT TOOLS QUALITY CONTROL TOOLS
Process Mapping (Continued) Most flow charting uses certain standardized symbols. Computer flow charting software may contain 15 to 185 shapes with customized variations extending to the 500 range. Many software programs have the ability to create flow charts or process maps, although the information must come from someone knowledgeable about the process. Some common flow chart or process mapping symbols are shown below:
© QUALITY COUNCIL OF INDIANA CQE 2006
VII-8 (788)
VII. QUALITY & MANAGEMENT TOOLS QUALITY CONTROL TOOLS
Flow Chart Example There are a number of flow chart styles including conceptual, person-to-person and action-to-action. Start Material received
Visual inspection
No
Visual defects?
Yes
Inform purchasing of rejection. Generate corrective action report
Return to supplier Dimensional inspection required?
Yes
Dimensional inspection
End
No No Acceptable?
Yes
Place in inventory End
© QUALITY COUNCIL OF INDIANA CQE 2006
VII-9 (789)
VII. QUALITY & MANAGEMENT TOOLS QUALITY CONTROL TOOLS
Check Sheets Check sheets are tools for organizing and collecting facts and data. By collecting data, individuals or teams can make better decisions, solve problems faster and earn management support.
© QUALITY COUNCIL OF INDIANA CQE 2006
VII-10 (790)
VII. QUALITY & MANAGEMENT TOOLS QUALITY CONTROL TOOLS
Recording Check Sheets A recording check sheet is used to collect measured or counted data. The simplest form of the recording check sheet is for counted data. Data is collected by making tick marks in this particular check sheet. DAYS OF WEEK ERRORS
1
2
3
4
5
6
TOTAL
Defective Pilot Light
40
Loose Fasteners
16
Scratches
21
Missing Parts
3
Dirty Contacts
32
Other TOTAL
9 19
19
16
19
23
25
121
© QUALITY COUNCIL OF INDIANA CQE 2006
VII-10 (791)
VII. QUALITY & MANAGEMENT TOOLS QUALITY CONTROL TOOLS
Checklists The second major type of check sheet is called the checklist. A grocery list is a common example of a checklist. On the job, checklists may often be used for inspecting machinery or product. Checklists are also very helpful when learning how to operate complex or delicate equipment.
Measles Charts Not illustrated is a locational variety of check sheet called a measles chart. This check sheet could be used to show defect or injury locations using a schematic of the product or a human.
© QUALITY COUNCIL OF INDIANA CQE 2006
VII-11 (792)
VII. QUALITY & MANAGEMENT TOOLS QUALITY CONTROL TOOLS
Histograms Histograms are frequency column graphs that display a static picture of process behavior. Histograms usually require a minimum of 50-100 data points in order to adequately capture the measurement or process in question. A histogram is characterized by the number of data points that fall within a given bar or interval. This is commonly referred to as “frequency.” A stable process is most commonly characterized by a histogram exhibiting unimodal or bell-shaped curves. A stable process is predictable.
Column Graph
Bar Graph
Normal Histogram
© QUALITY COUNCIL OF INDIANA CQE 2006
VII-11 (793)
VII. QUALITY & MANAGEMENT TOOLS QUALITY CONTROL TOOLS
Histogram Example .50 .51 .52 .53 .54 .55 .56 .57 .58 .59 .60 .61 .62 .63 .64 .65
Tally
28 26 24 22 20 18 16 14 12 10 8 6 4 2
MEASUREMENT (INCHES)
Histogram
© QUALITY COUNCIL OF INDIANA CQE 2006
VII-12 (794)
VII. QUALITY & MANAGEMENT TOOLS QUALITY CONTROL TOOLS
Histograms Examples
Histogram with special causes
Bimodal histogram (May also be polymodal)
LSL
Negatively skewed distribution
USL
Truncated histogram (After 100% inspection)
© QUALITY COUNCIL OF INDIANA CQE 2006
VII-12 (795)
VII. QUALITY & MANAGEMENT TOOLS QUALITY CONTROL TOOLS
Histogram Comments C As a rule of thumb the number of cells should approximate the square root of the number of observations. As an alternative, use the table below: N 31 - 50 51 - 100 101 - 250 Over 250
K 5-7 6 - 10 7 - 12 10 - 20
C An unstable normal distribution process is often characterized by a histogram that does not exhibit a bell-shaped curve. C For a normal distribution, variation inside the bellshaped curve is chance or natural variation. Other variations are due to special or assignable causes. C There are many distributions that do not follow the normal curve. Examples include the Poisson, binomial, exponential, lognormal, rectangular, Ushaped and triangular distributions.
© QUALITY COUNCIL OF INDIANA CQE 2006
VII-13 (796)
VII. QUALITY & MANAGEMENT TOOLS QUALITY CONTROL TOOLS
Histogram - Classroom Exercise Foil Pouch Powder Weights (In Grams) 19.5 19.6 19.6 21.3 21.6 21.4 19.4 19.5 19.8 21.3 21.3 21.3 21.4 21.4 21.5 19.7 21.5 21.0 21.1 21.4
21.3 21.3 21.4 21.3 20.4 21.5 21.4 21.3 21.3 21.2 20.2 19.5 21.4 19.5 21.3 21.4 21.4 20.3 19.3 19.6
21.3 21.4 21.5 19.7 21.4 21.4 21.4 21.2 21.2 21.3 21.4 21.3 21.2 21.4 19.9 21.6 19.8 19.7 21.1 21.0
21.3 21.3 19.8 21.4 21.4 21.5 21.3 21.5 21.4 21.6 19.7 21.5 21.5 21.4 19.8 19.4 21.3 21.4 21.3 20.0
21.3 21.3 21.0 21.4 21.4 21.4 21.3 19.9 21.6 21.4 21.4 19.7 21.4 21.2 19.6 21.4 21.4 21.3 21.5 21.4
21.2 20.9 20.6 19.9 21.4 19.8 19.7 21.5 21.4 21.5 20.1 21.3 21.3 21.4 21.3 21.4 21.5 21.3 19.6 19.7
21.4 19.5 21.5 21.3 19.6 19.8 20.1 19.6 19.8 20.2 21.3 19.5 21.5 21.4 19.7 19.6 21.4 19.6 21.3 19.8
21.4 21.3 19.7 19.8 21.5 21.2 19.9 21.2 21.3 19.4 21.4 21.5 21.3 21.3 20.2 21.2 19.5 21.2 21.4 21.3
21.4 21.5 21.3 19.8 21.2 21.3 21.3 21.4 19.4 21.1 21.5 21.5 19.8 21.3 21.4 19.2 21.4 19.8 19.7 21.6
© QUALITY COUNCIL OF INDIANA CQE 2006
VII-14 (797)
VII. QUALITY & MANAGEMENT TOOLS QUALITY CONTROL TOOLS
Histogram - Classroom Exercise (Cont.) Column 1 2 3 4 5 6 7 8 9 10 11 12
Intervals 19.2 - 19.39 19.4 - 19.59 19.6 - 19.79 19.8 - 19.99 20.0 - 20.19 20.2 - 20.39 20.4 - 20.59 20.6 - 20.79 20.8 - 20.99 21.0 - 21.19 21.2 - 21.39 21.4 - 21.60
Tally Sheet
Does the above tally sheet indicate two distinct populations? The data represents product returned because of weight variation. The material had been produced on two different filling lines.
© QUALITY COUNCIL OF INDIANA CQE 2006
VII-15 (798)
VII. QUALITY & MANAGEMENT TOOLS QUALITY CONTROL TOOLS
Characteristics of a Normal Distribution C C C C C
Most of the points (data) are near the centerline The centerline divides the curve into two halves Some points approach the min and max values The normal histogram is bell-shaped Very few points are outside the bell-shaped curve
© QUALITY COUNCIL OF INDIANA CQE 2006
VII-15 (799)
VII. QUALITY & MANAGEMENT TOOLS QUALITY CONTROL TOOLS
The Normal Distribution When all special causes of variation are eliminated, the process will produce a product that, when sampled and plotted, has a bell-shaped distribution. If the base of the histogram is divided into six (6) equal lengths (three on each side of the average), the amount of data in each interval exhibits the following percentages:
68.26%
95.44% : – 3F
: – 2F
:–F
: 99.73%
:+F
: + 2F
: + 3F
© QUALITY COUNCIL OF INDIANA CQE 2006
VII-16 (800)
VII. QUALITY & MANAGEMENT TOOLS QUALITY CONTROL TOOLS
Control Charts Control charts are effective statistical tools to analyze variation in many processes. They are line graphs that display a dynamic picture of process behavior. A process which is under statistical control is characterized by points that do not exceed calculated upper or lower control limits. Charts for variables are generally most costly since each separate variable (thought to be important) must have data gathered and analyzed. Variables charts are also the most valuable and useful. Control charts are covered in substantial detail in Section X of this Primer.
© QUALITY COUNCIL OF INDIANA CQE 2006
VII-16 (801)
VII. QUALITY & MANAGEMENT TOOLS QUALITY CONTROL TOOLS
Control Chart Advantages C C C C C C C
They provide a display of process performance They are statistically sound They can plot both attributes and variables They can detect special and assignable causes They indicate the time that things change Variables charts can measure process capability They can determine if improvements are effective
© QUALITY COUNCIL OF INDIANA CQE 2006
VII-16 (802)
VII. QUALITY & MANAGEMENT TOOLS QUALITY CONTROL TOOLS
Control Chart Disadvantages C C C C C C C C C
They require mathematical calculations They can provide misleading information The sample frequency can be inappropriate There may be an inappropriate chart selection The control limits can be miscalculated They can have differing interpretations The assumed population distribution can be wrong Very small but sustained shifts can be missed Statistical support may be necessary
© QUALITY COUNCIL OF INDIANA CQE 2006
VII-17 (803)
VII. QUALITY & MANAGEMENT TOOLS QUALITY CONTROL TOOLS
Pareto Diagrams Pareto diagrams are very specialized forms of column graphs. They are used to prioritize problems so that the major problems can be identified. Pareto diagrams can help teams get a clear picture of where the greatest contribution can be made. Briefly stated, the principle suggests that a few problem categories (approximately 20 %) will present the most opportunity for improvement (approximately 80 %).
© QUALITY COUNCIL OF INDIANA CQE 2006
VII-17 (804)
VII. QUALITY & MANAGEMENT TOOLS QUALITY CONTROL TOOLS
Pareto Diagrams (Continued) Dr. Joseph M. Juran, world renowned leader in the quality field, needed a short name to apply to the phenomenon of the “vital few” and the “trivial many.” He depicted some cumulative curves in The Quality Control Handbook and put a caption under them, “Pareto's principle of unequal distribution...” The text makes it clear that Pareto only applied this principle in his studies of income and wealth; Dr. Juran applied this principle as “universal.” Pareto diagrams are used to:
C C C C
Analyze a problem from a new perspective Focus attention on problems in priority order Compare data changes during different time periods Permit the construction of a cumulative line
“First things first” is the thought behind the Pareto diagram. Our attention is focused on problems in priority order.
© QUALITY COUNCIL OF INDIANA CQE 2006
VII-18 (805)
VII. QUALITY & MANAGEMENT TOOLS QUALITY CONTROL TOOLS
Typical Pareto Diagram The defects for a book product are shown in Pareto form below: 100
300
75 Cumulative Line
200
50 100 25
A
B
C
D
E
F
G
H
I
J
K
L
M
N
0
Problem Categories
The “all others” category is placed last. Cumulative lines are convenient for answering such questions as, “What defect classes constitute 70 % of all defects?” The Pareto method assumes that there will be segregation of the significant few from the trivial many. Pareto diagrams can also be arranged based on costs or criticality (not just the number of occurrences).
© QUALITY COUNCIL OF INDIANA CQE 2006
VII-21 (806)
VII. QUALITY & MANAGEMENT TOOLS QUALITY CONTROL TOOLS
Scatter Diagram A scatter diagram (correlation chart) is a graphic display of many data points which represent the relationship between two different variables.
Low-positive
High-positive
No-correlation
High-negative
In most cases, there is an independent variable and a dependent variable. By tradition, the dependent variable is represented by the vertical axis and the independent variable is represented by the horizontal axis.
© QUALITY COUNCIL OF INDIANA CQE 2006
VII-22 (807)
VII. QUALITY & MANAGEMENT TOOLS QUALITY CONTROL TOOLS
Scatter Diagrams (Continued) The ability to meet specifications in many processes are dependent upon controlling two interacting variables and, therefore, it is important to be able to control the effect one variable has on another. The dependent variable can be controlled if the relationship is understood. Correlation originates from the following:
C A cause-effect relationship C A relationship between one cause and another cause C A relationship between one cause and two other causes
© QUALITY COUNCIL OF INDIANA CQE 2006
VII-22 (808)
VII. QUALITY & MANAGEMENT TOOLS QUALITY CONTROL TOOLS
Scatter Diagrams (Continued) Not all scatter diagrams display linear relationships.
© QUALITY COUNCIL OF INDIANA CQE 2006
VII-23 (809)
VII. QUALITY & MANAGEMENT TOOLS MANAGEMENT & PLANNING TOOLS
Quality Management and Planning Tools Formal research on the seven new quality tools began in 1972, as part of the Japanese Society of QC Technique Development meetings. It took several years of research before the new 7 tools were formalized. The 7 new tools as written by Japanese authors are: 1. 2. 3. 4. 5. 6. 7.
Relations diagram Affinity diagram (KJ method) Systematic diagram Matrix diagram Matrix data analysis Process decision program chart (PDPC) Arrow diagram
The American adaptations are: 2. 3. 6. 5. 1. 4. 7.
Affinity diagram (KJ method) Tree diagram* Process decision program chart (PDPC) Matrix diagram Interrelationship digraph (I.D.)* Prioritization matrices* Activity network diagram* * Renamed or modified tool
© QUALITY COUNCIL OF INDIANA CQE 2006
VII-24 (810)
VII. QUALITY & MANAGEMENT TOOLS MANAGEMENT & PLANNING TOOLS
Affinity Diagrams The affinity diagram uses an organized technique to gather facts and ideas to form developed patterns of thought. It can be widely used in the planning stages of a problem to organize the ideas and information. The steps can be organized as follows:
C Define the problem under consideration C Have 3" x 5" cards for use C Enter ideas, facts, opinions, etc. on the cards C Place the cards or notes on a table or wall C Arrange the groups into similar categories C Develop a main category for each group C Outline the affinity groups
© QUALITY COUNCIL OF INDIANA CQE 2006
VII-25 (811)
VII. QUALITY & MANAGEMENT TOOLS MANAGEMENT & PLANNING TOOLS
Example Affinity Diagram
GET CQE PRIMER
WATCH VIDEO PRESENTATION
GET OTHER PRIMERS
TAKE QUALITY ENGINEERING SEMINARS
GET MANY OTHER QUALITY TEXTBOOKS
ATTEND CQE REFRESHER
CALL ASQ TO OBTAIN BODY OF KNOWLEDGE
STUDY IN GROUPS HAVE A TUTOR TAKE UNIVERSITY LEVEL COURSES IN QUALITY HAVE A Q & A SOURCE
TEACH CQE SUBJECTS HAVE PRACTICAL EXPERIENCE STUDY INTENSIVELY START EARLY 1-2 YEARS STUDY 1 SUBJECT AT A TIME FOR 3 - 4 WEEKS
MOTIVATE SELF
GET BONUS
LISTEN TO SUCCESSFUL PASSED CQE’S
PRIDE
BE AROUND OTHERS WHO ARE POSITIVE
STUDY OLD CQE TESTS MAKE YOUR OWN CQE EXAMS
PUMP YOURSELF UP
© QUALITY COUNCIL OF INDIANA CQE 2006
VII-26 (812)
VII. QUALITY & MANAGEMENT TOOLS MANAGEMENT & PLANNING TOOLS
Tree Diagram The tree diagram is a systematic method to outline all the details needed to complete a given objective. The tree diagram can also be referred to as a systematic diagram. It is an orderly structure similar to a family tree chart or an organization chart. The method of logic is similar to that of value analysis. The organization is by levels of importance (i.e., why - how, goals - means). The tree diagram can be used to:
C C C C
Develop the elements for a new product Show the relationships of a production process Create new ideas in problem solving Outline project implement steps
The supplies needed for tree diagram development should include 3" x 5" cards, Post-it® notes, flip charts, or a large board.
© QUALITY COUNCIL OF INDIANA CQE 2006
VII-27 (813)
VII. QUALITY & MANAGEMENT TOOLS MANAGEMENT & PLANNING TOOLS
Example Tree Diagram ASK FOR BONUS
EXAMINE MOTIVATION
BE AROUND OTHERS WHO ARE POSITIVE
TEACH CQE SUBJECTS
TAKE UNIVERSITY LEVEL COURSES IN QUALITY
PASS THE CQE EXAM
HAVE A TUTOR OBTAIN KNOWLEDGE
ATTEND CQE REFRESHER
TAKE CQE SEMINARS OBTAIN VIDEOS
NEED RESOURCES
GET CQE PRIMER
PRIDE
MAKE UP YOUR OWN CQE EXAMS
STUDY OLD CQE TESTS
NEED TO PREPARE
ASK FOR HELPFUL TIPS
REWARD YOURSELF FOR EACH STEP
MOTIVATE YOURSELF
USE PRACTICAL EXPERIENCE
LISTEN TO SUCCESSFUL CQES
STUDY BOK
START EARLY 1 - 2 YEARS
HAVE A CONTACT SOURCE FOR Q/A
STUDY VIA TUTOR
STUDY IN A GROUP
STUDY AT HOME
RESTUDY SEMINAR MATERIALS CRITIQUE VIDEOS
CALL ASQ FOR BOK
STUDY VIDEOS
GET OTHER TEXTBOOKS
© QUALITY COUNCIL OF INDIANA CQE 2006
VII-28 (814)
VII. QUALITY & MANAGEMENT TOOLS MANAGEMENT & PLANNING TOOLS
Process Decision Program Charts (PDPC) The process decision program chart (PDPC) method is used to chart the course of events that will take us from a start point to a final complex goal. This method is similar to contingency planning. Some uses for PDPC charts include:
C The problem is new, unique, or complex in nature. It may involve a sequence that can have very difficult and challenging steps. C The opportunity to create contingencies and to counter problems are available to the team. Sidesteps in the problem solving sequence are unknown, but anticipated. The PDPC method is dynamic.
© QUALITY COUNCIL OF INDIANA CQE 2006
VII-29 (815)
VII. QUALITY & MANAGEMENT TOOLS MANAGEMENT & PLANNING TOOLS
PDPC Examples Major Categories
2nd Level
Last Level
Last Level "What- ifs"
A2
A4
RESULT RA4
A5
RA5
A3 A1
Solutions to "What- ifs" CONTINGENCY
CONTINGENCY
START GOAL B2
B4
RB4 CONTINGENCY
B1 B3
B5
RB5 CONTINGENCY
HAVE FRIENDS SUPPORT
ENROLL IN CQE REFRESHER
NEED FOR THE CQE
OBTAIN RESOURCES
STUDY WITH CLASS
LOSS OF MOTIVATION
GET PUMPED UP
GET TUTOR
STUDY VIA TUTOR
NO CQE CLASSES
FIND OTHERS
STUDY IN A GROUP
STUDY ALONE
FIND A CQE
PASS THE TEST
CALL EXPERT
© QUALITY COUNCIL OF INDIANA CQE 2006
VII-30 (816)
VII. QUALITY & MANAGEMENT TOOLS MANAGEMENT & PLANNING TOOLS
Matrix Diagram The matrix diagram method is used to show the relationship between objectives and methods, results and causes, tasks and people, etc. The objective is to determine the strength of relationships between a grid of rows and columns. The intersection of the grid will clarify the problem strength. There are several basic types of matrices:
C L-type...elements on the Y-axis and elements on the X-axis C T-type...2 sets of elements on the Y-axis, split by a set of elements on the X-axis C X-type...2 sets of elements on both the Y-axis and Xaxis C Y-type...2 L-type matrices joined at the Y-axis to produce a matrix design in 3 planes
© QUALITY COUNCIL OF INDIANA CQE 2006
VII-31 (817)
VII. QUALITY & MANAGEMENT TOOLS MANAGEMENT & PLANNING TOOLS
L-Type Matrix Example Knowledge Factors Work Experience
Quality Mgmt Concepts
Quality Costs
±
Metrology Basic Advanced Control Probability & Sampling Auditing Reliability Statistics Statistics Charts Distributions Inspection
±
Have Tutor
Î
Study In Group
± ±
Î
±
Æ
±
±
±
Æ
±
Æ
Attend CQE Refresher Study Old Tests
Î
±
±
Æ
±
Æ
±
±
±
±
High Motivation
Æ
Æ
Can Call Expert
Î
Î
Æ Strong Relationship (3) Relationship (2)
Î Possible (1)
Î
© QUALITY COUNCIL OF INDIANA CQE 2006
VII-32 (818)
VII. QUALITY & MANAGEMENT TOOLS MANAGEMENT & PLANNING TOOLS
Interrelationship Digraph (I.D.) This technique is created for the more complex problems or issues that management may face. If the issue is very complex, exact relationships may be difficult to determine. There may be intertwined causal relationships involved. The idea is to have a process of creative problem solving that will eventually indicate some key causes. Several other tools can be used as material for this technique: affinity diagrams, tree diagrams, or causeand-effect diagrams. The fun begins when relationship arrows are drawn in. The relationship arrow goes from the cause item to the effect item (cause ----> effect). This is done for every card until completed.
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VII-33 (819)
VII. QUALITY & MANAGEMENT TOOLS MANAGEMENT & PLANNING TOOLS
Interrelationship Digraph Example BONUS FOR CQE
GET CQE PRIMER
ATTEND CQE REFRESHER
TAKE ASQ CQE WORKSHOP
HAVE A TUTOR
HOW TO PASS THE CQE EXAM
STUDY IN GROUPS
PEERS HAVE CQE CALL ASQ
HAVE A CALL-IN SOURCE
MOTIVATION OF SELF STUDY OLD CQE TESTS
JOB EVALUATION NEEDS CQE NEXT PROMOTION NEEDS CQE
TAKE UNIVERSITY COURSES STUDY INTENSIVELY
A high number of outgoing arrows indicates a root cause or driver. A high number of incoming arrows indicates an outcome.
© QUALITY COUNCIL OF INDIANA CQE 2006
VII-34 (820)
VII. QUALITY & MANAGEMENT TOOLS MANAGEMENT & PLANNING TOOLS
Prioritization Matrix The original Japanese matrix data-analysis tool is not as easy to use, due to its heavy emphasis on statistical analysis. To use the prioritization matrices, the key issues and concerns must be identified and with alternatives generated. There are several approaches: 1.
The full analytical criteria method
2.
The consensus criteria method
3.
The combination I.D./matrix method
Examples of the prioritization matrices follow.
© QUALITY COUNCIL OF INDIANA CQE 2006
VII-35 (821)
VII. QUALITY & MANAGEMENT TOOLS MANAGEMENT & PLANNING TOOLS
Prioritization Matrix Example The Criteria
Composite Ranking (4 People)
A. Work Experience
0.05
+
0.10
+
0.10
+
0.20
=
Total 0.45
B. Have Tutor
0.10
+
0.20
+
0.30
+
0.10
=
0.70
C. Study In Group
0.15
+
0.10
+
0.05
+
0.20
=
0.50
D. Attend CQE Refresher
0.25
+
0.20
+
0.20
+
0.30
=
0.95
E. Study Old Tests
0.15
+
0.15
+
0.25
+
0.10
=
0.65
F. High Motivation
0.30 1.00
+
0.25 1.00
+
0.10 1.00
+
0.10 1.00
= =
0.75 4.00
Completed Rank Order Scores Criteria
0.45 Work Experience
0.70 Have Tutor
0.50 Study Group
0.95 Attend Refresher
0.65 Study Old Tests
0.75 High Motivation
Total
Quality Management
1(0.45)
1(0.70)
1(0.50)
1(0.95)
1(0.65)
1(0.75)
4.00
Quality Costs
5(0.45)
2(0.70)
2(0.50)
3(0.95)
2(0.65)
2(0.75)
10.30
Inspection Methods
4(0.45)
4(0.70)
5(0.50)
4(0.95)
3(0.65)
3(0.75)
15.10
Metrology
3(0.45)
5(0.70)
6(0.50)
5(0.95)
5(0.65)
4(0.75)
18.85
Sampling
2(0.45)
3(0.70)
4(0.50)
2(0.95)
4(0.65)
5(0.75)
13.25
Auditing
12(0.45)
6(0.70)
3(0.50)
6(0.95)
6(0.65)
7(0.75)
25.95
9(0.45)
7(0.70)
11(0.50)
7(0.95)
12(0.65)
6(0.75)
33.40
*Advanced Statistics
11(0.45)
12(0.70)
12(0.50)
12(0.95)
8(0.65)
12(0.75)
44.95
*Control Charts
10(0.45)
11(0.70)
7(0.50)
8(0.95)
9(0.65)
8(0.75)
35.15
*Probability
8(0.45)
10(0.70)
9(0.50)
10(0.95)
11(0.65)
10(0.75)
39.25
*Probability Distributions
7(0.45)
9(0.70)
10(0.50)
11(0.95)
10(0.65)
11(0.75)
39.65
*Reliability
6(0.45)
8(0.70)
8(0.50)
9(0.95)
7(0.65)
9(0.75)
32.15
Factors
*Basic Statistics
*Important Areas
© QUALITY COUNCIL OF INDIANA CQE 2006
VII-36 (822)
VII. QUALITY & MANAGEMENT TOOLS MANAGEMENT & PLANNING TOOLS
Activity Network Diagram The arrow diagram is the original Japanese name for this tool. The activity network diagram describes a methodology that includes program evaluation and review techniques (PERT), critical path method (CPM), node/activity on node diagrams (AON), precedence diagrams (PDM), and other network diagrams. As with other methods, the use of Post-it® notes or 3" x 5" cards will help in the preparation stage of the planning of the chart. After the identification of activities, the following would occur:
C C C C C C C C C C
Arrange the cards in sequence Identify links to other activities Record times for each activity Verify the critical path Calculate the earliest start and finish times Calculate the latest start and finish times Calculate the slack times Review the activity network diagram Find ways to reduce the time needed Put diagram on paper and distribute
© QUALITY COUNCIL OF INDIANA CQE 2006
VII-37 (823)
VII. QUALITY & MANAGEMENT TOOLS MANAGEMENT & PLANNING TOOLS
Example Activity Network Diagram 1 KEY
TASK LENGTH (DAYS)
0
20
0
20
DETERMINE NEED FOR CQE
20
EARLIEST START FINISH LATEST START FINISH
2
20
25
20
25
DETERMINE REQUIREMENTS
5 25
45
44
64
20 3
COMPANY FUNDING
10
35
45
45
55
10
25
35
25
35
5
FIND ASQ CLASS
GET OTHER RESOURCES 11
4
STUDY 10 LIKE CRAZY 45
145
55
155
35
45
45
55
100 45
145
55
155
12
35
125
35
125
ATTEND CLASS 8
0
100
FINAL PREP
STUDY IN GROUPS 14
13
0
0
155
156
155
156
1
125
155
125
155
30
9
10 CQE TEST DAY
50
64
69
50
51
69
70
6
90 FORM STUDY GROUP
45 5
APPLY FOR EXAM
ASQ OK'S
1
7
© QUALITY COUNCIL OF INDIANA CQE 2006
VII-39 (824)
VII. QUALITY & MANAGEMENT TOOLS QUESTIONS 7.2. What other problem solving tool is customarily used to complement the fishbone diagram? a. b. c. d.
Scatter diagrams Pareto diagrams Brainstorming Force field analysis
7.4. The seven basic tools of quality focus on: a. b. c. d.
Quantitative and qualitative data Management directed analysis Customer requirements External and internal customer satisfaction
7.8. An advantage of process mapping is the ability to: a. b. c. d.
Accumulate data for Pareto analysis Detect assignable causes of behavior Discover the underlying distribution of a process Check current processes for duplication or redundancy
Answers: 7.2. c, 7.4. a, 7.8. d
© QUALITY COUNCIL OF INDIANA CQE 2006
VII-40 (825)
VII. QUALITY & MANAGEMENT TOOLS QUESTIONS 7.12. For organizing information, facts or data into a systematic, logical manner, which of the following new quality tools would be used? a. b. c. d.
An interrelationship digraph A tree diagram An activity network diagram Prioritization matrix
7.14. Which of the following would be the best application of a Pareto chart? a. b. c. d.
To determine when to make proactive adjustments to a process To detect special behavior causes in the process To gather data and to design experimental controlled changes To evaluate the results of other problem solving techniques
7.20. As a problem solving technique, which of the following would be the best application for an Ishikawa diagram? a. b. c. d.
Problem identification and corrective action To support the PDCA cycle The determination of potential root problem causes The determination of short-term corrective action
Answers: 7.12. b, 7.14. d, 7.20. c
© QUALITY COUNCIL OF INDIANA CQE 2006
VII-41 (826)
VII. QUALITY & MANAGEMENT TOOLS QUESTIONS 7.21. What is the major advantage in flow charting or process mapping procedures and work instructions? a. b. c. d.
So that computer programs with standardized symbols can be used So that concurrent engineering activities may be planned So that improvements in product or process flow are apparent So that the process of concern can be easily visualized
7.24. Which of the following statements can be safely made about Pareto diagrams? a. b. c. d.
They have little application outside of the quality area They reflect an observation of fact They are bound by a universal set of laws They have no validity for discrete data
7.27. Which of the following statements is the major technical criticism of the use of the cause-and-effect diagram? a. It is too time consuming when the major contributing factors to a problem are known b. It tends to oversimplify the problem by ignoring contributing factor interactions c. It tends to ignore contributing factors that do not start with the letter M d. It treats contributing factors equally, but some may be more significant
Answers: 7.21. d, 7.24. b, 7.27. b
© QUALITY COUNCIL OF INDIANA CQE 2006
VII-42 (827)
VII. QUALITY & MANAGEMENT TOOLS QUESTIONS 7.30. The new problem solving tool which incorporates PERT and CPM techniques into a project flow chart is called a/an: a. b. c. d.
Activity network diagram Prioritization matrix Tree diagram Process decision program chart
7.31. Which of the following process mapping symbols would NOT be associated with a decision point? a. b. c. d. 7.33. Which of the following quality tools would be LEAST important in the problem definition phase? a. b. c. d.
Fishbone diagrams Control charts Process flow diagrams Pareto diagrams
Answers: 7.30. a, 7.31. b, 7.33. b
© QUALITY COUNCIL OF INDIANA CQE 2006
VIII.
VIII-1 (828)
IMPROVEMENT TECHNIQUES
YOU CAN HELP AN ELEPHANT UP, IF IT’S TRYING TO GET UP. BUT, YOU CANNOT HELP AN ELEPHANT IF IT’S TRYING TO LIE DOWN OLD THAI SAYING
© QUALITY COUNCIL OF INDIANA CQE 2006
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VIII-2 (829)
IMPROVEMENT TECHNIQUES IMPROVEMENT MODELS
Improvement Techniques are presented in the following topic areas:
C Improvement models C Corrective and preventive actions
Improvement Models Using any improvement approach, the problem or opportunity statement must be clearly defined. Often problem statements are unclear.
C The true problem must be clearly identified. There is often a tendency to work on a downstream symptom of an upstream problem. C A problem is the gap between: C What is and what should be C Current results and desired results C A clearly defined problem statement should be measurable and include a target timetable.
© QUALITY COUNCIL OF INDIANA CQE 2006
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VIII-3 (830)
IMPROVEMENT TECHNIQUES IMPROVEMENT MODELS
Plan/Do/Check/Act The historical evolution of the PDCA problem solving cycle is interesting. Kolsar (1994) states that Deming presented the following product design cycle (which he attributed to Shewhart) to the Japanese in 1951: 1. 2. 3. 4. 5.
Design the product Make the product Put the product on the market Test the product in service Redesign the product, using consumer reaction and continue the cycle
© QUALITY COUNCIL OF INDIANA CQE 2006
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VIII-3 (831)
IMPROVEMENT TECHNIQUES IMPROVEMENT MODELS
PDCA (Continued) Perhaps from this concept, the Japanese evolved a general management control process called PDCA. Refer to the illustration below:
Action (A): Implement necessary reforms when the results are not as expected.
Plan (P): Establish a plan for achieving a goal.
Check: Measure and analyze the results.
Do (D): Enact the Plan.
The PDCA Cycle
The PDCA cycle is very popular in many problem solving situations because it is a logical representation of how most individuals already solve problems.
© QUALITY COUNCIL OF INDIANA CQE 2006
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VIII-4 (832)
IMPROVEMENT TECHNIQUES IMPROVEMENT MODELS
Plan/Do/Study/Act Deming (1986) was somewhat disappointed with the Japanese PDCA adaption. He proposed a PDSA continuous improvement spiral, which he considered principally a team oriented problem solving technique. 1.
Plan - What changes might be desirable? What data is needed?
2.
Do - Carry out the change or test decided upon, preferably on a small scale.
3.
Study - Observe the effects of the change
4.
Act - Study the results. What was learned? What can one predict from what was learned?
5.
Repeat step 1 with new knowledge accumulated.
6.
Repeat step 2 and onward.
Both PDCA or PDSA are very helpful techniques in product and/or process improvement projects.
© QUALITY COUNCIL OF INDIANA CQE 2006
VIII.
VIII-5 (833)
IMPROVEMENT TECHNIQUES IMPROVEMENT MODELS
Process Improvement Most companies, that survive, effect process improvement. However, progress is often at an evolutionary rate. What is needed in many cases (particularly in high-tech fields) is revolutionary progress. See the following schematic:
From an internal perspective, Company A is making progress. It is proceeding along at a steady improvement rate. Without competition, Company A is in good shape. However, Company B is proceeding at a revolutionary improvement rate and will soon have all but the most loyal of Company A’s customers.
© QUALITY COUNCIL OF INDIANA CQE 2006
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VIII-5 (834)
IMPROVEMENT TECHNIQUES IMPROVEMENT MODELS
Break Through Achievement Some companies fail when making either evolutionary or revolutionary progress. This could certainly be the case if a competitor enters the market with an entirely new concept.
Companies producing tube-style television sets or mainspring watches were shocked when solid state TVs and quartz crystal watches took their markets away.
© QUALITY COUNCIL OF INDIANA CQE 2006
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VIII-6 (835)
IMPROVEMENT TECHNIQUES IMPROVEMENT MODELS
Six Sigma Approach Six Sigma is a highly disciplined process that focuses on developing and delivering near-perfect products and services consistently. Six sigma is also a management strategy to use statistical tools and project work to achieve breakthrough profitability and quantum gains in quality. Snee (1999) provides some reasons why six sigma works:
C C C C C C C C
Bottom line results Senior management is involved A disciplined approach is used (DMAIC) Short project completion times (3 to 6 months) Clearly defined measures of success Trained individuals (black belts, green belts) Customers and processes are the focus A sound statistical approach
© QUALITY COUNCIL OF INDIANA CQE 2006
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VIII-7 (836)
IMPROVEMENT TECHNIQUES IMPROVEMENT MODELS
Six Sigma Approach (Continued) Six sigma black belts serve as project managers for business improvement projects to ensure timely completion of the improvement objectives. All projects need charters, plans, and boundaries. Six sigma projects may be selected from a broad range of areas including:
C C C C C C C C C C
Improved process capabilities Lean manufacturing principles Reduction in customer complaints Improved work flows Reduction of internal defects Administrative improvements Cost reduction opportunities Cycle time reductions Supplier related improvements Market share growth
The actual project should be consistent with company strategies for survival and/or growth.
© QUALITY COUNCIL OF INDIANA CQE 2006
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VIII-8 (837)
IMPROVEMENT TECHNIQUES IMPROVEMENT MODELS
DMAIC Process Many six sigma improvement teams employ a problem solving methodology called DMAIC. Define the customer’s critical-to-quality issues and core business process.
C Define customer requirements and expectations C Define project boundaries C Define the process to be improved by mapping Measure the performance of the core business process involved.
C Develop a data collection plan C Collect data from many sources C Collect customer survey results Analyze the data and determine root causes or improvement opportunities.
C Identify performance gaps C Identify improvement opportunities C Identify objective statistical procedures
© QUALITY COUNCIL OF INDIANA CQE 2006
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VIII-8 (838)
IMPROVEMENT TECHNIQUES IMPROVEMENT MODELS
DMAIC Process (Continued) Improve the target process with creative solutions to fix and prevent problems.
C Create innovative solutions using technology C Develop and deploy improvement Control the improvements to keep the process on the new course.
C Develop a monitoring plan to prevent relapse C Institutionalize the improvements The DMAIC steps as described by Hahn (1999) are: Define: Measure: Analyze: Improve: Control:
Select the appropriate area to improve Measure the response variable Identify the root causes Reduce variability or eliminate the cause Sustain the improvements
© QUALITY COUNCIL OF INDIANA CQE 2006
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VIII-9 (839)
IMPROVEMENT TECHNIQUES IMPROVEMENT MODELS
Six Sigma Responsibilities Potential black belts often undertake a 4 month training program consisting of one week of instruction each month. A set of software packages are used to aid in the presentation of projects, including Excel or Minitab for the statistics portion. There are portions of the course focusing on team and project management. Dependent on the provider of the course, specific elements will differ, but all stress an understanding of variation reduction and a statistical approach. Breyfogle (2000) defines the roles and responsibilities of six sigma black belts to include:
C C C C C C C C
Lead the (cross-function) team Possess interpersonal and facilitation skills Develop and manage a detailed project plan Schedule and lead team meetings Sustain team motivation and stability Communicate project benefits to key parties Track and report milestones and tasks Interface between key management areas
© QUALITY COUNCIL OF INDIANA CQE 2006
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VIII-9 (840)
IMPROVEMENT TECHNIQUES IMPROVEMENT MODELS
Six Sigma Responsibilities (Continued) Black belts have the following duties in their company: Mentor: Teacher: Coach: Identifier: Influencer:
Provide a six sigma assistance network Train local personnel Provide support to project personnel Discover opportunities for improvement Be an advocate of six sigma strategy (Harry,1998)
Harry (1998) reports that the average black belt project will save about $175,000. There should be about 5 - 6 projects per year per black belt. The ratio of one black belt per 100 employees, can provide a 6% cost reduction per year. For larger companies there is usually one master black belt for every 100 black belts.
© QUALITY COUNCIL OF INDIANA CQE 2006
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VIII-10 (841)
IMPROVEMENT TECHNIQUES IMPROVEMENT MODELS
Six Sigma Management Support Effective six sigma programs do not happen accidentally. Careful management planning and implementation are required to ensure that the proper resources are available and applied to the right problems. Key resources may include people trained in problem solving tools, measurement equipment, analysis tools, and capital resources. Assigning human resources may be the most difficult element, since highly skilled problem solvers are a valuable resource and may need to be pulled from other areas where their skills are also needed.
© QUALITY COUNCIL OF INDIANA CQE 2006
VIII.
VIII-10 (842)
IMPROVEMENT TECHNIQUES IMPROVEMENT MODELS
Linking Six Sigma Projects to Goals Pande (2000) suggests that embarking on a six sigma initiative begins with a management readiness assessment, which includes a review of the following areas:
C Assess the outlook and future path of the business: C Is the strategy course clear for the company? C Can we meet our financial and growth goals? C Does our organization respond effectively to new circumstances? C Evaluate the current organizational performance: C What are our current overall business results? C Do we meet customer requirements? C How effectively are we operating? C Review the capacity for systems change and improvement: C How well do we manage system changes? C Do our cross-functional processes work? C Are there conflicts with our current efforts?
© QUALITY COUNCIL OF INDIANA CQE 2006
VIII.
VIII-11 (843)
IMPROVEMENT TECHNIQUES IMPROVEMENT MODELS
Kaizen Kaizen is Japanese for continuous improvement (Imai, 1997). The word kaizen is taken from the Japanese kai “change” and zen “good.” This is usually referred to as incremental improvement, but on a continuous basis and involving everyone. Kaizen is an umbrella term for:
C C C C C
Productivity Total quality control Zero defects Just-in-time production Suggestion systems
The kaizen strategy involves:
C C C C C C
Management maintains operating standards Progress improvement is the key to success PDCA improvement cycles are used Problems are solved with hard data The next process is considered the customer Quality is of the highest priority
© QUALITY COUNCIL OF INDIANA CQE 2006
VIII.
VIII-11 (844)
IMPROVEMENT TECHNIQUES IMPROVEMENT MODELS
The Kaizen Blitz While most kaizen activities are considered to be of a long-term nature by numerous individuals, a different type of kaizen strategy can occur. This has been termed a kaizen event, kaizen workshop, or kaizen blitz, which involves a kaizen activity in a specific area within a short time period. The kaizen blitz, using cross-functional volunteers in a 3 to 5 day period, results in a rapid workplace change on a project basis. Various metrics are used to measure the outcomes of a kaizen blitz:
C C C C C C C
Floor space saved More line flexibility Improved work flow Improvement ideas Increased quality levels Safer working environment Reduced non-value added time
© QUALITY COUNCIL OF INDIANA CQE 2006
VIII.
VIII-12 (845)
IMPROVEMENT TECHNIQUES IMPROVEMENT MODELS
Lean Techniques There are a large number of lean manufacturing techniques that are widely used by organizations today. Some of the more common processes include:
C C C C C C C C C C C C C C
Minimization of non-value added activities (muda) Decreased cycle times Single minute exchange of dies (SMED) Set-up reduction (SUR) The use of standard operating procedures The use of visual workflow displays Total productive maintenance Poka-yoke techniques to prevent or detect errors Principles of motion study and material handling Systems for workplace organization (5S approach) Just-in-time principles A large number of kaizen methods Continuous flow manufacturing concepts Value stream mapping
Many of these approaches support and complement each other.
© QUALITY COUNCIL OF INDIANA CQE 2006
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VIII-13 (846)
IMPROVEMENT TECHNIQUES IMPROVEMENT MODELS
Lean Glossary Andon board - A visual control device. It is typically a lit overhead display, giving the current status of the production system and alerting employees to problems. Continuous flow manufacturing (CFM) - Material moves one piece at a time, at a rate determined by the needs of the customer, in a smooth and uninterrupted sequence. Cycle time - The time required to complete one cycle of an operation. Inventory turns - The number of times inventory is consumed in a given period. Just-in-time (JIT) - A system for producing and delivering the right items at the right time in the right amounts. Level loading - The smoothing or balancing of the work load in all steps of a process. Muda - A Japanese term meaning any activity that consumes resources but creates no value.
© QUALITY COUNCIL OF INDIANA CQE 2006
VIII.
VIII-13 (847)
IMPROVEMENT TECHNIQUES IMPROVEMENT MODELS
Lean Glossary (Continued) Non-value added - Any activity that does not add value to the product or service. Perfection - The complete elimination of muda so that all activities along a value stream create value. Poka-yoke - A mistake proofing device or procedure to prevent or detect an error which adversely affects the product and results in the waste of correction. Pull - A system of cascading production and delivery instructions from downstream to upstream activities in which nothing is produced by the upstream supplier until the downstream customer signals a need. Queue time - The time a product spends awaiting the next processing step. Single minute exchange of dies (SMED) - A series of techniques for rapid changeovers of production machinery. Ten minutes is a common initial objective. Single piece flow - A situation in which one complete product proceeds through various operations without interruptions, back flows, or scrap.
© QUALITY COUNCIL OF INDIANA CQE 2006
VIII.
VIII-14 (848)
IMPROVEMENT TECHNIQUES IMPROVEMENT MODELS
Lean Glossary (Continued) Small lot principles - Effectively reducing lot size until the optimum of one piece flow is realized. Standard work - A precise description of each work activity, specifying cycle time, takt time, the work sequence of specific tasks, and the minimum inventory of parts needed to conduct the activity. Takt time - The available production time divided by the rate of customer demand. For example, if a customer wants 480 widgets per day, and the factory operates 960 minutes per day, takt time is two minutes. Takt time becomes the heartbeat of any lean organization. Value stream - The specific activities required to design, and provide a specific product, from concept to launch, from order to delivery. Visual control - The placement in plain view of all the tools, parts, production activities, and indicators of production system performance, such that the status of the system can be understood easily and quickly.
© QUALITY COUNCIL OF INDIANA CQE 2006
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VIII-14 (849)
IMPROVEMENT TECHNIQUES IMPROVEMENT MODELS
Lean Glossary (Continued) Waste - All overproduction ahead of demand, waiting for the next processing step, unnecessary transport of materials, excessive inventories, unnecessary employee movements, and production of defective parts. Work cell - The layout of machines or business processes of different types, performing different operations in a tight sequence, typically a U or L shape, to permit single piece flow and flexible deployment of human effort. Work center - One process station in a work cell.
© QUALITY COUNCIL OF INDIANA CQE 2006
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VIII-15 (850)
IMPROVEMENT TECHNIQUES IMPROVEMENT MODELS
Cycle Time Reduction Cycle time is the amount of time required to complete one transaction of a process. The reduction in cycle time is customarily undertaken for many of the following reasons:
C C C C C C
To please customers To reduce wastes To increase capacity To simplify the operation To reduce product damage To remain competitive
© QUALITY COUNCIL OF INDIANA CQE 2006
VIII.
VIII-15 (851)
IMPROVEMENT TECHNIQUES IMPROVEMENT MODELS
Value Stream Mapping A value stream map is created to identify all of the activities involved in product manufacturing from start to finish. This value stream may include suppliers, production operations and the end customer. For product development, value stream mapping includes the design flow from product concept to launch. Benefits of a value stream map include:
C C C C C C C C C
Seeing the complete process flow Identifying sources and locations of waste Providing common terminology for discussions Helping to make decisions about the flow Tying multiple lean concepts together Providing a blueprint for lean ideas Linking information and material flows Describing how the process can change Determining effects on various metrics (Rother, 1999)
© QUALITY COUNCIL OF INDIANA CQE 2006
VIII.
VIII-16 (852)
IMPROVEMENT TECHNIQUES IMPROVEMENT MODELS
Current State Mapping A current state map of the process is developed to facilitate process analysis. Basic tips on drawing a current state map include:
C C C C C C
Start with a quick orientation of process routes Personally follow the material and information flows Map the process with a backward flow Collect the data personally Map the whole stream Create a pencil drawing of the value stream
Some of the typical process data includes: cycle time (CT), changeover time (COT), uptime (UT), number of operators, pack size, working time (minus breaks, in seconds), WIP, and scrap rate.
© QUALITY COUNCIL OF INDIANA CQE 2006
VIII.
VIII-16 (853)
IMPROVEMENT TECHNIQUES IMPROVEMENT MODELS
Future State Map A future stream map is an attempt to make the process lean. This involves creativity and teamwork on part of the lean team to identify creative solutions. Everything the team knows about lean manufacturing principles is used to create the process of the future. Questions to ask when developing a future state map are:
C C C C C C C C
What is the required takt time? Do manufactured items move directly to shipping? Are items available for customer pull? Is continuous flow processing applicable? What is the pacemaker process? What is the increment of work to be released? What improvements can be used? Can the process be leveled? (Rother, 1999)
© QUALITY COUNCIL OF INDIANA CQE 2006
VIII.
VIII-16 (854)
IMPROVEMENT TECHNIQUES IMPROVEMENT MODELS
Implementation Planning The final step in the value stream mapping process is to develop an implementation plan for establishing the future state. This includes a step-by-step plan, measurable goals, and checkpoints to measure progress. A Gantt chart may be used to illustrate the implementation plan. (Rother, 1999)
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VIII-17 (855)
IMPROVEMENT TECHNIQUES IMPROVEMENT MODELS
Value Stream Mapping Icons The following icons are used:
Electronic Flow
Inventory
FIFO
Kaizen Burst
Kanban Production Kanban Signal
Manual Information Flow
Operator
Finished Goods
Kanban Batches
Kanban Withdrawal
Process Box
Push Arrow Pull Circle
Supermarket
Go See
Kanban Post
Load Leveling
Pull Arrow
Source Schedule Box
Truck Shipment
Buffer Stock
Data Box
© QUALITY COUNCIL OF INDIANA CQE 2006
VIII.
VIII-18 (856)
IMPROVEMENT TECHNIQUES IMPROVEMENT MODELS
5S Workplace Organization The presence of a 5S program is indicative of the commitment of senior management to workplace organization, lean manufacturing and the elimination of muda (waste). The 5S program mandates that resources be provided in the required location, and be available as needed to support work activities. The five Japanese “S” words for workplace organization are:
C C C C C
Seiko (proper arrangement) Seiton (orderliness) Seiketso (personal cleanliness) Seiso (cleanup) Shitsuke (personal discipline)
Imai (1997)
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VIII.
VIII-18 (857)
IMPROVEMENT TECHNIQUES IMPROVEMENT MODELS
5S Workplace Organization (Cont’d) For American companies, the 5Ss are translated into approximate English equivalents:
C Sort: Separate what is unneeded and eliminate it. C Straighten: Put everything in its place. C Scrub: Make the workplace spotless. C Systematize: Make cleaning and checking routine. C Standardize: Sustain the previous 4 steps. The 5S approach exemplifies a determination to organize the workplace, keep it neat and clean, establish standardized conditions, and maintain the discipline that is needed to do the job. Numerous modifications have been made on the 5S structure.
© QUALITY COUNCIL OF INDIANA CQE 2006
VIII.
VIII-19 (858)
IMPROVEMENT TECHNIQUES IMPROVEMENT MODELS
Non-Value Added Activities Non-value added activities are classified as muda. It is another term for waste that exists in the process. The useful activities that the customer will pay for are considered value added. The other activities are not value added. Imai (1997) provides a list of seven muda categories that have been widely used in industry:
C C C C
Overproduction Inventory Repair/rejects Motion
C Processing C Waiting C Transport
Overproduction The muda of overproduction is producing too much at a particular point in time. Overproduction is characterized by:
C Producing more than needed by the next process C Producing earlier than needed by the next process C Producing faster than needed by the next process
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VIII.
VIII-19 (859)
IMPROVEMENT TECHNIQUES IMPROVEMENT MODELS
Inventory Parts, raw materials, work-in-process (semi-finished goods), inventory, supplies, and finished goods are all forms of inventory. Inventory is considered muda since it does not add value to the product. Inventory will require extra space, transportation and materials.
Repair/ Rejects Rejects involving scrapping the part are a definite waste of resources. Having rejects on a continuous flow line defeats the purpose of continuous flow. Line operators and maintenance will be used to correct problems, putting the takt time off course.
Motion Extra unneeded operator motions are wasteful. The layout of the workplace should be redesigned to take advantage of proper ergonomics.
© QUALITY COUNCIL OF INDIANA CQE 2006
VIII.
VIII-20 (860)
IMPROVEMENT TECHNIQUES IMPROVEMENT MODELS
Processing Processing muda consists of additional steps or activities in the manufacturing process.
Waiting The muda of waiting occurs when an operator is ready for the next operation, but must remain idle. The operator is idle due to machine downtime, lack of parts, unwarranted monitoring activities, or line stoppages.
Transport All forms of transportation are muda. This describes the use of forklifts, conveyors, pallet movers, and trucks.
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VIII.
VIII-21 (861)
IMPROVEMENT TECHNIQUES IMPROVEMENT MODELS
Continuous Flow Manufacturing (CFM) In the lean environment, continuous flow manufacturing is a basic principles. Material should always be moving one piece at a time, at a rate determined by the needs of the customer. The flow of product must be smooth and uninterrupted by:
C C C C C C C C C
Quality issues Setups Machine reliability Breakdowns Distance Handling methods Transportation arrangements Staging areas Inventory problems (Productivity, 1999)
© QUALITY COUNCIL OF INDIANA CQE 2006
VIII.
VIII-22 (862)
IMPROVEMENT TECHNIQUES IMPROVEMENT MODELS
Continuous Flow Manufacturing (Cont’d) The following techniques are important for continuous flow manufacturing:
C Poka-yoke: To prevent defects from proceeding to the next step C Source inspection: To catch errors to correct the process C Self-checks: Operator checks to catch defects and to correct the process C Successive checks: Checks by the next process to catch errors C TPM is used to help achieve high machine capability (Womack, 1996), (Robinson, 1990)
© QUALITY COUNCIL OF INDIANA CQE 2006
VIII.
VIII-22 (863)
IMPROVEMENT TECHNIQUES IMPROVEMENT MODELS
Takt Time Takt time is a term used (first by Toyota) to define a time element that equals the demand rate. In a CFM or one piece flow line, the time allowed for each line operation is limited. The line is ideally balanced so that each operator can perform their work in the time allowed. The word takt is German meaning baton, as used by an orchestra conductor (Imai, 1997). This provides a rhythm to the process. (Conner, 2001), (Sharma, 2001)
© QUALITY COUNCIL OF INDIANA CQE 2006
VIII.
VIII-22 (864)
IMPROVEMENT TECHNIQUES IMPROVEMENT MODELS
Total Productive Maintenance (TPM) Total productive maintenance promotes coordinated group activities for greater equipment effectiveness and requires operators to share responsibility for routine machine maintenance. The professional maintenance staff retains responsibility for major maintenance activities and act as coaches for the routine and minor items. There are “six big losses” that contribute negatively to equipment effectiveness:
C C C C C C
Equipment failure Setup and adjustment Idling and minor stoppages Reduced speed Process defects Reduced yields
© QUALITY COUNCIL OF INDIANA CQE 2006
VIII.
VIII-23 (865)
IMPROVEMENT TECHNIQUES IMPROVEMENT MODELS
Visual Factory Imai (1997) provides three reasons for using visual management tools:
C To make problems visible C To keep all workers in contact with the workplace C To clarify targets for improvement Production boards and schedule boards are examples of a visual factory. These generally include the posting of daily production, maintenance items, or quality problems for everyone to see and understand. Jidohka is defined as a device that stops a machine whenever a defective product is produced. The operator or maintenance personnel must respond to find the source of the problem and to resolve it.
© QUALITY COUNCIL OF INDIANA CQE 2006
VIII.
VIII-23 (866)
IMPROVEMENT TECHNIQUES IMPROVEMENT MODELS
Visual Factory (Continued) The kanban system provides material control for the factory floor. The cards control the flow of production and inventory. The tool board is a display designed for the tools needed at a work station. This method is a part of 5S activities. The board is constructed to hold or mark the place for the tools and includes only the tools required for that work station. The visual factory places an emphasis on setting and displaying targets for improvement. The concept is that various operations have a target or goal to achieve. The visual factory enables management and employees to see the status of the factory floor at a glance. The current conditions and progress are evident. Any problems can be seen by everyone.
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VIII-24 (867)
IMPROVEMENT TECHNIQUES IMPROVEMENT MODELS
Kanban Kanban is the Japanese word for “sign.” It is a signal to internal processes to provide some product. Kanbans are usually cards, but they can be flags, a space on the floor, etc. Kanban provides some indication of:
C C C C C C C
Part numbers Quantities Locations Delivery frequencies Times of delivery Color of shelves at destination Bar codes, etc.
All of the above items can be forms of material control. Kanban is intended to help provide product to the customer with the shortest possible lead times. The order to produce parts at any one station is dependent on receiving an instruction, the kanban card. Only upon receiving a kanban card will an operator produce more goods. This system aims at simplifying paperwork, minimizing WIP and finished goods inventories.
© QUALITY COUNCIL OF INDIANA CQE 2006
VIII.
VIII-25 (868)
IMPROVEMENT TECHNIQUES IMPROVEMENT MODELS
Standard Work Standard work provides the discipline for attaining perfect flow in a process. Under normal work conditions, with no abnormalities in the system, the flow is perfect. The standard work conditions are determined for takt time, ergonomics, parts flow, maintenance procedures, and routines. Sharma (2001) provides a definition of standard work: “The best combination of machines and people working together to produce a product or provide a service at a particular point in time.” Standard work is the documentation of each action required to complete a specified task. Standard work should always be displayed at the workplace. If abnormalities appear in the system, those items can be spotted and eliminated.
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VIII-25 (869)
IMPROVEMENT TECHNIQUES IMPROVEMENT MODELS
Standard Work (Continued) The elements that comprise the standard work operations are:
C Cycle time: the time allowed to make a piece of production. This will be based on the takt time. The actual time will be compared to the required takt time to see if improvements are needed. C Work sequence: the order of operations that the worker must use to produce a part: grasp, move, hold, remove, delay, etc. The same order of work must be done every time. C Standard inventory: the minimum allowable inprocess material in the work area, including the amount of material on the machinery, needed to maintain a smooth flow. For continuous flow, one piece in the machine and one piece for hand offs is optimal. (Shingo, 1986), (Sharma, 2001)
© QUALITY COUNCIL OF INDIANA CQE 2006
VIII.
VIII-26 (870)
IMPROVEMENT TECHNIQUES IMPROVEMENT MODELS
SMED SMED is an acronym for single minute exchange of dies. The concept is to take a long setup change of perhaps 4 hours in length and reduce it to 3 minutes. Single minute exchange of dies does not literally require die changes or changeover of tooling to be performed in only one minute. It merely implies that die changes are to be accomplished under a single digit of time. Nine minutes or less to change a die will qualify. There are 3 myths regarding setup times:
C The skill for setup changes comes from practice C Long production runs are more efficient C Long production runs are economically better (Robinson, 1990)
© QUALITY COUNCIL OF INDIANA CQE 2006
VIII.
VIII-27 (871)
IMPROVEMENT TECHNIQUES IMPROVEMENT TOOLS
Theory of Constraints The theory of constraints (TOC) is a system developed by E. Goldratt. Goldratt describes the theory of constraints as an intuitive framework for managing based on the desire to continually improve a company. Using TOC, a definition of the goals of the company are established along with metrics for critical measures. (Goetsch, 2000) The Goal reminds readers that there are three basic measures to be used in the evaluation of a system.
C Throughput C Inventory C Operational expenses These measures are more reflective of the true system impact than machine efficiency, equipment utilization, downtime, or balanced plants.
© QUALITY COUNCIL OF INDIANA CQE 2006
VIII.
VIII-27 (872)
IMPROVEMENT TECHNIQUES IMPROVEMENT TOOLS
Theory of Constraints (Continued) A few of the most widely used TOC concepts are detailed below:
C Bottleneck resources are: “resources whose capacity is equal to or less than the demand placed upon it.” If a resource presents itself as a bottleneck, then things must be done to lighten the load. C Balanced plants are not always a good thing. Do not balance capacity with demand, but “balance the flow of product through the plant with demand from the market.” The idea is to make the flow through the bottleneck equal to market demand. C Dependent events and statistical fluctuations are important. A subsequent event depends upon the ones prior to it. A bottleneck will restrain the entire throughput.
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VIII-28 (873)
IMPROVEMENT TECHNIQUES IMPROVEMENT TOOLS
Theory of Constraints (Continued) C Throughput is: “the rate at which the system generates money through sales.” The finished product must be sold before it generates money. C Inventory is: “all the money that the system has invested in purchasing things which it intends to sell.” This can also be defined as sold investments. C Operational expenses are: “all the money (that) the system spends in order to turn inventory into throughput.” This includes depreciation, lubricating oil, scrap, carrying costs, etc. C The terms throughput, inventory and operational expenses define money as: “incoming money, money stuck inside, and money going out.” Goldratt (1986)
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VIII.
VIII-28 (874)
IMPROVEMENT TECHNIQUES IMPROVEMENT TOOLS
Theory of Constraints (Continued) Goldratt (1990) provides more TOC details using the following 5 step method: 1.
Identify the system’s constraints
2.
Decide how to exploit the system’s constraints
3.
Subordinate everything else to the above decisions
4.
Elevate the system’s improving the system
5.
Back to step 1
constraints
to
keep
© QUALITY COUNCIL OF INDIANA CQE 2006
VIII.
VIII-29 (875)
IMPROVEMENT TECHNIQUES IMPROVEMENT TOOLS
Total Quality Management Total quality management is a management style based upon producing quality service as defined by the customer. TQM is defined as a quality centered, customer focused, fact based, team driven, senior management led process to achieve an organization’s strategic goals through continuous process improvement. The word “total” in total quality management means that everyone in the organization must be involved in the continuous improvement effort, the word “quality” shows a concern for customer satisfaction, and the word “management” refers to the people and processes needed to achieve the quality. Total quality management is not a program; it is a systematic, integrated, and organizational way-of-life directed at the continuous improvement of an organization.
© QUALITY COUNCIL OF INDIANA CQE 2006
VIII.
VIII-29 (876)
IMPROVEMENT TECHNIQUES IMPROVEMENT TOOLS
Total Quality Management (Continued) Total quality management differs from other management styles in that it is more concerned with quality during production than it is with the quality of the result of production. Other management styles have different concerns. Total quality management requires an organizational transformation - a totally new and different way of thinking and behaving. This transformation is not easy to achieve. Dr. Armand Feigenbaum championed the concept of total quality control at General Electric in the 1940s.
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VIII-30 (877)
IMPROVEMENT TECHNIQUES IMPROVEMENT TOOLS
Total Quality Management (Continued) Before total quality management implementation, upper management must first determine the organization’s common purpose or focus. Once an organization determines its focus, it must begin empowering its employees. TQM advocates using the cumulative skills and expertise of employees to solve problems and improve service quality. It calls for all members of a organization to share authority, responsibility, accountability, and decision making. Although it emphasizes group effort, a leader may be needed to keep the group on track. In a routine TQM improvement process, a steering committee is first made aware of a problem by input from employees or customers. If it deems the problem worthy of further study, it charters an action team to analyze the problem in detail and solve it. Total quality management requires extensive statistical analysis to study processes and improve quality.
© QUALITY COUNCIL OF INDIANA CQE 2006
VIII.
VIII-31 (878)
IMPROVEMENT TECHNIQUES IMPROVEMENT TOOLS
Continuous Quality Improvement Continuous quality improvement may be a stand alone quality methodology, or it may be incorporated into, or with, any number of other approaches, such as TQM, six sigma, lean manufacturing, the Juran Quality Trilogy, or benchmarking. In most cases, the process of quality improvement attacks what Juran (1993) calls sporadic (special cause) or chronic (common cause) problems. The classic Japanese solution to many of these problems is called kaizen. This technique is discussed later in this Primer Section. It involves teamwork and a variety of tools, such as:
C C C C C C C C
Reduced material handling Standard operating procedures Visual display management Just-in-time principles Value added activities Workplace organization Elimination of waste Mistake proofing
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VIII.
VIII-31 (879)
IMPROVEMENT TECHNIQUES IMPROVEMENT TOOLS
Continuous Quality Improvement (Cont’d) Problems that are chronic (common cause) require trained teams, with adequate resources, using an established problem solving methodology, and management endorsement. Juran (1993) states that effective improvement is accomplished on a project-byproject basis and in no other way. This contains a variety of quality, quality management, planning, and statistical tools to assist an improvement team. Carrying out each project involves:
C C C C C
Verifying the project need Diagnosing the causes Providing a remedy and proving its effectiveness Dealing with any resistance to change Instituting controls to hold the gains
© QUALITY COUNCIL OF INDIANA CQE 2006
VIII.
VIII-32 (880)
IMPROVEMENT TECHNIQUES IMPROVEMENT TOOLS
Reengineering The definition of reengineering by Lowenthal (1994) is: “The fundamental rethinking and redesign of operating processes and organizational structure, focused on the organization’s core competencies to achieve dramatic improvements in organizational performance.” Since most reengineering projects will involve several functional departments, a senior executive is needed to head up the effort. A process owner and a reengineering cross functional team are needed. No company can reengineer all of its processes simultaneously. Lowenthal (1994) recommends that a selection criteria be used on one or more of the major processes in an organization:
C Which process is in trouble? C Which process has the greatest impact? C Which process can be successful redesigned? The redesign should be a dramatic or breakthrough process for the company. A competitive advantage will often be gained by this effort.
© QUALITY COUNCIL OF INDIANA CQE 2006
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VIII-33 (881)
IMPROVEMENT TECHNIQUES CORRECTIVE & PREVENTIVE ACTIONS
Corrective and Preventive Actions Six sigma methodology as well as ISO 9001:2000 and ISO/TS 16949 require corrective and preventive actions to prevent defect occurrence. Companies buying products recognize that sorting usually doesn’t catch all defects and only adds to their purchase price as well. ISO 9001:2000 requires organizations to eliminate the cause of nonconformities in order to prevent their recurrence. Corrective actions shall be appropriate to their potential effects. Documented procedures should be established to define requirements for:
C C C C C C
Reviewing nonconformities Determining the causes of nonconformities Evaluating the need for action Determining and implementing the necessary action Maintaining records of the results of action taken Reviewing the results of corrective actions taken
Many companies and organizations now require at least two improvement activity responses for each corrective action request; temporary (short-term), and permanent (long-term).
© QUALITY COUNCIL OF INDIANA CQE 2006
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VIII-34 (882)
IMPROVEMENT TECHNIQUES CORRECTIVE & PREVENTIVE ACTIONS
Corrective Actions ISO/TS 16949 (2002) has the following additional corrective action requirements:
C An organization have a defined process for problem-solving, including root cause determination and elimination. C If a customer prescribed problem solving format exists, this prescribed method must be used. C An organization shall use error proofing methods in their corrective action process. C Any nonconformity related corrective action shall be extended to similar processes and products. C Rejected parts shall be analyzed. Records of this analysis shall be maintained. C The cycle time of this rejected part analysis shall be minimized.
© QUALITY COUNCIL OF INDIANA CQE 2006
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VIII-34 (883)
IMPROVEMENT TECHNIQUES CORRECTIVE & PREVENTIVE ACTIONS
Preventive Actions ISO 9001:2000 states that an organization shall determine actions to eliminate the causes of potential nonconformities to prevent their occurrence. Preventive actions shall be appropriate to their potential effects. Documented procedures shall be established to define requirements for:
C Determining potential nonconformities and their causes C Evaluating the need for action to prevent their occurrence C Determining and implementing the necessary action C Maintaining records of the results of preventive actions taken C Reviewing the results of preventive actions taken
© QUALITY COUNCIL OF INDIANA CQE 2006
VIII.
VIII-35 (884)
IMPROVEMENT TECHNIQUES CORRECTIVE & PREVENTIVE ACTIONS
Corrective Action Definitions The following definitions are important: CAR: An acronym meaning corrective action request. CAT: An acronym meaning corrective action team. Containment action: Measures taken to screen and eliminate defective products via such techniques as inspection and removal. This should be viewed as a temporary fix and not a management philosophy. Corrective action: An action taken to reduce or eliminate the causes of an existing nonconformity, defect or other undesirable situation. Often implied is the extension of this activity to one of preventing recurrence. Preventive action: Measures taken to prevent the occurrence of a quality deficiency. Root cause analysis: The review necessary to determine the original or true cause of a product or process nonconformance. This effort extends beyond the effects of a problem to discover its most fundamental cause.
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VIII-36 (885)
IMPROVEMENT TECHNIQUES CORRECTIVE & PREVENTIVE ACTIONS
Corrective Action Procedure There are countless varieties of corrective and preventive action procedures. An example is shown on Primer pages VIII - 36/37.
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VIII-38 (886)
IMPROVEMENT TECHNIQUES CORRECTIVE & PREVENTIVE ACTIONS
Corrective Action Request Form CORRECTIVE ACTION REQUEST TO:________________________________________________________
CAR#_________ DATE_________
FROM:_____________________________________________________ PROJECT NAME
PART NAME
PART NO.
MRR NO.
THE FOLLOWING CONDITION IS BROUGHT TO YOUR ATTENTION FOR CORRECTIVE ACTION. PLEASE INDICATE THE CAUSE AND CORRECTIVE ACTION IN THE SPACES BELOW INCLUDING SCHEDULED COMPLETION DATES. PLEASE SIGN AND DATE YOUR RESPONSE AND RETURN THIS FORM TO THE SENDER WITHIN ______ WORKING DAYS. DISCREPANT CONDITION AND APPARENT CAUSE _______________________________________________________________________ _______________________________________________________________________ _______________________________________________________________________ INVESTIGATIVE PORTION ROOT CAUSE _______________________________________________________________________ _______________________________________________________________________ _______________________________________________________________________ ACTION TO CORRECT OBSERVED DISCREPANCY (AND SIMILAR DISCREPANCIES) _______________________________________________________________________ _______________________________________________________________________ _______________________________________________________________________ ACTION TO PREVENT RECURRENCE _______________________________________________________________________ _______________________________________________________________________ _______________________________________________________________________ SCHEDULED COMPLETION DATE _____________________________________________ SIGNATURE______________________________DATE____________________________ REVIEW APPROVED
SIGNATURE_________________________ DISAPPROVED
DATE________________
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VIII-39 (887)
IMPROVEMENT TECHNIQUES CORRECTIVE & PREVENTIVE ACTIONS
Corrective Action Commitment Upper management is responsible for developing and implementing a corrective action program. Most chronic system’s problems cannot be solved by simple troubleshooting. The corrective action procedure typically follows the following sequence:
C C C C C C
Assignment of responsibility Evaluation of potential importance Investigation of possible causes Analysis of the problem Corrective (or preventive) action Follow-up to ensure that corrective (preventive) action is effective
The principal corrective action sources include the following:
C C C C C
Internal inspection and audit results Customer returns Customer complaints Employee interviews and comments System and management audits
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VIII-39 (888)
IMPROVEMENT TECHNIQUES CORRECTIVE & PREVENTIVE ACTIONS
Customer Returns All quality systems should have customer satisfaction as the ultimate goal. Therefore, any indication of customer dissatisfaction should be treated with utmost gravity. A return should be viewed for what it is, an indictment of the quality system. After all, the quality system is supposed to protect the customer from unsatisfactory materials.
Customer Complaints Customer complaints are the second most important source of quality system effectiveness information. Most customers don’t complain, they just quit doing business with your company. Therefore, a complaint probably represents many more similar complaints that are unreported. Each complaint should be recorded, then investigated until the root cause is established.
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VIII-40 (889)
IMPROVEMENT TECHNIQUES CORRECTIVE & PREVENTIVE ACTIONS
Types of Corrective Action As indicated earlier, many companies require two or three step corrective action responses. The three step corrective action process entails:
C Immediate actions (Actions taken to stop the problem immediately.) C Temporary actions (Actions taken to stop the problem in the near term.) C Permanent actions (Actions taken to stop the problem forever.) When a floor level employee takes care of a problem, the actions are usually limited to “immediate actions.” Temporary and permanent actions are missed.
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VIII-41 (890)
IMPROVEMENT TECHNIQUES CORRECTIVE & PREVENTIVE ACTIONS
Corrective Action Planning A company should have a documented procedure for corrective and preventive action. The procedure should assign responsibilities for short-term, immediate action to contain a product or process nonconformity. Permanent corrective actions must address the root cause and strive to eliminate it. Short-term, containment activities are concerned with detection, segregation, and disposition. Guidelines for short-term containment activities include the following:
C C C C
Clearly define the problem Present the problem to team members Develop an immediate action plan Determine the following: C How to contain? How to repair? How to inspect? C What tools or gages are needed? C Who will perform sorting, and/or repairing? C Put the short-term plan into effect quickly C Document the containment activity and results C Notify the appropriate personnel
© QUALITY COUNCIL OF INDIANA CQE 2006
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VIII-41 (891)
IMPROVEMENT TECHNIQUES CORRECTIVE & PREVENTIVE ACTIONS
Corrective Action Planning (Continued) Long-term actions may take a more in-depth approach. The following steps represent the process:
C C C C C C C C C C C C C C C
Organize the appropriate team members or experts Investigate and verify the problem Clearly define the problem statement Inform the team of any short-term activities Present all known evidence Brainstorm and reach consensus on cause(s) Delegate problem solving activities Perform investigation (gather evidence or data) Perform an analysis and present results Perform any further investigation if needed Clearly define the suspect root cause(s) Determine action(s) to correct the root cause Implement action to correct root cause(s) Verify the effects of corrective action(s) Report the results to management
© QUALITY COUNCIL OF INDIANA CQE 2006
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VIII-42 (892)
IMPROVEMENT TECHNIQUES CORRECTIVE & PREVENTIVE ACTIONS
Corrective Action Planning (Continued) When the result is ineffective: Check the method of corrective action implementation. If unsatisfactory, repeat the process. Seek assistance from other problem solving sources. When the result is effective: Assign follow-up verification using periodic checks. Check for similar process applications and implement the same solution where applicable. The results may be presented in a meeting with upper management. The corrective action plans, the subject system(s) or process(es), assigned personnel, commitment dates, and any standardization must be documented on the corrective action request form.
© QUALITY COUNCIL OF INDIANA CQE 2006
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VIII-42 (893)
IMPROVEMENT TECHNIQUES CORRECTIVE & PREVENTIVE ACTIONS
Root Cause Analysis An individual or team is given the responsibility of determining the root cause of a deficiency and correcting it. The solution to some problems may be complex and difficult. In other cases, the solution may be known but considerable time will be required to implement it. The proposed action may take several steps. See the illustration below: Situation
Immediate Action
Intermediate Action
Root Cause Action
The dam leaks
Plug it
Patch the dam
Find out what caused the leak so it won't happen again. Then rebuild the dam.
Parts are oversized
100% Inspection
Put an oversize kickout device in line
Analyze the process and take action to eliminate the production of oversize parts.
© QUALITY COUNCIL OF INDIANA CQE 2006
VIII.
VIII-43 (894)
IMPROVEMENT TECHNIQUES CORRECTIVE & PREVENTIVE ACTIONS
Root Cause Analysis (Continued) Most of us tend to focus on a downstream symptom of an upstream problem. To help locate the system’s true problem, a variety of problem solving tools are available. Some 24 commonly used techniques are listed in the Primer. When permanent corrective action is proposed, management must determine if:
C The root cause analysis has identified the full extent of the problem C The corrective action is satisfactory to eliminate or prevent recurrence C The corrective action is realistic and maintainable
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VIII-43 (895)
IMPROVEMENT TECHNIQUES CORRECTIVE & PREVENTIVE ACTIONS
Standardizing Corrective Actions Standardization is the act of identifying other systems or processes with similar nonconformance problems (or the potential for similar problems) and applying the same corrective action, once it has been proven effective. A company must prevent similar problems from occurring by means of such preventive actions. Make the most of the solution by extending the fix. Ask, “what other situations or parts might benefit from this fix?” Additionally, one should extend the cause. Ask, “what other things could have been affected by this cause?”, and “are there other similar situations where trouble is waiting to happen?”
© QUALITY COUNCIL OF INDIANA CQE 2006
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VIII-44 (896)
IMPROVEMENT TECHNIQUES CORRECTIVE & PREVENTIVE ACTIONS
Mistake Proofing Shigeo Shingo (1986) is widely associated with a Japanese concept called poka-yoke (pronounced pokeryolk-eh) which means to mistake proof the process. The success of poka-yoke is to provide some intervention device or procedure to catch the mistake before it is translated into nonconforming product. There are numerous adaptive approaches. Gadgets or devices can stop machines from working if a part or operation sequence has been missed by an operator. A specialized tray or dish can be used prior to assembly to ensure that all parts are present. In this case, the dish acts as a visual checklist. Other service oriented checklists can be used to assist an attendant in the case of interruption. Numerous mechanical screening devices can be used in fabrication. The author has seen applications based on length, width, height, and weight. Obviously, mistake proofing is a preventive technique.
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VIII-44 (897)
IMPROVEMENT TECHNIQUES CORRECTIVE & PREVENTIVE ACTIONS
Mistake Proofing (Continued) Other than eliminating the opportunity for errors, mistake proofing is relatively inexpensive to install and engages the operator in a contributing way. Work teams can often contribute by brainstorming potential ways to thwart error prone activities. A disadvantage is that technical or engineering assistance is often required. Other design improvements to “error proof” the process include:
C C C C C C C C C
Elimination of error-prone components Amplification of human senses Ergonomic design to optimize human response Redundancy in design (back up systems) Simplification by using fewer components Consideration of environmental factors Providing failsafe cut-off mechanisms Enhancing product producibility and maintainability Selecting proven components and circuits
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IMPROVEMENT TECHNIQUES CORRECTIVE & PREVENTIVE ACTIONS
Prevention Activities A prevention activity is an effort to prevent a product or service failure. Examples include:
C C C C C C C C C C C C C C C C C C C
Applicant screening Capability studies Pilot projects Controlled storage Design reviews Procedure writing Maintenance and repair Prototype testing Field testing Safety reviews Forecasting Surveys Housekeeping Time and motion studies Job descriptions Training and education Market analysis Personnel reviews Vendor evaluation and selection
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VIII-45 (899)
IMPROVEMENT TECHNIQUES CORRECTIVE & PREVENTIVE ACTIONS
Other Activities Preventive and corrective improvement activities also include topics covered elsewhere in this and other Sections of the Primer. Examples include:
C C C C C C C C C C C C C
Benchmarking Reengineering Kaizen techniques Cycle time reduction Trend analysis Check sheets DFSS techniques FMEA/FMECA Automated controls Lean techniques Six sigma techniques Control plans Creative prob lem solving tools
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VIII-49 (900)
IMPROVEMENT TECHNIQUES QUESTIONS
8.2. A lowered rejection rate following corrective action: a. Gives positive indication that one cause of nonconformance has been removed b. May be unrelated to the corrective action c. Indicates that the corrective action was directly related to the problem d. Has no significance 8.6. Modifying or redesigning a product would most likely occur during which two of the PDCA phases? a. b. c. d.
Plan and do Check and act Do and act Plan and act
8.8. When comparing breakthrough achievement with Kaizen techniques, which of the following statements is true? a. b. c. d.
Kaizen techniques provide more rapid improvement Breakthrough achievement is generally less expensive Breakthrough achievement would be used for low tech products Kaizen techniques are more easily applied at the floor level
Answers: 8.2. b, 8.6. c, 8.8. d
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IMPROVEMENT TECHNIQUES QUESTIONS
8.11. The theory of constraints is concerned with the basic measures of throughput, inventory, and operational expenses, which can be expressed as all of the following, EXCEPT: a. b. c. d.
Incoming money Money on hold Money stuck inside Money going out
8.14. Using a PDCA process to design a customer survey while implementing a customer feedback and improvement process is an example of: a. b. c. d.
The critical path method A customer driven company A PDCA process within a PDCA process A reactive versus a proactive approach
8.17. Which of the following actions or techniques is most useful in determining the original fundamental cause of a product or process nonconformance? a. b. c. d.
Continuous improvement Pareto analysis Root cause analysis Corrective action
Answers: 8.11. b, 8.14. c, 8.17. c
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IMPROVEMENT TECHNIQUES QUESTIONS
8.21. What is the best definition of takt time? a. It is a calculated time element that equals customer demand b. It is the speed at which parts must be manufactured in order to satisfy demand C. It is the heartbeat of any lean system d. It is the application of kaizen to continuous flow manufacturing 8.27. Corrective action is complete when: a. b. c. d.
The customer is satisfied The action taken is determined to be effective The quality manager signs off on it The production department agrees to the change
8.29. Which of the following is a non-value added activity? a. b. c. d.
Design reviews Vendor assessments Inventory reductions Receiving inspection
Answers: 8.21. a, 8.27. b, 8.29. d
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VIII-52 (903)
IMPROVEMENT TECHNIQUES QUESTIONS
8.31. It’s obvious that a corrective action needs follow-up attention when the result is unsatisfactory. Which of the following is the best reason for corrective action follow-up when the result is very satisfactory? a. To recognize the corrective action team for their achievement b. To assign the CAT members to the most difficult problems in the future c. To make the most of the solution by extending the fix to other products or services d. To develop standardized approaches to solving all future corrective actions 8.32. Using the DMAIC approach to six sigma improvement, at what step would the root causes of defects be identified? a. b. c. d.
Measure Control Improve Analyze
8.35. Lean enterprise may be summarized as: a. b. c. d.
An entire organization involved with improvement Implementation of SMED cycle time techniques Poka-yoke techniques in action Ergonomic principles in the workplace
Answers: 8.31. c, 8.32. d, 8.35. a
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IX. BASIC STATISTICS
DO NOT PUT YOUR FAITH IN WHAT STATISTICS SAY UNTIL YOU HAVE CAREFULLY CONSIDERED WHAT THEY DO NOT SAY. WILLIAM W. WATT
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IX. BASIC STATISTICS COLLECTING DATA / TYPES OF DATA
Basic Statistics Basic Statistics is presented in the following topic areas: C Collecting and summarizing data C Quantitative concepts C Probability distributions
Collecting and Summarizing Data Collecting and Summarizing Data is presented in the following topic areas:
C C C C C C C
Types of data Measurement scales Data collection methods Data accuracy Descriptive statistics Graphical relationships Graphical distributions
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IX. BASIC STATISTICS COLLECTING DATA / TYPES OF DATA
Types of Data The three types of data are attribute data, variable data, and locational data. Of these three, attribute and variable data are more widely used.
Attribute Data Attribute data is discrete. This means that the data values can only be integers, for example, 3, 48, or 1029. Counted data or attribute data would be the answer to questions like “how many,” “how often,” or “what kind.” In some situations, data will only occur as counted data.
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IX. BASIC STATISTICS COLLECTING DATA / TYPES OF DATA
Variable Data Variable data is continuous. This means that the data values can be any real number, for example, 1.037, -4.69, or 84.35. Variable data is the answer to questions like “how long,” “what volume,” “how much time,” and “how far.” This data is generally measured with some instrument or device. Variable data is regarded as being better than counted data. It is more precise and contains more information. For example, one would certainly know much more about the climate of an area, if they knew how much it rained each day, rather than how many days it rained.
Locational Data The third type of data does not fit into either category above. This data is known as locational data, which simply answers the question “where.” Charts that utilize locational data are often called measles charts or concentration charts.
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IX. BASIC STATISTICS COLLECTING DATA / TYPES OF DATA
Data Comparison Variable Characteristics measurable continuous may derive from counting Types of data length volume time Examples width of a door lug nut torque fan belt tension Data examples 1.7 inches 32.06 psi 10.542 seconds
Attribute countable discrete units or occurrences good/bad no. of defects no. of defectives no. of scrap items audit points lost paint chips per unit defective lamps 10 scratches 6 rejected parts 25 paint runs
A Comparison of Variable and Attribute Data
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IX. BASIC STATISTICS COLLECTING DATA / TYPES OF DATA
Family of Numbers Complex Numbers
Imaginary Numbers
Real Numbers
Rational Numbers
Integers
Whole Numbers
Natural Numbers
Prime Numbers
Irrational Numbers
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IX. BASIC STATISTICS COLLECTING DATA / TYPES OF DATA
Mathematical Definitions Denominator The divisor in a fraction. Exponent
A symbol indicating the raising to a power. In 23, 3 is the exponent.
Factors
Numbers used in multiplication, e.g. 8 (factor) x 6 (factor) = 48 (product).
Inequality
An expression that contains a sign: =/ < > _ > etc.
Irrational number
A number that is not the quotient of two integers, e.g. .
Numerator
In 3/4, the numerator is 3.
Pi (B)
Ratio of the circumference of a circle to its diameter. B is approximately 3.1416.
Prime number
Any number that cannot be obtained by multiplying smaller whole numbers, e.g. are: 2, 3, 5, 7, 11, 13
Rational number
A number that is the quotient of two integers.
Reciprocal
Two numbers are reciprocals if their product is 1. 3/4 x 4/3 = 1
Scientific notation
A number which is the product of a number between 1 and 10 and a power of 10. 7.1 X 106 is 7,100,000.
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IX-7 (911)
IX. BASIC STATISTICS COLLECTING DATA / MEASUREMENT SCALES
Measurement Scales Level
Description
Example
Nominal
Data consists of names or categories only. No ordering scheme is possible.
A bag of candy contained the following colors: Brown 17, Yellow 11, Red 10, Tan 6, Orange 5, Green 7
Ordinal
Data is arranged in some order but differences between values cannot be determined or are meaningless.
Product defects are tabulated as follows: A 16, B 32, C 42, D 30, where, A defects are more critical than D.
Interval
Data is arranged in order and differences can be found. However, there is no inherent starting point and ratios are meaningless.
The temperatures of three aluminum ingots were 200°F, 400°F and 600°F. Note, that three times 200°F is not the same as 600°F.
Ratio
An extension of the i nt e r v a l l e v e l t h a t includes an inherent zero starting point. Both differences and ratios are meaningful.
Product A costs $300 and product B costs $600. Note, that $600 is twice as much as $300.
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IX-8 (912)
IX. BASIC STATISTICS COLLECTING DATA / MEASUREMENT SCALES
Measurement Scales (Continued) Level
Central Location
Dispersion
Significance Tests
Nominal
Mode
Information Only
Chi-square
Ordinal
Median
Percentages
Sign or Run Test
Interval
Arithmetic Mean
Standard or Average Deviation
t test F test Correlation Analysis
Geometric or Harmonic Mean
Percent Variation
(many interval measures are useful for ratio data)
Ratio
Statistical Measures for Measurement Levels
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IX-9 (913)
IX. BASIC STATISTICS COLLECTING DATA / DATA COLLECTION METHODS
Data Collection Methods To ensure that the collected data is relevant to the problem, some prior thought must be given. Manual data collection requires a data form. Some data collection guidelines are:
C C C C C C C C C
Formulate a clear statement of the problem Define precisely what is to be measured List all the important characteristics to be measured Carefully select the right measurement technique Construct an uncomplicated data form Decide who will collect the data Arrange for an appropriate sampling method Decide who will analyze and interpret the results Decide who will report the results
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IX-10 (914)
IX. BASIC STATISTICS COLLECTING DATA / DATA COLLECTION METHODS
Automatic Measurement Computer controlled measurement systems may offer distinct advantages over their human counterparts. (Improved test quality, shorter inspection times, lower operating costs, automatic report generation, improved accuracy, and automatic calibration). Automated measurement systems have the capacity and speed to be used in high volume operations. Automated systems have the disadvantages of higher initial costs, and a lack of mobility and flexibility compared to humans. Automated systems may require technical malfunction diagnostics. When used properly, they can be a powerful tool to aid in the improvement of product quality.
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IX-10 (915)
IX. BASIC STATISTICS COLLECTING DATA / DATA COLLECTION METHODS
Automatic Measurement (Continued) Applications for automatic measurement and digital vision systems are quite extensive. The following incomplete list is intended to show examples:
C C C C C C C C C C C C C C C C C
Error proofing a process Avoiding human boredom and errors Sorting acceptable from defective parts Detecting flaws, surface defects, or foreign material Creating CAD drawings from an object Building prototypes by duplicating a model Making dimensional measurements Performing high speed inspections Machining, using laser or mechanical methods Marking and identifying parts Inspecting solder joints on circuit boards Verifying and inspecting packaging Providing bar code recognition Identifying missing components Controlling motion Assembling components Verifying color
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IX-11 (916)
IX. BASIC STATISTICS COLLECTING DATA / DATA COLLECTION METHODS
Data Coding The efficiency of data entry and analysis is frequently improved by data coding. Coding by adding or subtracting a constant or by multiplying or dividing by a factor: Let the subscript, lowercase c, represents a coded statistic; the absence of a subscript represents raw data; uppercase C indicates a constant; and lowercase f represents a factor. Then:
Coding by substitution: Consider a dimensional inspection procedure in which the specification is nominal plus and minus 1.25". The measurement resolution is 1/8 of an inch and inspectors, using a ruler, record plus and minus deviations from nominal. Coding by truncation of repetitive place values: Measurements such as 0.55303, 0.55310, 0.55308, in which the digits 0.553 repeat in all observations, can be recorded as the last two digits expressed as integers.
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IX. BASIC STATISTICS COLLECTING DATA / DATA ACCURACY
Data Accuracy Bad data is costly to capture and corrupts the decision making process. Data accuracy and integrity techniques include:
C Avoid emotional bias relative to targets or tolerances when measuring or recording data. C Avoid unnecessary rounding. C If data occurs in time sequence, record it in order. C If an item characteristic changes over time, record the measurement as soon as possible and again after a stabilization period. C To apply statistics which assume a normal population, determine if the data can be represented by at least 8 to 10 resolution increments. If not, the default statistic may be the count of observations. C Screen data to detect and remove data entry errors. C Use objective statistical tests to identify outliers. C Each important classification identification should be recorded along with the data.
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IX-13 (918)
IX. BASIC STATISTICS COLLECTING DATA / DESCRIPTIVE STATISTICS
Descriptive Statistics Numerical descriptive measures create a mental picture of a set of data. These measures which are calculated from a sample are numerical descriptive measures, called statistics. When these measures describe a population, they are called parameters. The two most important measures are measures of central tendency and measures of dispersion.
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IX-13 (919)
IX. BASIC STATISTICS COLLECTING DATA / DESCRIPTIVE STATISTICS
Measures of Central Tendency The Mean (X-bar,
)
The mean is the sum total of all data values divided by the number of data points.
X 6 is the mean X represents each number 3 means summation n is the sample size The arithmetic mean is the most widely used measure of central tendency.
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IX-14 (920)
IX. BASIC STATISTICS COLLECTING DATA / DESCRIPTIVE STATISTICS
Measures of Central Tendency (Cont.) The Mode The mode is the most frequently occurring number in a data set. It is possible for groups of data to have more than one mode.
The Median (Midpoint) The median is the middle value when the data is arranged in ascending or descending order. For an even set of data, the median is the average of the middle two values. For a Normal Distribution For a Skewed Distribution
MEAN = MEDIAN = MODE
Comparison of Central Tendency in a Normal and a Right Skewed Distribution
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IX-16 (921)
IX. BASIC STATISTICS COLLECTING DATA / DESCRIPTIVE STATISTICS
The Central Limit Theorem If a random variable, X, has mean µ, and finite variance F2, as n increases, X 6 approaches a normal distribution with mean µ and variance . Where, and n is the number of observations on which each mean is based.
Distributions of Individuals Versus Means
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IX-16 (922)
IX. BASIC STATISTICS COLLECTING DATA / DESCRIPTIVE STATISTICS
The Central Limit Theorem States: C The sample means X 6 i will be more normally distributed around : than individual readings Xj. The distribution of sample means approaches normal regardless of the shape of the parent population. This is why X 6 - R control charts work! C The spread in sample means X 6 i is less than Xj with the standard deviation of X 6 i equal to the standard deviation of the population (individuals) divided by the square root of the sample size. SX6 is referred to as the standard error of the mean:
Example: Assume the following are weight variation results: X 6 = 20 grams and F = 0.124 grams. Estimate FX6 for a sample size of 4: Solution:
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IX. BASIC STATISTICS COLLECTING DATA / DESCRIPTIVE STATISTICS
Illustration of Central Tendency The significance of the central limit theorem on control charts is that the distribution of sample means approaches a normal distribution.
Population Distribution
Population Distribution
n=2
Population Distribution
n=2
Population Distribution
n=2
n=2
n=4
n=4
n=4
n=4
n = 25 n = 25 n = 25
Sampling Distribution of X
Sampling Distribution of X
Sampling Distribution of X
n = 25
Sampling Distribution of X
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IX-18 (924)
IX. BASIC STATISTICS COLLECTING DATA / DESCRIPTIVE STATISTICS
Measures of Dispersion Other than central tendency, the other important parameter to describe a set of data is spread or dispersion. Three main measures of dispersion will be reviewed: range, variance, and standard deviation.
Range (R) The range of a set of data is the difference between the largest and smallest values. Example: Find the range of the following data: 5 3 7 9 8 5 4 5 8 Answer: 9 - 3 = 6
Variance (F2, s2) The variance, F2 or s2, is equal to the sum of the squared deviations from the mean, divided by the sample size. The formula for variance is:
The variance is equal to the standard deviation squared.
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IX-18 (925)
IX. BASIC STATISTICS COLLECTING DATA / DESCRIPTIVE STATISTICS
Measures of Dispersion (Continued) Standard Deviation (F, s) The standard deviation is the square root of the variance.
Note: N is used for a population, and n - 1 for a sample (to remove bias in small samples - less than 30)
Coefficient of Variation (COV) The coefficient of variation equals the standard deviation divided by the mean and is expressed as a percentage.
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IX. BASIC STATISTICS COLLECTING DATA / DESCRIPTIVE STATISTICS
Other Ways to Get Standard Deviation The long and short cut methods of determining standard deviation are illustrated in the Primer. No one uses these techniques these days. The student should be familiar with determining standard deviation using a statistical calculator or variable control chart information.
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IX. BASIC STATISTICS COLLECTING DATA / DESCRIPTIVE STATISTICS
Determine
and s Using a Calculator
Formerly this Primer attempted to instruct the student on how to determine X 6 and standard deviation on a Sharp calculator. However, many varieties of Texas Instrument, Casio, Hewlett Packard, and Sharp calculators can accomplish this task. The functions on all of these calculators are subject to change. Most technical people determine the mean and dispersion for a set of data using a calculator. The following general procedures apply: 1. Turn on the calculator. Put it in statistical mode. 2. Enter all observation values following the model instructions. 3. Determine the sample mean ( ). 4. Determine the population standard deviation F, or the sample standard deviation, s.
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IX. BASIC STATISTICS COLLECTING DATA / DESCRIPTIVE STATISTICS
Standard Deviation from Control Charts Standard deviation can be estimated from control charts using R 6 . This technique is discussed in Section X of this Primer, and relates to the determination of process capability. The control chart method of estimating standard deviation makes the big assumption that the process being charted is in control and many processes aren’t. Using a calculator or software program to determine s from individual data is often more accurate.
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IX. BASIC STATISTICS COLLECTING DATA / DESCRIPTIVE STATISTICS
Tchebysheff's Theorem Given a number, K, which is greater or equal to 1 and for any set of n measurements, at least (1-1/K2) of the measurements will lie within K standard deviations of their mean. Tchebysheff's theorem applies to any set of measurements. The distribution need not be normal. If the mean and standard deviation of a sample of 25 measurements are 75 and 10 respectively:
C At least 3/4 of the measurements will lie in the interval ± 2S = 75 ± 20. C At least 8/9 of the measurements will lie in the interval ± 3S = 75 ± 30. The theorem is very conservative because it applies to all distributions. In most situations, the fraction of measurements falling in the specified interval will exceed 1 - 1/K2.
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IX. BASIC STATISTICS COLLECTING DATA / DESCRIPTIVE STATISTICS
Selected Distributions Shown below are various ways to display distributions. 6 5 4 3 2 1 0 2
4
6
8
10 12 14 16 Days a Defect Report is Open
18
20
22
24
A Simple Ungrouped Distribution 16
15
14
12
12
11
10
8
8
6
6
5
5
4 2 0
2 3
6
9
12
15
18
21
24
Days a Defect Report is Open
A Grouped Frequency Polygon (Histogram)
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IX. BASIC STATISTICS COLLECTING DATA / DESCRIPTIVE STATISTICS
Selected Distributions (Continued)
A Simple Pie Chart 93
40
98
100
86 76 30
75
Cumulative Line
59 20
50
38 25
10
A
B
C
D
E
F
G
CATEGORIES
A Grouped Column Chart
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IX. BASIC STATISTICS COLLECTING DATA / GRAPHICAL RELATIONSHIPS
Graphical Methods The average human brain is not good at comparing more than a few numbers at a time. Therefore, a large amount of data is often difficult to analyze, unless it is presented in some easily digested format. Graphs, charts, histograms, tallies and Pareto diagrams are used to analyze and present data. Graphical methods are scattered throughout the CQE Primer. Only a few examples are shown here.
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IX. BASIC STATISTICS COLLECTING DATA / GRAPHICAL RELATIONSHIPS
Boxplots The boxplots technique is credited to John W. Tukey. The data median is a line dividing the box. The upper and lower quartiles define the ends of the box. The minimum and maximum are drawn as points at the end of lines (whiskers) extending from the box. Boxplots can be notched to indicate variability of the median. Boxplots can have variable widths proportional to the log of the sample size. Outliers are identified as points (asterisks).
Simple Boxplot
Complex Boxplots
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IX. BASIC STATISTICS COLLECTING DATA / GRAPHICAL RELATIONSHIPS
Stem and Leaf Plots The stem and leaf diagram consists of grouping the data by class intervals, as stems, and the smaller data increments as leaves. Example: Shear Strength, 50 observations given in the Primer. 14 12 10 Frequency
8 6 4 2 0 41#
43#
45#
47#
49#
51#
53#
Strength
Shear Strength Histogram
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IX. BASIC STATISTICS COLLECTING DATA / GRAPHICAL RELATIONSHIPS
Stem and Leaf Plots (Continued) Example: Show the previous data in a stem and leaf diagram.
Leaf Stem
5 2 538 69 8709 1688591 514644966 8 6212408644 2 48245068302 0123456789012 4444444444555
Shear Strength Stem and Leaf Plot
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IX. BASIC STATISTICS COLLECTING DATA / GRAPHICAL RELATIONSHIPS
Weibull Probability Plot
Cumulative Percent %
The Weibull distribution can be used for a variety of applications. The Weibull distribution can be graphically represented on chart paper. 99 95 90 80 70 60 50 40 30
Shape Correlation
1.667 0.998
20 10 5 3 2 1 1000
10000
Cycles to Failure
The graph indicates that $ = 1.667. This indicates that the slide has entered the period of early wearout. The scale, characteristic life, 0, is the point at which 63.2% of the slides have failed (at 9,421 cycles). Value of $
Stage
Corrective Action
$<1
Infant mortality
Additional screening or burn-in
$=1
Random failure
Failure are inherent
Early wearout
Perform preventative maintenance
$>1 and <4 $>4
Old age wearout Requires design changes to improve
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IX. BASIC STATISTICS COLLECTING DATA / GRAPHICAL RELATIONSHIPS
Probability Density Function The probability density function, f(x), describes the behavior of a random variable. The area under the probability density function must equal one. 100
Frequency
80 60 40
250
245
240
235
230
225
220
215
210
205
200
195
190
185
180
175
170
165
160
155
0
150
20
Length
Histogram with Overlaid Model For continuous distributions with f(x) _ > 0:
For discrete distributions for all values of n with f(x) _ > 0:
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IX. BASIC STATISTICS COLLECTING DATA / GRAPHICAL RELATIONSHIPS
Cumulative Distribution Function The cumulative distribution function, F(x), denotes the area beneath the probability density function to the left of x. 0.030 0.025 0.020 0.015 0.010 0.005 0.000 155
159 163 167
171 175 179
183 187
191 195 199
203 207 211
215 219
223 227 231
235 239
243
Lengt h 1.000
0.800
0.600
0.400
0.200
0.000
155 159 163 167 171 175 179 183 187 191 195 199 203 207 211 215 219
223 227 231 235 239 243
Lengt h
The cumulative distribution function is equal to the integral of the probability density function to the left of x.
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IX. BASIC STATISTICS COLLECTING DATA / GRAPHICAL RELATIONSHIPS
Normal Probability Plots A normal probability plot places observed data values on the vertical axis and plots them with their corresponding values from a standard normal table on the horizontal axis. The purpose of this activity is to determine if the data follows a normal, or near normal, distribution. The steps used in constructing a normal probability plot are: 1. Place the values in the data set in ascending order 2. Find the corresponding standardized normal values 3. Plot the matching values on a two dimensional chart 4. Evaluate the resulting chart for normalcy In finding the standardized normal values, a standard normal or Z table is used. The first value is the Z value below which the proportion 1/(n+1) of the area under the normal curve is found. This procedure continues until the nth (and largest) Z value is obtained, using the calculation n/(n+1).
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IX. BASIC STATISTICS COLLECTING DATA / GRAPHICAL RELATIONSHIPS
Normal Probability Plots (Continued) To illustrate the Z value determinations for various distributions of data, refer to the Table below. This is hypothetical data. Class Test Scores A B C 48 47 47 52 54 48 55 58 50 57 61 51 58 64 52 60 66 53 61 68 53 62 71 54 64 73 55 65 74 56 66 75 57 68 76 59 69 77 62 70 77 64 72 78 66 73 79 69 75 80 72 78 82 76 82 83 83
D 38 41 44 47 50 53 56 59 62 65 68 71 74 77 80 83 86 89 92
Corresponding Z values - 1.65 - 1.28 - 1.04 - 0.84 - 0.67 - 0.52 - 0.39 - 0.25 - 0.13 0.00 0.13 0.25 0.39 0.52 0.67 0.84 1.04 1.28 1.65
CQE Test Scores and Corresponding Z Values
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IX. BASIC STATISTICS COLLECTING DATA / GRAPHICAL RELATIONSHIPS
Normal Probability Plots (Continued) The data sets for classes A, B, C, and D were organized to respectively represent normal, negative skewed (tail pointed left), positive skewed, and rectangular distributions. The corresponding probability plots are shown below. 90
90
80
80
70
70
60
60
50 40
50
Normal distribution
40
30
30 -1.8 -1.4 -1 -0.6 -0.2 0.2 0.6 Z Value
1
1.4 1.8
90
-1.8 -1.4 -1 -0.6 -0.2 0.2 0.6 Z Value
1
1.4 1.8
100
80
90
70
80
60
70 60
50 40
Negative skewed distribution
Positive skewed distribution
50 40
30 -1.8 -1.4 -1 -0.6 -0.2 0.2 0.6 Z Value
1
1.4 1.8
Rectangular distribution
30 -1.8 -1.4 -1 -0.6 -0.2 0.2 0.6 1 Z Value
1.4 1.8
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IX. BASIC STATISTICS QUANTITATIVE CONCEPTS / TERMINOLOGY
Quantitative Concepts Quantitative Concepts is presented in the following topic areas:
C Terminology C Drawing statistical conclusions C Probability terms and concepts
Statistical Terminology Continuous A distribution containing infinite distribution (variable) data points that may be displayed on a continuous measurement scale. Examples: normal, exponential, and Weibull distributions. Discrete A distribution resulting from countable distribution (attribute) data that has a finite number of possible values. Examples: binomial, Poisson, and hypergeometric distributions.
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IX. BASIC STATISTICS QUANTITATIVE CONCEPTS / TERMINOLOGY
Statistical Terminology (Continued) Expected value
The mean, :, of a probability distribution is the expected value, E(x), of its random variable.
Parameter
The true numeric population value, often unknown, estimated by a statistic.
Population
All possible observations of similar items from which a sample is drawn.
Statistic
A numerical data value taken from a sample that may be used to make an inference about a population.
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IX. BASIC STATISTICS QUANTITATIVE CONCEPTS / TERMINOLOGY
Expected Value Bernoulli stated that the “Expected value equals the sum of the values of each of a number of outcomes multiplied by the probability of each outcome relative to all the other possibilities.” If E represents the expected value operator and V represents the variance operator, such that: If x is a random variable and c is a constant, then: 1. E(c) = c 2. E(x) = 3. E(cx)
= cE(x) = c
4.
V(c) = 0
5.
V(x) =
6. V(cx) =
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IX-35 (945)
IX. BASIC STATISTICS QUANTITATIVE CONCEPTS / STATISTICAL CONCLUSIONS
Enumerative Statistics Enumerative data is data that can be counted. Useful tools for tests of hypothesis conducted on enumerative data are the chi-square, binomial, and Poisson distributions. Deming (1986) defined a contrast between enumeration and analysis: Enumerative study
A study in which action will be taken on the universe.
Analytic study
A study in which action will be taken on a process to improve performance in the future.
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IX-35 (946)
IX. BASIC STATISTICS QUANTITATIVE CONCEPTS / STATISTICAL CONCLUSIONS
Robustness A statistical procedure is considered robust when it can be used even when the basic assumptions are violated to a moderate degree. The normal distribution is explained by two facts:
C The central limit theorem shows the standard error of sample means from any continuous data distribution to be approximately normal. C A number of commonly used statistical procedures are robust to deviations from theoretical normalcy. Tests of means such as the t test and ANOVA are rather insensitive to the normality assumption. ANOVA assumes the means are normally distributed and variances equal. Variance: Whether normal or not, the mean value of s2 is F2. If the population is normal, the variance of s2 is:
When not normal, the variance of s2 is:
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IX-37 (947)
IX. BASIC STATISTICS QUANTITATIVE CONCEPTS / STATISTICAL CONCLUSIONS
Conditions for Probability The probability of any event (E) lies between 0 and 1. The sum of the probabilities of all possible events (E) in a sample space (S) = 1.
Simple Events An event that cannot be decomposed is a simple event (E). The set of all sample points for an experiment is called the sample space (S). If an experiment is repeated a large number of times, (N), and the event (E) is observed nE times, the probability of E is approximately:
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IX-38 (948)
IX. BASIC STATISTICS QUANTITATIVE CONCEPTS / STATISTICAL CONCLUSIONS
Compound Events Compound events are formed by a composition of two or more events. They consist of more than one point in the sample space. EA = A and EB = B. I. Composition. A. Union of A and B - If A and B are two events in a sample space (S), the union of A and B (A c B) contains all sample points in event A or B or both. B. Intersection of A and B - If A and B are two events in a sample space (S), the intersection of A and B (A 1 B) is composed of all sample points that are in both A and B.
Venn Diagrams of Union and Intersection
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IX-39 (949)
IX. BASIC STATISTICS QUANTITATIVE CONCEPTS / STATISTICAL CONCLUSIONS
Compound Events (Continued) II.
Event Relationships. A. Complement of an Event - The complement of an event A is all sample points in the sample space (S), but not in A. The complement of A is 1-PA.
Example: If PA (cloudy days) is 0.3, the complement of A would be 1 - PA = 0.7 (clear).
B. Conditional Probabilities - The conditional probability of event A given that B has occurred is:
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IX-39 (950)
IX. BASIC STATISTICS QUANTITATIVE CONCEPTS / STATISTICAL CONCLUSIONS
Compound Events (Continued) Example: If event A (rain) = 0.2, and event B (cloudiness) = 0.3, what is the probability of rain on a cloudy day? (Note that it will not rain without clouds)
Two events A and B are said to be independent if either: P(A|B) = P(A) or P(B|A) = P(B) However for this example: P(A|B) = 0.67 and P(A) = 0.2= no equality, and P(B|A) = 1.00 and P(B) = 0.3 = no equality Therefore, the events are said to be dependent.
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IX-40 (951)
IX. BASIC STATISTICS QUANTITATIVE CONCEPTS / STATISTICAL CONCLUSIONS
Compound Events (Continued) C. Mutually Exclusive Events - If event A contains no sample points in common with event B, then they are said to be mutually exclusive. D. Testing for Event Relationships Example: Refer to the data on page 38. Event A: E1, E2, E3
Event B: E1, E3, E5
Are A and B, mutually exclusive, complementary, independent or dependent? A and B contain two sample points in common so they are not mutually exclusive. They are not complementary because B does not contain all points in S that are not in A.
By definition, events A and B are dependent.
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IX-41 (952)
IX. BASIC STATISTICS QUANTITATIVE CONCEPTS / STATISTICAL CONCLUSIONS
The Additive Law If the two events are not mutually exclusive: 1.
P (A c B) = P(A) + P(B) - P (A 1 B)
Note that P (A c B) is shown in many texts as P (A + B) and is read as the probability of A or B. Example: If one owns two cars and the probability of each car starting on a cold morning is 0.7, what is the probability of getting to work? P (A c B) = 0.7 + 0.7 - (0.7 x 0.7) = 1.4 - 0.49 = 0.91 = 91 %
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IX-41 (953)
IX. BASIC STATISTICS QUANTITATIVE CONCEPTS / STATISTICAL CONCLUSIONS
The Additive Law (Continued) If the two events are mutually exclusive: 2. P (A c B) = P(A) + P(B) also P (A + B) = P(A) + P(B) Example: If the probability of finding a black sock in a dark room is 0.4 and the probability of finding a blue sock is 0.3, what is the chance of finding a blue or black sock? P (A c B) = 0.4 + 0.3 = 0.7 = 70 %
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IX-42 (954)
IX. BASIC STATISTICS QUANTITATIVE CONCEPTS / STATISTICAL CONCLUSIONS
The Multiplicative Law If events A and B are dependent, the probability of A influences the probability of B. This is known as conditional probability and the sample space is reduced. For any two events A and B such that P(B) =/ 0: 1. P ( A|B ) =
P ( A ∩ B) and P ( A ∩ B ) = P ( A|B ) P ( B ) P (B)
Note in some texts P (A 1 B) is shown as P(A C B) and is read as the probability of A and B. P(B|A) is read as the probability of B given that A has occurred. Example: If a shipment of 100 T.V. sets contains 30 defective units and two samples are obtained, what is probability of finding both defective? P ( A ∩ B) =
30 29 870 x = = 0.088 100 99 9900
P(A 1 B) = 8.8 %
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IX-42 (955)
IX. BASIC STATISTICS QUANTITATIVE CONCEPTS / STATISTICAL CONCLUSIONS
The Multiplicative Law (Continued) If events A and B are independent: 2.
P (A 1 B) = P(A) X P(B)
Example: One relay in an electric circuit has a probability of working equal to 0.9. Another relay in series has a chance of 0.8. What's the probability that the circuit will work? P (A 1 B) = 0.9 X 0.8 = 0.72 P (A 1 B) = 72 %
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IX-43 (956)
IX. BASIC STATISTICS QUANTITATIVE CONCEPTS / STATISTICAL CONCLUSIONS
Permutations An ordered arrangement of n distinct objects is called a permutation. The number of ways of ordering n distinct objects taken r at a time are designated by the symbols: Pnr or P(n,r) or nPr
Counting Rule for Permutations The number of ways that n distinct objects can be arranged taking them r at a time is:
Note: 0! = 1 Example: Three lottery numbers are drawn from a total of 50. How many arrangements can be expected?
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IX-44 (957)
IX. BASIC STATISTICS QUANTITATIVE CONCEPTS / STATISTICAL CONCLUSIONS
Combinations The number of distinct combinations of n distinct objects taken r at a time are denoted by the symbols: n
Cnr, or nCr, or C(n,r), or ( r )
Counting Rule for Combinations The number of different combinations that can be formed from n distinct objects taken r at a time is:
Example: A set of gages contains 81 blocks. How many 3 stack combinations exist?
Example: In the question above, how many 4 stack combinations exist?
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IX-46 (958)
IX. BASIC STATISTICS PROBABILITY DISTRIBUTIONS / CONTINUOUS DISTRIBUTIONS
Probability Distributions are presented in the following topic areas:
C Continuous Distributions C Discrete Distributions C Sampling Distributions
Common Continuous Distributions Normal (Gaussian)
: = Mean F = Standard deviation e = 2.718
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IX-47 (959)
IX. BASIC STATISTICS PROBABILITY DISTRIBUTIONS / CONTINUOUS DISTRIBUTIONS
Common Continuous Distributions (Cont.) Exponential
or
: = 2 = Mean X = X axis reading 8 = failure rate
Weibull 0=1 $=1/2 $=1 0 = Scale parameter $ = Shape parameter ( = Location parameter
$=3
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IX-47 (960)
IX. BASIC STATISTICS PROBABILITY DISTRIBUTIONS / CONTINUOUS DISTRIBUTIONS
Normal Distribution When a sample of several random measurements are averaged, distribution of such repeated sample averages tends to be normally distributed regardless of the distribution of the measurements being averaged. Mathematically, if:
the distribution of X 6 s becomes normal as n increases. If the set of samples being averaged have the same mean and variance then the mean of the X 6 s is equal to the mean (:) of the individual measurements, and the variance of the X 6 s is:
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IX-47 (961)
IX. BASIC STATISTICS PROBABILITY DISTRIBUTIONS / CONTINUOUS DISTRIBUTIONS
Normal Distribution (Continued) The normal probability density function is: f (x ) =
1 e σ 2Π
1⎛ x − μ ⎞ − ⎜ ⎟ 2⎝ σ ⎠
2
, −∞ < x < ∞
Where : is the mean and F is the standard deviation.
Probability Density
0.4
0.3
0.2
0.1
0.0 -3
-2
-1
0 X
1
2
3
The Standard Normal Probability Density Function
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IX-48 (962)
IX. BASIC STATISTICS PROBABILITY DISTRIBUTIONS / CONTINUOUS DISTRIBUTIONS
Uniform Distribution A uniform distribution is also called a rectangular distribution and may be either continuous or discrete. Probability Density Function ⎧ ⎫ 0 if x<-a ⎪ ⎪ ⎪ 1 ⎪ if -a ≤ x ≤ +a ⎬ PDF(x) = ⎨ ⎪ (2a) ⎪ ⎪⎩ ⎪⎭ 0 if x>+a
s=
a 3
Cumulative Density Function ⎧ ⎫ 0 if x<-a ⎪ ⎪ ⎪ (a + x) ⎪ CDF(x) = ⎨ if -a ≤ x ≤ +a ⎬ ⎪ (2a) ⎪ ⎪⎩ ⎪⎭ 1 if x>+a
The continuous uniform distribution is used when only the variation limits are known and the probability is constant. For a discrete uniform distribution:
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IX-49 (963)
IX. BASIC STATISTICS PROBABILITY DISTRIBUTIONS / CONTINUOUS DISTRIBUTIONS
Bivariate Normal Distribution The joint distribution of two variables is called a bivariate distribution. Bivariate distributions may be discrete or continuous. There may be total independence of the two independent variables, or there may be a covariance between them. The bivariate normal density is:
:1 and :2 are the two means F1 and F2 are the two variances and are each > 0 D is the correlation coefficient
Bivariate Normal Distribution Surface
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IX-50 (964)
IX. BASIC STATISTICS PROBABILITY DISTRIBUTIONS / CONTINUOUS DISTRIBUTIONS
Exponential Distribution The exponential distribution is used to model items with a constant failure rate. If a random variable, x, is exponentially distributed, 1/x follows a Poisson distribution. The exponential probability density function is:
Probability Density
8 is the failure rate and 2 is the mean It can be seen that 8 = 1/2.
X
Exponential Probability Density Function The variance of the exponential distribution is:
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IX-51 (965)
IX. BASIC STATISTICS PROBABILITY DISTRIBUTIONS / CONTINUOUS DISTRIBUTIONS
Lognormal Distribution The most common transformation is made by taking the natural logarithm, but any base logarithm, also yields an approximate normal distribution. The natural logarithm denoted as “ln”.
The standard lognormal probability density function is:
f(x) =
1 e xσ 2Π
1 ⎛ ln x −μ ⎞ − ⎜ ⎟ 2⎝ σ ⎠
2
, x>0
: is the location parameter. F is the scale parameter.
Probability Density
σ=2
σ = 0.25
σ=1
σ = 0.5
X
Lognormal Probability Density Function
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IX-53 (966)
IX. BASIC STATISTICS PROBABILITY DISTRIBUTIONS / CONTINUOUS DISTRIBUTIONS
Weibull Distribution The Weibull distribution is one of the most widely used distributions in reliability and statistical applications. Common versions are the two parameter and three parameter. The three parameter Weibull has a location parameter when there is some non-zero time to first failure. The three parameter Weibull probability density function:
$ is the shape parameter 2 is the scale parameter * is the location parameter The three parameter Weibull distribution can also be expressed as:
$ is the shape parameter 0 is the scale parameter ( is the non-zero location parameter
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IX-54 (967)
IX. BASIC STATISTICS PROBABILITY DISTRIBUTIONS / CONTINUOUS DISTRIBUTIONS
Weibull Distribution (Continued) 0.025 β=6
0.020 Probability Density
Effect of Shape Parameter, $ with 2 = 100 and * = 0
β = 0.8
0.015
β = 3.6 β=2
0.010 β=1
0.005 0.000 0
50
100
150
200
X
Effect of Scale Parameter
Probability Density
0.020
β=1 θ = 50
β = 2.5 θ = 50
0.015
0.010
β = 2.5 θ = 100
0.005 β=1 θ = 100
0.000 0
50
100
X
150
200
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IX-55 (968)
IX. BASIC STATISTICS PROBABILITY DISTRIBUTIONS / CONTINUOUS DISTRIBUTIONS
Weibull Distribution (Continued) δ=0 δ = 30
Effect of Location Parameter
Probability Density
0.015
0.010
0.005
0.000 0
50
100
150
X
The mean of the Weibull distribution is:
The variance of the Weibull distribution is:
The variance of the Weibull distribution decreases as the value of the shape parameter increases. The gamma ' value comes from a gamma function table.
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IX-56 (969)
IX. BASIC STATISTICS PROBABILITY DISTRIBUTIONS / CONTINUOUS DISTRIBUTIONS
Chi-Square Distribution The chi-square distribution is formed by summing the squares of standard normal random variables. For example, if z is a standard normal random variable, then the following is a chi-square random variable with n degrees of freedom.
y = z12 + z 22 + z 23 + ... + zn2 The chi-square probability density function where < is the degrees of freedom, and '(x) is the gamma function is: x ( ν / 2−1) e − x / 2 f(x) = ν / 2 , x>0 2 Γ ( ν / 2)
Probability Density
0.40
0.30
ν=2 ν=1
0.20
ν=5 ν=10
0.10
0.00
0
5
10 X
15
20
Chi-square Probability Density Function
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IX-57 (970)
IX. BASIC STATISTICS PROBABILITY DISTRIBUTIONS / CONTINUOUS DISTRIBUTIONS
F Distribution If X is a chi-square random variable with <1, degrees of
freedom and Y is a chi-square random variable with <2 degrees of freedom and if X and Y are independent, then the following is an F distribution with <1 and <2 degrees of freedom: X / ν1 F= Y / ν2 The F distribution is used extensively to test for equality of variances from two normal populations. The F probability density function is:
⎞ ⎛ ⎛ ν + ν ⎞ ⎛ ν ⎞ ν1 / 2 ⎞ ⎛ 1 2 ⎟ ⎜ Γ⎜ ⎟⎜ ⎟⎜ ⎟ ν1 / 2 − 1 x ⎟ ⎜ ⎝ 2 ⎠ ⎝ ν2 ⎠ ⎟⎜ f(x) = ⎜ , x>0 ν1 + ν 2 ) / 2 ⎟ ( ⎜ ⎟ ⎛ν ⎞ ⎛ν ⎞ Γ ⎜ 1 ⎟ Γ ⎜ 2 ⎟ ⎟ ⎜ ⎛ 1 + ν 1x ⎞ ⎟ ⎜ ⎜ ⎟ 2 2 ⎜ ⎟ ⎝ ⎠ ⎝ ⎠ ⎟⎜ ν2 ⎠ ⎝ ⎠⎝ ⎝ ⎠
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IX-58 (971)
IX. BASIC STATISTICS PROBABILITY DISTRIBUTIONS / CONTINUOUS DISTRIBUTIONS
F Distribution (Continued) Probability Density
1.00
v1=1, v2=1 v1=1, v2=10
0.80 v1=15, v2=15
0.60 0.40 0.20 v1=10, v2=1
0.00
0
0.5
1
1.5 X
2
2.5
3
F Probability Density Function Most texts only give one tail, and require the other tail to be computed using the expression:
Example: Given F0.05 with <1 = 8 and <2 = 10 is 3.07, find
the value of F0.95 with <1 = 10 and <2 = 8.
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IX-59 (972)
IX. BASIC STATISTICS PROBABILITY DISTRIBUTIONS / CONTINUOUS DISTRIBUTIONS
Student’s t Distribution If z is a standard normal random variable, and P2 is a chisquare random variable with < degrees of freedom, then a random variable with a t-distribution is:
t=
z Χ2 ν
The t probability density function with < degrees of freedom is: - (ν + 1)/2 τ ( ν + 1) / 2 ⎛ x2 ⎞ f(x) = , -∞ < x < ∞ ⎜1 + ⎟ ν ⎠ τ ( ν/2 ) πν ⎝ 0.40
Probability Density
Standard Normal
ν=10
0.30
ν=3 0.20
ν=1 0.10
0.00 -4
-2
0 X
2
t Probability Density Function
4
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IX-60 (973)
IX. BASIC STATISTICS PROBABILITY DISTRIBUTIONS / CONTINUOUS DISTRIBUTIONS
Student’s t-Distribution (Continued) The mean and variance of the t-distribution are:
μ=0
ν σ = , ν ≥ 3 ν-2 2
From a random sample of n items, the probability that:
falls between any two specified values is equal to the area under the t-probability density function between the corresponding values on the x-axis with n-1 degrees of freedom. Example: The burst strength of 15 randomly selected seals has a mean of 495.13 and a sample standard deviation of 8.467. What is the probability that the burst strength of the population is greater than 500? The area under the t probability density function, with 14 degrees of freedom, to the left of -2.227 is 0.0214.
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IX-61 (974)
IX. BASIC STATISTICS PROBABILITY DISTRIBUTIONS / DISCRETE DISTRIBUTIONS
Common Discrete Distributions Poisson p=0.1
n = sample size r = number of occurrences p = probability np 6 = : = average
n=30 p=0.3 p=0.5
r
Binomial n=30
p=0.1 p=0.3
p=0.5
n = sample size r = number of occurrences p = probability q=1-p
r
Hypergeometric N=60 n=30
p=0.1 p=0.3
n = sample size r = number of occurrences d = occurrences in population N = population size
p=0.5
r
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IX-62 (975)
IX. BASIC STATISTICS PROBABILITY DISTRIBUTIONS / DISCRETE DISTRIBUTIONS
Binomial Probability Distribution The binomial distribution applies when the population is large (N > 50) and the sample size is small compared to the population. Generally, n is less than 10% of N. It is most appropriate to use when proportion defective is equal to or greater than (0.1).
Example: A random sample of 10 units is taken from a steady stream of product. Past experience has shown 10% defective parts. Find the probability of exactly one bad part. n = 10
r = 1 p = 0.1
Solve for 2 bad parts (Answer = 19.37%). Solve for 0 bad parts (Answer = 34.87%)
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IX-63 (976)
IX. BASIC STATISTICS PROBABILITY DISTRIBUTIONS / DISCRETE DISTRIBUTIONS
Binomial Probability Distribution (Cont.)
Example: A continuous process averaged 6% defectives. In a sample of 300 units, 22 defective units were found. What is the expected sample average and 3 sigma variation? n = 300
p = 22/300 = 0.073
1 - p = 0.927
Sigma =
Limits = p ± 3S = 0.073 ± 0.045 = 0.028 and 0.118
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IX-64 (977)
IX. BASIC STATISTICS PROBABILITY DISTRIBUTIONS / DISCRETE DISTRIBUTIONS
Poisson Probability Distribution The Poisson distribution can be used to model defect counts and an approximation to the binomial, when p_ < 0.1 and the sample size is fairly large.
Example: A continuous process is running a 2% defective rate. What is the probability that a 100 piece sample will contain exactly 2 defectives?
: = np 6 = (100)(0.02) = 2,
r=2
Solve for r = 0 Answer 0.135 (13.5%) Solve for r = 1 Answer 0.27 (27%) Solve for r = 3 Answer 0.18 (18%)
The Poisson distribution average and sigma are:
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IX-66 (978)
IX. BASIC STATISTICS PROBABILITY DISTRIBUTIONS / DISCRETE DISTRIBUTIONS
Hypergeometric Probability Distribution The hypergeometric distribution applies when the population is small compared to the sample size. Sampling is done without replacement.
Example: From a group of 20 products, 10 are selected at random. What is the probability that the 10 selected contain the 5 best units? N = 20, n = 10, d = 5, (N-d) = 15 and r = 5
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IX-67 (979)
IX. BASIC STATISTICS PROBABILITY DISTRIBUTIONS / DISCRETE DISTRIBUTIONS
Multinomial Distribution Let events E1, E2, ... Ek occur with probabilities p1, p2, ... pk respectively. Then, the probability that those events will occur n1, n2, ... nk times respectively is:
N = n1 + n2 + ... + nk and p1 + p2 + ... + pk = 1 The multinomial distribution is a generalization of the binomial distribution. It is the general term in the multinomial expansion (p1 + p2 + ... + pk)N. Example: An inspection of units over time reveals four defective causes A, B, C, and good quality G. Historically, pA=0.03, pB = 0.05, pC =0.06 and pG =0.86. If a sample of 170 units was drawn from the population, what would be the probability of: nA=9, nB=7, nC=16 and nG=138? P(A=9, B=7, C=16, G=138) =
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IX-69 (980)
IX. BASIC STATISTICS QUESTIONS 9.2. Which of the following statements is NOT true regarding a probability density function? a. f(x) must be greater than, or equal to, zero for all values of x b. The integral of f(x) over all x is equal to 1, if f(x) represents a continuous distribution c. The sum of f(x) over all values of x is equal to 1, if f(x) represents a discrete distribution d. The cumulative distribution function is the probability of being greater than 0 and less than x 9.5. Which of the following distributions does NOT require the use of the natural logarithmic base for probability calculations? a. b. c. d.
Normal Poisson Weibull Binomial
9.8. The hypergeometric distribution is: a. A continuous distribution b. Used to describe sampling from a finite population without replacement c. The limiting distribution of the sum of several independent discrete random variables d. A special case of the Poisson distribution
Answers: 9.2. d, 9.5. d, 9.8. b
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IX-70 (981)
IX. BASIC STATISTICS QUESTIONS 9.10. What is the most widespread use of the F distribution? a. To model discrete data when the population size is small compared to the sample size b. To test for equality of variances from two normal populations c. To compensate for error in the estimated standard deviation for small sample sizes d. To construct confidence intervals by summing the squares of random variables 9.13. Calculate the standard deviation of the following complete set of data: 52, 20, 24, 31, 35, 42 a. b. c. d.
10.8 11.8 12.8 13.8
9.14. The equation for joint probability of two fault events under any circumstance is given by: P(A ∩ B) = P(A|B) x P(B)
If event A does not enhance occurrence of event B in any way, the probability of occurrence, when P(A) = 0.1, P(B) = 0.05, is given by: a. b. c. d.
0.00025 0.10000 0.05000 0.00500
Answers: 9.10. b, 9.13. a, 9.14. d
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IX-71 (982)
IX. BASIC STATISTICS QUESTIONS 9.19. A set of measurements is arranged in order of magnitude with a frequency associated with each measurement. This action describes: a. b. c. d.
A grouped frequency distribution A cumulative frequency distribution An ungrouped frequency distribution A histogram
9.24. When performing calculations on sample data: a. The cumulative relative frequency graph that is often used is called a histogram b. Rounding the data has no effect on the mean and standard deviation c. Coding the data has no effect on the mean and standard deviation d. Coding and rounding affect both the mean and standard deviation 9.28. The distribution of a characteristic is negatively skewed. The sampling distribution of the mean for large samples is: a. b. c. d.
Negatively skewed Approximately normal Positively skewed Lognormal
Answers: 9.19. c, 9.24. d, 9.28. b
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IX-72 (983)
IX. BASIC STATISTICS QUESTIONS 9.31. Defining the sample space S as {rock, book, cigar, guitar, dog}, what is the complement of {cigar, dog}? a. b. c. d.
{rock, book, cigar, guitar, dog} {cigar, guitar, dog} {dog} {rock, book, guitar}
9.32. The hypergeometric distribution should be used instead of the binomial distribution when: a. b. c. d.
There are more than 2 outcomes on a single trial Each trial is independent Sampling does not involve replacement There is a fixed number of trials
9.34. A sample of n observations has a mean X-bar and standard deviation Sx > 0. If a single observation, which equals the value of the sample mean X-bar is removed from the sample, which of the following is true? a. b. c. d.
X 6 and Sx both change X 6 and Sx remain the same X 6 remains the same but Sx increases X 6 remains the same but Sx decreases
Answers: 9.31. d, 9.32. c, 9.34. c
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X. STATISTICAL APPLICATIONS
A STATE OF STATISTICAL CONTROL IS NOT A NATURAL STATE FOR A MANUFACTURING PROCESS. IT IS INSTEAD AN ACHIEVEMENT, ARRIVED AT BY ELIMINATING ONE BY ONE, BY DETERMINED EFFORT, THE SPECIAL CAUSES OF EXCESSIVE VARIATION. W. EDWARDS DEMING
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X. STATISTICAL APPLICATIONS SPC / OBJECTIVES AND BENEFITS
Statistical Applications Statistical Applications are reviewed in two topic areas:
C Statistical process control C Process and performance capability
Statistical Process Control (SPC) Statistical Process Control (SPC) is presented in the following topic areas:
C C C C C C C C
Objectives and benefits Common and special causes Selection of variable Rational subgrouping Control charts Control chart analysis Pre-control charts Short-run SPC
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X-2 (986)
X. STATISTICAL APPLICATIONS SPC / OBJECTIVES AND BENEFITS
Objectives and Benefits Statistical process control (SPC) is a technique for applying statistical analysis to measure, monitor, and control processes. The major component of SPC is the use of control charting methods. The basic assumption made in SPC is that all processes are subject to variation. This variation may be classified as one of two types, chance cause variation and assignable cause variation. When assignable cause variation does occur, the statistical analysis facilitates identification of the source so it can be eliminated. Statistical process control also provides the ability to determine process capability, monitor processes, and identify whether the process is operating as expected, or whether the process has changed and corrective action is required.
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X-4 (987)
X. STATISTICAL APPLICATIONS SPC / COMMON AND SPECIAL CAUSES
Common and Special Causes An important consideration, on the road to process improvement, is the differentiation between special and common causes. Refer to the Figure on the left. When the circled special (bad) events occur, most of the available company resources converge on the process, fix the problem, and then go back to sleep.
A process improvement team is required to investigate the reasons for the multitudes of chance causes, and to recommend an improved system. The resulting performance chart might look like the figure on the right. It appears that the process has been improved, and it is both better and sustainable at the lower rate.
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X-5 (988)
X. STATISTICAL APPLICATIONS SPC / COMMON AND SPECIAL CAUSES
Common and Special Causes (Continued) One of the best ways to illustrate what happens when a stable system is inappropriately adjusted is the Nelson funnel. A moveable funnel is placed over a grid and a ball is dropped through the funnel creating a “mark.” LIFE EXAMPLES
C WORKERS TWEAKING THE MACHINE C MANAGERS TAMPERING WITH WORKER PERFORMANCE
LIFE EXAMPLES
LIFE EXAMPLES
C US TAX POLICY
C WORKER TRAINING WORKER
C SOME CORPORATE “ RIGHT SIZING”
C USING PAINT MATCHES FROM PRIOR RUN C SOME CORPORATE CULTURES
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X-7 (989)
X. STATISTICAL APPLICATIONS SPC / SELECTION OF VARIABLE
Selection of Variable Given the benefits of control charting, one might be tempted to control chart every characteristic or process variable. The risk of charting many parameters is that the operator will spend so much time and effort completing the charts, that the actual process becomes secondary. Some considerations for the selection of a control chart variable include:
C C C C C C C C C C C C
Items that protect human safety Items that protect the environment or community Items that are running at a high defective rate Key process variables that impact the product Major sources of customer complaints Items that show adherence to applicable standards Items that are requested by key customers Variables that have caused processing difficulties Variables that can be measured by the operator Items that can be counted by the person charting Items that contribute to high internal costs Variables that help control the process
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X-7 (990)
X. STATISTICAL APPLICATIONS SPC / SELECTION OF VARIABLE
Selection of Variable (Continued) In an ideal case, one process variable is so critical that it is indicative of the process as a whole. Key process input variables (KPIVs) may be analyzed to determine the degree of their effect on a process. Key process output variables (KPOVs) are ideal for determining process capability and for process monitoring using control charts.
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X-8 (991)
X. STATISTICAL APPLICATIONS SPC / RATIONAL SUBGROUPING
Rational Subgrouping A control chart provides a statistical test to determine if the variation from sample-to-sample is consistent with the average variation within the sample. The key idea in the Shewhart control chart is the division of observations into what are called rational subgroups. The success of charting depends in large measure on the selection of these subgroups. Generally, subgroups are selected in a way that makes each subgroup as homogeneous as possible, and that gives the maximum opportunity for variation from one subgroup to another. In production control charting, it is very important to maintain the order of production.
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X-8 (992)
X. STATISTICAL APPLICATIONS SPC / RATIONAL SUBGROUPING
Rational Subgrouping (Continued) Where order of production is used as a basis for subgrouping, two fundamentally different approaches are possible:
C The first subgroup consists of product produced as nearly as possible at one time. This method follows the rule for selection of rational subgroups by permitting a minimum chance for variation within a subgroup and a maximum chance for variation from subgroup to subgroup. C Another subgroup option consists of product intended to be representative of all the production over a given period of time. Product may accumulate at the point of production, with a random sample chosen from all the product made since the last sample. The choice of subgroup size should be influenced, in part, by the desirability of permitting a minimum chance for variation within a subgroup.
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X-9 (993)
X. STATISTICAL APPLICATIONS SPC / RATIONAL SUBGROUPING
Sources of Variability Much of the discussion of process capability will concentrate on the analysis of sources of variability. It is therefore worthwhile to consider the possible sources of variation in a manufactured product.
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X. STATISTICAL APPLICATIONS SPC / RATIONAL SUBGROUPING
Breakdown of Variation
X-10 (994)
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X-11 (995)
X. STATISTICAL APPLICATIONS SPC / CONTROL CHARTS
Control Charts Control charts are the most powerful tools to analyze variation in most processes - either manufacturing or administrative. Control charts were originated by Walter Shewhart (1931). A process which is in statistical control is characterized by plot points that do not exceed the upper or lower control limits. When a process is in control, it is predictable. There are many variations of possible control charts. The two primary types are variables and attributes.
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X-11 (996)
X. STATISTICAL APPLICATIONS SPC / CONTROL CHARTS
Control Charts for Variables Plots specific measurements of a process characteristic (temperature, size, weight, sales volume, shipments, etc.).
Types C C C C C C C C C
X 6 - R charts (when data is readily available) Run charts (limited single point data) MX 6 - MR charts (moving average/moving range) X - MR charts (or I - MR charts) (limited data) X 6 - s charts (when sigma is readily available) Median charts CuSum charts (cumulative sum) Moving average EWMA charts (exponentially weighted moving average)
Charts for variables are costly since each measured variable must have data gathered and analyzed. This is also the reason they are the most valuable and useful.
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X-11 (997)
X. STATISTICAL APPLICATIONS SPC / CONTROL CHARTS
Control Charts for Attributes Control charts for attributes plot a general measurement of the total process (the number of complaints per order, number of orders on time, absenteeism frequency, number of errors per letter, etc.).
Types C C C C
p charts (fraction defective) np charts (number of defectives) c charts (number of defects) u charts (number of defects per unit)
In some cases, the relatively larger sample sizes associated with attribute charts can prove to be expensive. There are short run varieties of these four types.
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X-12 (998)
X. STATISTICAL APPLICATIONS SPC / CONTROL CHARTS
and R Chart Terms n
Sample size (subgroup size)
X
A reading (the data) Average of readings in a sample Average of all the s. It is the value of the central line on the chart.
R
The range. The difference between the largest and smallest value in each sample. Average of all the Rs. It is the value of the central line on the R chart.
UCL Upper and lower control limits. The control LCL boundaries for 99.73 % of the population. They are not specification limits.
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X-12 (999)
X. STATISTICAL APPLICATIONS SPC / CONTROL CHARTS
Typical
- R Control Chart
20.5 UCLX = 20.0
20.0 19.5
X Average
19.0
X = 18.9
18.5 18.0
LCLX = 17.8
17.5 1
5
10
15
20
25
30
4.5 4.0
R Range
UCLR = 4.0
3.5 3.0 2.5 2.0
R = 1.9
1.5 1.0 0.5 LCLR = 1.9
0 1
5
10
15
20
25
30
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X-13 (1000)
X. STATISTICAL APPLICATIONS SPC / CONTROL CHARTS
- R Charts Control Limits
- R Charts Factors n
A2
D3
D4
d2
2
1.88
0
3.27
1.13
3
1.02
0
2.57
1.69
4
0.73
0
2.28
2.06
5
0.58
0
2.11
2.33
6
0.48
0
2.00
2.53
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X. STATISTICAL APPLICATIONS SPC / CONTROL CHARTS
- R Control Charts
X-15 (1001)
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X-16 (1002)
X. STATISTICAL APPLICATIONS SPC / CONTROL CHARTS
X-Bar and Sigma Charts X-bar ( ) and sigma (S) charts are often used for increased sensitivity to variation (especially when larger sample sizes are used). These charts may be more difficult to work with manually than the - R charts due to the tedious calculation of the sample standard deviation (S). Often, S comes from automated process equipment so the charting process is much easier. The control limit for the average chart formulas are:
The control limits for the sigma (S) chart are calculated using the following formulas and table:
is the average sample standard deviation and is the centerline of the sigma chart.
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X-16 (1003)
X. STATISTICAL APPLICATIONS SPC / CONTROL CHARTS
Sigma Chart Factors n
2
3
4
5
6
7
8
9
10
25
B4 3.27 2.57 2.27 2.09 1.97 1.88 1.82 1.76 1.72 1.44 B3
*
*
*
*
0.03 0.12 0.18 0.24 0.28 0.56
A3 2.66 1.95 1.63 1.43 1.29 1.18 1.10 1.03 0.98 0.61 *The lower control limit for a sigma chart when (n) is less than 6 is zero.
X-17 (1004)
© QUALITY COUNCIL OF INDIANA CQE 2006
X. STATISTICAL APPLICATIONS SPC / CONTROL CHARTS
Capability from X ¯ -S Charts The estimated standard deviation, called sigma hat, can be calculated by: s σˆ = C4 If both and S charts are in control, and the individual measurements are normally distributed, process capability can be assessed. n
2
3
4
5
6
7
8
9
10
C4 0.798 0.886 0.921 0.940 0.952 0.959 0.965 0.969 0.973
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X-17 (1005)
X. STATISTICAL APPLICATIONS SPC / CONTROL CHARTS
Median Control Charts There are several varieties of median control charts. One type plots only the individual measured data on a single chart. The middle value is circled. Median charts may use an odd number of readings to make the median value more obvious. Another variety records the data and plots the median value and range on two separate charts. Minimal calculations are needed for each subgroup. The control limits for the median chart are calculated using the same formulas as the - R chart:
The values are somewhat different than the A 2 values for the - R chart since the median is less efficient and therefore exhibits more variation. n
2
3
4
5
6
1.88 1.19 0.80 0.69 0.55
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X-17 (1006)
X. STATISTICAL APPLICATIONS SPC / CONTROL CHARTS
Median Control Charts (Continued) The range factors (D3 and D4) and process standard deviation factor (d2) are the same as used for the - R chart. The specific advantages of a median chart are:
C It is easy to use and requires fewer calculations C It shows the process variation C It shows both the median and the spread
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X-18 (1007)
X. STATISTICAL APPLICATIONS SPC / CONTROL CHARTS
MX 6 -MR Charts MX 6 -MR (moving average-moving range) charts are used where data is less readily available. An example for n = 3 is shown below. Control limits are calculated using the X 6 -R formulas and factors.
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X-20 (1008)
X. STATISTICAL APPLICATIONS SPC / CONTROL CHARTS
X-MR Charts Control charts plotting individual data points on one graph and a moving range on another (similar to X-barR) are the most common and most applicable charts for calibration and testing. Usually single data are measured for each required point. The X-MR chart (for individuals and moving ranges) is the only control chart which may have specification limits shown. However, there are some drawbacks in the interpretation and use of X-MR charts:
C All interpretation is faulty if the data is not normal C X-MR charts do not separate piece to piece repeatability of the process C Averages and limits can have wide variability until 80100 readings are taken C X-MR charts are not as sensitive to process changes as the X 6 -R chart
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X-20 (1009)
X. STATISTICAL APPLICATIONS SPC / CONTROL CHARTS
X-MR Charts (Continued) The control limits for the X-MR charts are calculated using the formulas and factor table below.
n
2
3
4
5
D4
3.27
2.57
2.28
2.11
D3
0
0
0
0
E2
2.66
1.77
1.46
1.29
The control limits for the range chart are calculated exactly as for the X 6 -R chart.
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X-21 (1010)
X. STATISTICAL APPLICATIONS SPC / CONTROL CHARTS
X - MR Chart Example Product Name Apple Strudel Variable Stick Weights 1 2 3
Process Line A Specification Limit 4 5 6 7 8 9
Chart No. 7 Operator you T85, High 88, Low 82 Grams Units of Measure 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25
Measurement
95
UCL = 94.4
90 X = 85.4
85 80
LCL = 76.4
75
Range
15
5 0
Date Time
UCL=11.1
10
MR = 3.4 1 2 3 4/16/03
4
5
6
7
8
9
LCL = 0 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25
1 2 3 Sample 4 Measurements 5 Measurement, X 85 87 86 86 77 83 84 87 90 84 89 82 84 86 88 85 90 83 84 87 87 Range, R 2 1 0 9 6 1 3 3 6 5 7 2 2 2 3 5 7 1 3 0 Notes
X = 85.4 MR = 3.4
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X-22 (1011)
X. STATISTICAL APPLICATIONS SPC / CONTROL CHARTS
CuSum Control Charts Cumulative sum (CuSum) control charts have been shown to be more efficient in detecting small shifts in the mean of a process than Shewhart charts. They are better to detect 2 sigma or less shifts in the mean. To create a CuSum chart, collect m sample groups, each of size n, and compute the mean of each sample. Determine Sm or S'm from the following equations:
Where :0 is the estimate of the in-control mean and F 6X is the known (or estimated) standard deviation of the sample means. The CuSum control chart is formed by plotting Sm or S'm as a function of m. If the process remains in control, centered at :0, the CuSum plot will show variation in a random pattern centered about zero. A visual procedure proposed by Barnard, known as the V-Mask, may be used to determine whether a process is out of control. A V-Mask is an overlay V shape that is superimposed on the graph of the cumulative sums. As long as all the previous points lie between the sides of the V, the process is in control.
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X-22 (1012)
X. STATISTICAL APPLICATIONS SPC / CONTROL CHARTS
CuSum Control Charts (Continued) The behavior of the V-Mask is determined by the distance k (which is the slope of the lower arm) and the rise distance h. Note that we could also specify d and the vertex angle (or, as is more common in the literature, q = 1/2 the vertex angle). For an alpha and beta design approach, we must specify:
C ", the probability of concluding that a shift in the process has occurred, when in fact it did not. C $, the probability of not detecting that a shift in the process mean has, in fact, occurred. C * (delta), the detection level for a shift in the process mean, expressed as a multiple of the standard deviation of the data points. Assume a process has an estimated mean of 5.000 with h set at 2 and k at 0.5. As h and k are set to smaller values, the V-Mask becomes sensitive to smaller changes in the process average. Consider the following 16 data points, each of which is average of 4 samples (m=16, n=4).
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X-23 (1013)
X. STATISTICAL APPLICATIONS SPC / CONTROL CHARTS
CuSum Control Charts (Continued) The CuSum control chart with 16 data groups and shows the process to be in control.
If data collection is continued until there are 20 data points (m=20, n=4), the CuSum control chart shows the process shifted upward, as indicated by data points 16, 17 and 18 below the lower arm of the V-Mask.
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X-25 (1014)
X. STATISTICAL APPLICATIONS SPC / CONTROL CHARTS
Moving Average Past data may be summarized by computing the mean of successive sets of data. Single moving average is a method of smoothing the data and is then used as an estimate of future values. Single moving average is:
X are individual data values, t is the current time period, and N is the moving group size Moving average is best used when the process mean is stable, but is a poor predictor when the process exhibits trends.
Single Moving Average with N = 3
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X-26 (1015)
X. STATISTICAL APPLICATIONS SPC / CONTROL CHARTS
Exponentially Weighted Moving Average (EWMA) The exponentially weighted moving average (EWMA) is a statistic for monitoring a process by averaging the data in a way that gives less and less weight to data as they are further removed in time. By the choice of a weighting factor, 8, the EWMA control procedure can be made sensitive to a small or gradual drift in the process. The statistic that is calculated is: EWMA t = 8 Y t + ( 1- 8 ) EWMA t-1 for t = 1, 2, ..., n
C EWMA 0 is the mean of historical data (target) C Y t is the observation at time t C n is the number of observations to be monitored, including EWMA 0 C 0 < 8 # 1 is a constant that determines the depth of memory of the EWMA The parameter, 8 determines the rate at which “older” data enters into the calculation of the EWMA statistic. A large value of 8 gives more weight to recent data and a small value of 8 gives more weight to older data. The value of 8 is usually set between 0.2 and 0.3 although this choice is somewhat arbitrary.
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X-26 (1016)
X. STATISTICAL APPLICATIONS SPC / CONTROL CHARTS
EWMA (Continued) The estimated variance of the EWMA statistic is approximately:
when t is not small, and where s is the standard deviation calculated from the historical data. The center line for the control chart is the target value or EWMA 0 . The control limits are: UCL = EWMA 0 + ks EWMA LCL = EWMA 0 - ks EWMA Where the factor k is either set equal to 3 or chosen using the Lucas and Saccucci tables. The data are assumed to be independent and these tables also assume a normal population.
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X-27 (1017)
X. STATISTICAL APPLICATIONS SPC / CONTROL CHARTS
EWMA (Continued) Example: Parameters calculated from historical data: EWMA 0 = 50, s = 2.0539, and 8 = 0.3 UCL = 50 + 3 (0.4201)(2.0539) = 52.5884 LCL = 50 - 3 (0.4201) (2.0539) = 47.4115
EWMA Plot of Example Data The process is in control however, there seems to be a trend upwards for the last 5 sample periods. The EWMA is often superior to the CuSum charting technique for detecting “larger” shifts.
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X-29 (1018)
X. STATISTICAL APPLICATIONS SPC / CONTROL CHARTS
Attribute Charts An attribute chart plots characteristics. Attributes are discrete, counted data. Unlike variables charts, only one chart is plotted for attributes. There are four types of attribute charts, as summarized below: Chart p np
Records Fraction Defective
Subgroup size Varies
Number of Defectives
Constant
c
Number of Defects
Constant
u
Number of defects per unit
Varies
Percent Defectives
Varies
100p*
The best use of an attribute chart is to:
C Follow trends and cycles C Evaluate any change in the process * The p chart reflected in percentage.
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X-29 (1019)
X. STATISTICAL APPLICATIONS SPC / CONTROL CHARTS
Attribute Charts (Continued) Key points to consider when using attribute charts:
C Normally the subgroup size is greater than 50 (for p charts). C The average number of defects/defectives is equal to or greater than 4 or 5. C If the actual p chart subgroup size varies by more than ± 20 % from the average subgroup size, the data point must either be discarded or the control limits calculated for the individual point. C The most sensitive attribute chart is the p chart. The most sensitive and expensive chart is the - R. C The defects and defectives plotted in attribute charts are often categorized in Pareto fashion to determine the vital few. To actually reduce the defect or defective level, a fundamental change in the system is often necessary.
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X-30 (1020)
X. STATISTICAL APPLICATIONS SPC / CONTROL CHARTS
Attribute Chart Formulas Defectives (Binomial Distribution) p Chart %Defectives
np Chart Defectives
k = number of samples Defects (Poisson Distribution) u Chart Average Number of Defects
c Chart Number of Defects
k = number of samples Sample Size Varies
Sample Size Fixed
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X. STATISTICAL APPLICATIONS SPC / CONTROL CHARTS
p Chart Example
Note the change at plot point 15.
X-32 (1021)
© QUALITY COUNCIL OF INDIANA CQE 2006
X-34 (1022)
X. STATISTICAL APPLICATIONS SPC / CONTROL CHARTS
np Chart Example p
Attributes Control Chart Form SPC Checklist
: Encyclopedia PART DESCRIPTION: Binding Department SOURCE: UCL: LCL:
np
c
OPERATOR: 0
u Any Defective
CHARACTERISTIC:
INSPECTOR:
DATE: You
9/25 - 10/1
AVERAGE:
14 12 UCL np = 10.7 10 8 6 np = 4.5
4 2 LCLnp= 0
0 1 Sample (n) Number (np,c) 9 Fraction %(p,u) Date/ 9 Time 25 Notes
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
4
5
2
3
2
8
4
3
2
3
4
8
6
100 Units Fixed 6
7
3
4
6
3
3
3
4
4
6
10 1
© QUALITY COUNCIL OF INDIANA CQE 2006
X-36 (1023)
X. STATISTICAL APPLICATIONS SPC / CONTROL CHARTS
c Chart Example p
Attributes Control Chart Form SPC Checklist
: Encyclopedia PART DESCRIPTION: Binding Department SOURCE: UCL: LCL:
np
c
CHARACTERISTIC:
OPERATOR: 0
u Defects
DATE: You
INSPECTOR:
10/1
AVERAGE:
14 12 UCL = 11 10 8 6 4 2 LCL = 0
0 1 Sample (n) Number (np,c) 5 Fraction %(p,u) Date/ 10 Time 1 Notes
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
1
9
6
7
7
4
7
1
6
5
4
One Fixed Standard Sample 8
7
5
7
3
3
4
2
2
3
3
2
3
c = 4.6 Shift Change
Is the shift between plot points 15 and 16 significant?
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X-37 (1024)
X. STATISTICAL APPLICATIONS SPC / CONTROL CHARTS
Out-of-control If a process is “out-of-control,” then special causes of variation are present in either the average chart or range chart, or both. These special causes must be found and eliminated in order to achieve an in-control process. A process out-of-control is detected on a control chart either by having any points outside the control limits or by unnatural patterns of variability.
± 1S = 68.26 %
Upper Control Limit
± 2S = 95.46 %
Grand Average
± 3S = 99.73 % Lower Control Limit
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X-37 (1025)
X. STATISTICAL APPLICATIONS SPC / CONTROL CHARTS
Out-of-control (Continued) Because there are two components to every control chart -- the average chart and the range chart -- four possible conditions could occur in the process. 1. Average Range
Out-of-Control In-Control
2. Average Range
In-Control Out-of-Control
3. Average Range
Out-of Control Out-of-Control
4. Average Range
In-Control In-Control
Process Out-of-Control
Process In-Control
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X-38 (1026)
X. STATISTICAL APPLICATIONS SPC / CONTROL CHARTS
1. Average Out-of-control Average Shifting Variation Stable
2. Variation Out-of-control Average Stable Variation Changing
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X-39 (1027)
X. STATISTICAL APPLICATIONS SPC / CONTROL CHARTS
3. Average & Variation Out-of-control Average Shifting Variation Changing
4. Process In-control Average Stable Variation Stable
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X-40 (1028)
X. STATISTICAL APPLICATIONS SPC / CONTROL CHARTS
Control Chart Interpretation Five Common Rules
Other Unusual Patterns
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X-41 (1029)
X. STATISTICAL APPLICATIONS SPC / CONTROL CHARTS
Process In-control with Chance Variation
This is an example of a process which is in-control. Notice that it looks good, but not too good.
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X-41 (1030)
X. STATISTICAL APPLICATIONS SPC / CONTROL CHARTS
Trends
X CHART CAUSES
C Deterioration of machine C Tired operator C Tool wear
R CHART CAUSES
C Change in operator skill C Tired operator C Change in incoming material quality
CORRECTIVE ACTION
C C C C C
Repair or use alternate machine if available Discuss operation with operator to find cause Rotate operator Change, repair, or sharpen tool Investigate material
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X-42 (1031)
X. STATISTICAL APPLICATIONS SPC / CONTROL CHARTS
Jumps in Process Level
X
C C C C
CHART CAUSES
Changes in proportions of materials coming from different sources New operator or machine Modification of production method or process Change in inspection device or method
R CHART CAUSES
C C C C
CORRECTIVE ACTION
C C C C C
Keep material supply consistent Investigate source of material Check out machine capability Examine operator methods and instruction Check calibration of measurement device
Change in material Change in method Change in operator Change in inspection
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X-42 (1032)
X. STATISTICAL APPLICATIONS SPC / CONTROL CHARTS
Recurring Cycles
X CHART CAUSES
R CHART CAUSES
C Physical environment C Temperature C Humidity C Tired operator C Regular rotation of machine or operator
C Scheduled maintenance C Tired operator C Tool wear
CORRECTIVE ACTION
C C C C C
If environment is controllable, adjust it Service equipment Rotate operators Evaluate machine maintenance Replace, sharpen, or repair tool
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X-43 (1033)
X. STATISTICAL APPLICATIONS SPC / CONTROL CHARTS
Points Near or Outside Limits
R CHART CAUSES
X CHART CAUSES C C C
Over control Large systematic differences in material quality Large systematic differences in test methods or equipment
C
Mixture of material of distinctly different quality
CORRECTIVE ACTION
C C C C C
Check control limits Investigate material variation Evaluate test procedures Evaluate inspection frequency or methods Eliminate operator over adjustment of the process
© QUALITY COUNCIL OF INDIANA CQE 2006
X-43 (1034)
X. STATISTICAL APPLICATIONS SPC / CONTROL CHARTS
Lack of Variability
R CHART CAUSES
X CHART CAUSES C C C
Incorrect calculation of control limits Improvement in process since limits were calculated Employee may not be making checks
C
C
Collecting in each sample a number of measurements from widely differing lots Improvement in process since limits were calculated
CORRECTIVE ACTION
C C C C C
Check control limits Validate rational sample subgroupings Verify checking procedure, gages, etc. Verify proper employee measurement Congratulate someone for improvement
© QUALITY COUNCIL OF INDIANA CQE 2006
X-44 (1035)
X. STATISTICAL APPLICATIONS SPC / CONTROL CHARTS
Runs Test for Randomness A run is a sequence of data that exhibit the same characteristic. The subject of time sequence analysis can apply to both variable and attribute data. To perform a runs test the following sequence should be followed: 1.
Determine the value of n1 and n 2 (either the total of two attributes or the readings above and below the center line on a run or control chart).
2.
Determine the number of runs (R).
3.
Consult a critical value table or calculate a test statistic (Refer to the non-parametric runs test).
© QUALITY COUNCIL OF INDIANA CQE 2006
X-44 (1036)
X. STATISTICAL APPLICATIONS SPC / CONTROL CHARTS
Critical Value Table for Number of Runs Consult the Critical Value Table below for the expected numbers of runs. Note that the expected number of runs can be approximated by adding the smallest and largest values together and dividing by two. n 1 +n 2 Plotted Points 8 10 12 14 16 18 20 22 24 26 28 30 34 40 50
Smallest Run Limit 1 2 3 3 4 5 6 7 7 8 9 10 11 14 20
Average # Runs 5 6 7 8 9 10 11 12 13 14 15 16 18 21 26
Largest Run Limit 9 (not possible) 10 11 13 14 15 16 17 19 20 21 22 25 28 32
© QUALITY COUNCIL OF INDIANA CQE 2006
X-45 (1037)
X. STATISTICAL APPLICATIONS SPC / CONTROL CHARTS
Runs Test Example 11 10 9 8 7 6 5
5
10
15
20
24
For the 24 plot points, one should expect between 8 and 18 total runs. Since there are 5 runs, one can say with 95% confidence that non-random variation exists.
© QUALITY COUNCIL OF INDIANA CQE 2006
X-46 (1038)
X. STATISTICAL APPLICATIONS SPC / PRE-CONTROL CHARTS
The Pre-Control Technique An easy method of controlling the process average is known as “pre-control.” Pre-control was developed in 1954 by a group of consultants (including Dorin Shainin) in an attempt to replace the control chart. Pre-control is most successful with processes which are inherently stable and not subject to rapid process drifts once they are set up. Pre-control cannot only act as a guide in setting process aim, but can also be used to monitor the continuing process. The idea behind pre-control is to divide the total tolerance into zones. The two boundaries within the tolerance are called precontrol lines. The location of these lines is halfway between the center of the specification and specification limits. It can be shown that 86 % of the parts will be inside the P-C lines with 7 % in each of the outer sections, if the process is normally distributed and the Cpk = 1. Usually, the process will occupy much less of the tolerance range, so this extreme case will not apply.
© QUALITY COUNCIL OF INDIANA CQE 2006
X-46 (1039)
X. STATISTICAL APPLICATIONS SPC / PRE-CONTROL CHARTS
A Pre-Control Schematic
The chance that two parts in a row will fall outside either P-C line is 1/7 (0.14) times 1/7 (0.14), or 1/49. This means that only once in every 49 pieces can one expect to get two pieces in a row outside the P-C lines just due to chance. There is a much greater chance (48/49) that the process has shifted.
© QUALITY COUNCIL OF INDIANA CQE 2006
X-47 (1040)
X. STATISTICAL APPLICATIONS SPC / PRE-CONTROL CHARTS
Pre-Control Rules C Set-up: The job is OK to run if five pieces in a row are inside the target C Running: Sample two consecutive pieces: C If the first piece is within target, run (don’t measure the second piece) C If the first piece is not within target, check the second piece C If the second piece is within target, continue to run C If both pieces are out of target, adjust the process, go back to set up C Any time a reading is out-of-specification, stop and adjust The ideal frequency of sampling is 25 checks until a reset is required. Sampling can be relaxed if the process does not need adjustment in greater than 25 checks. Sampling must be increased if the opposite is true. To make pre-control even easier to use, gauges for the target area may be painted green. Yellow is used for the outer zones and red for out-ofspecification.
© QUALITY COUNCIL OF INDIANA CQE 2006
X-47 (1041)
X. STATISTICAL APPLICATIONS SPC / PRE-CONTROL CHARTS
Pre-Control Advantages The advantages of pre-control include:
C Shifts in process centering or increases in process spread can be detected C The % non-conforming product will not exceed a pre-determined level C No recording, calculating or plotting is required C Attribute or visual characteristics can be used C Can serve as a set-up plan for short runs C The specification tolerance is used directly C Very simple instructions are needed for operators
© QUALITY COUNCIL OF INDIANA CQE 2006
X-47 (1042)
X. STATISTICAL APPLICATIONS SPC / PRE-CONTROL CHARTS
Pre-Control Disadvantages The disadvantages of pre-control include:
C There is no permanent paper record of adjustments C Subtle changes in process capability cannot be calculated C It will not work for an unstable process C It will not work effectively if the process spread exceeds the tolerance
© QUALITY COUNCIL OF INDIANA CQE 2006
X-48 (1043)
X. STATISTICAL APPLICATIONS SPC / SHORT-RUN SPC
Short Run SPC Most traditional SPC techniques require long, reasonably stable production runs. Short run charting may be desirable when the production lot size is extremely small (10-20) pieces or when the sample size, under typical operating conditions, is small. Two limited data charts have already been discussed: X - MR Charts M - MR Charts Various techniques have been suggested by a number of authors. However, the recommendations of some are not without controversy. The emphasis has been on short runs and multiple variables per chart, as this is increasingly the greatest need in an era of customization. An example is illustrated in the Primer.
© QUALITY COUNCIL OF INDIANA CQE 2006
X-53 (1044)
X. STATISTICAL APPLICATIONS CAPABILITY / CAPABILITY STUDIES
Process and Performance Capability Process and Performance Capability is presented in the following topic areas:
C C C C
Capability studies Performance vs. specifications Capability indices Performance indices
© QUALITY COUNCIL OF INDIANA CQE 2006
X-53 (1045)
X. STATISTICAL APPLICATIONS CAPABILITY / CAPABILITY STUDIES
Process Capability Studies The determination of process capability requires a predictable pattern of statistically stable behavior. A capable process is a process whose spread on the bellshaped curve is narrower than the tolerance range or specification limits. USL is the upper specification limit and LSL is the lower specification limit.
A process capability study includes three steps:
C Planning for data collection C Collecting data C Plotting and analyzing the results
© QUALITY COUNCIL OF INDIANA CQE 2006
X-54 (1046)
X. STATISTICAL APPLICATIONS CAPABILITY / CAPABILITY STUDIES
Process Capability Studies (Continued) The objective of process quality control is to establish a state of control over the manufacturing process and then maintain that state of control through time. When the natural process limits are compared with the specification range, any of the following possible courses of action may result:
C Do nothing. If the process limits fall well within the specification limits, no action may be required. C Change the specifications. The specification limits may be unrealistic. C Center the process. An adjustment to the centering of the process may bring the bulk of the product within specifications. C Reduce variability. This is often the most difficult option to achieve. C Accept the losses. In some cases, management must be content with a high loss rate.
© QUALITY COUNCIL OF INDIANA CQE 2006
X-54 (1047)
X. STATISTICAL APPLICATIONS CAPABILITY / CAPABILITY STUDIES
Process Capability Studies (Continued) Other capability applications:
C C C C C C
Provide set-up-data for a variables control chart Evaluate new equipment Review tolerances based on process variation Assign more capable equipment to tougher jobs Perform routine process performance audits Determine the effects of adjustments (Juran, 1999)
© QUALITY COUNCIL OF INDIANA CQE 2006
X-55 (1048)
X. STATISTICAL APPLICATIONS CAPABILITY / CAPABILITY STUDIES
Machine Capability Machine capability is a measure of the inherent best short-term capability of a machine or process. The calculations for machine capability are exactly as discussed previously for process capability with a few exceptions:
C Historical data from a control chart should not be used. Other forms of variation may be included in this data. C If multiple machines are producing the same part, then the capability of each machine should be determined independently. C Machine capability should come from consecutive part measurements from the same machine at or near the same time (perhaps 20 to 40 parts).
© QUALITY COUNCIL OF INDIANA CQE 2006
X-55 (1049)
X. STATISTICAL APPLICATIONS CAPABILITY / CAPABILITY STUDIES
Machine Capability (Continued) What normally results from a machine capability study is:
What a machine capability study is trying to determine is the inherent process (machine) variation by excluding elements like batch-to batch, stream-to-stream, and time-to-time variation and trying to minimize the measurement factors (operator and equipment), pieceto-piece variation, and within piece variation. This can never truly be achieved, but can be approximated.
© QUALITY COUNCIL OF INDIANA CQE 2006
X-56 (1050)
X. STATISTICAL APPLICATIONS CAPABILITY / CAPABILITY STUDIES
Process Performance vs. Specifications In the figure below, one can see that the control limits are determined by process average values. One can also see the process spread of the individual values. This process spread can be predicted, and will indicate the range of the individuals being produced.
If the R-bar is known from a control chart, then:
© QUALITY COUNCIL OF INDIANA CQE 2006
X-57 (1051)
X. STATISTICAL APPLICATIONS CAPABILITY / PERFORMANCE VS. SPECIFICATION
Calculating Performance vs. Specification All processes are not centered. For this reason, the customer may want to know the Cpk, since this calculation takes centerness into account.
Aim
© QUALITY COUNCIL OF INDIANA CQE 2006
X-58 (1052)
X. STATISTICAL APPLICATIONS CAPABILITY / PERFORMANCE VS. SPECIFICATION
The Normal Distribution When all special causes of variation are eliminated, many variable data processes, when sampled and plotted, produce a bell-shaped distribution. If the base of the histogram is divided into six (6) equal lengths (three on each side of the average), the amount of data in each interval exhibits the following percentages:
68.26%
95.46% :-3F
:-2F
:-1F
: 99.73%
:+1F
:+2F
:+3F
© QUALITY COUNCIL OF INDIANA CQE 2006
X-58 (1053)
X. STATISTICAL APPLICATIONS CAPABILITY / PERFORMANCE VS. SPECIFICATION
The Z Value The area outside of specification for a normal curve can be determined by a Z value.
The Z transformation formula is:
Where: x = Data value (The value of concern) : = Mean F = Standard deviation This transformation will convert the original values to the number of standard deviations away from the mean. The result allows one to use a standard normal table.
© QUALITY COUNCIL OF INDIANA CQE 2006
X-60 (1054)
X. STATISTICAL APPLICATIONS CAPABILITY / PERFORMANCE VS. SPECIFICATION
Z Value Examples To illustrate the z value, consider the following examples of typical 10th grade student weights. The weights are normally distributed with a mean : = 150 lbs and standard deviation F = 20.
© QUALITY COUNCIL OF INDIANA CQE 2006
X-60 (1055)
X. STATISTICAL APPLICATIONS CAPABILITY / PERFORMANCE VS. SPECIFICATION
Z Value Examples (Continued) Example: What is the probability of a student weighing more than 170 lbs.?
.1587
0
1
P(z=1 to + ∞) = 0.1587. 15.87 % of the students will weigh more than 170 lbs.
© QUALITY COUNCIL OF INDIANA CQE 2006
X-61 (1056)
X. STATISTICAL APPLICATIONS CAPABILITY / PERFORMANCE VS. SPECIFICATION
Z Value Examples (Continued) Example: What is the probability of a student weighing less than 100 lbs.?
100
150
Since the normal table has values about the mean, a Z value of - 2.5 can be treated as 2.5. P(z = - ∞ to -2.5) = 0.0062. That is, 0.62 % of the students will weigh less than 100 lbs.
© QUALITY COUNCIL OF INDIANA CQE 2006
X-61 (1057)
X. STATISTICAL APPLICATIONS CAPABILITY / PERFORMANCE VS. SPECIFICATION
Z Value Examples (Continued) Example: What is the probability a student weighing between 120 and 160 lbs?
120
150 160
The best technique to solve this problem using the standard normal table in this Primer would be to determine the tail area values, and to subtract them from the total probability of 1.
© QUALITY COUNCIL OF INDIANA CQE 2006
X-62 (1058)
X. STATISTICAL APPLICATIONS CAPABILITY / PERFORMANCE VS. SPECIFICATION
Z Value Examples (Continued) Example (Continued). First, determine the z value and probability below 120 lbs.
P(z = - ∞ to -1.5) = 0.0668 .0668
120
150
Second, determine the z value and probability above 160 lbs.
P(z = 0.5 to + ∞) = 0.3085
.3085
150 160
© QUALITY COUNCIL OF INDIANA CQE 2006
X-62 (1059)
X. STATISTICAL APPLICATIONS CAPABILITY / PERFORMANCE VS. SPECIFICATION
Z Value Examples (Continued) Example (Continued) Third, the total probability - below - above = probability between 120 and 160 lbs. 1 - 0.0668 - 0.3085 = 0.6247 Thus, 62.47 % of the students will weigh more than 120 lbs., but less than 160 lbs.
© QUALITY COUNCIL OF INDIANA CQE 2006
X-63 (1060)
X. STATISTICAL APPLICATIONS CAPABILITY / PERFORMANCE VS. SPECIFICATION
Process Capability from Control Charts Process capability (using Z value determinations) can be generated from a control chart as shown on Primer page X - 63.
© QUALITY COUNCIL OF INDIANA CQE 2006
X-64 (1061)
X. STATISTICAL APPLICATIONS CAPABILITY / CAPABILITY INDICES
Capability Index Failure Rates There is a direct link between the calculated Cp (and Pp values) with the standard normal (Z value) table. A Cp of 1.0 is the loss suffered at a Z value of 3.0 (doubled, since the table is one sided). Refer to the table below. Cp 0.33 0.67 1.00 1.10 1.20 1.30 1.33 1.40 1.50 1.60 1.67 1.80 2.00
Z value 1.00 2.00 3.00 3.30 3.60 3.90 4.00 4.20 4.50 4.80 5.00 5.40 6.00
ppm 317,311 45,500 2,700 967 318 96 63 27 6.8 1.6 0.57 0.067 0.002
© QUALITY COUNCIL OF INDIANA CQE 2006
X-64 (1062)
X. STATISTICAL APPLICATIONS CAPABILITY / CAPABILITY INDICES
Capability Index Failure Rates (Continued) In the prior table, ppm equals parts per million of nonconformance (or failure) when the process:
C C C C
Is centered on Has a two-tailed specification Is normally distributed Has no significant shifts in average or dispersion
When the Cp, Cpk, Pp, and Ppk values are 1.0 or less, Z values and the standard normal table can be used to determine failure rates. With the drive for increasingly dependable products, there is a need for failure rates in the Cp range of 1.5 to 2.0.
© QUALITY COUNCIL OF INDIANA CQE 2006
X-65 (1063)
X. STATISTICAL APPLICATIONS CAPABILITY / CAPABILITY INDICES
Process Capability Indices To determine process capability an estimation of sigma is necessary:
FR is an estimate of process capability sigma and comes from a control chart.
© QUALITY COUNCIL OF INDIANA CQE 2006
X-65 (1064)
X. STATISTICAL APPLICATIONS CAPABILITY / CAPABILITY INDICES
Process Capability Indices (Continued) The capability index is defined as:
As a rule of thumb:
The capability ratio is defined as:
As a rule of thumb:
© QUALITY COUNCIL OF INDIANA CQE 2006
X-66 (1065)
X. STATISTICAL APPLICATIONS CAPABILITY / CAPABILITY INDICES
Process Capability Indices (Continued) Cpk is the ratio giving the smallest answer between:
Example: For a process with = 12, FR = 2 an USL = 16 and LSL = 4, determine Cp and Cpk min:
© QUALITY COUNCIL OF INDIANA CQE 2006
X-66 (1066)
X. STATISTICAL APPLICATIONS CAPABILITY / CAPABILITY INDICES
Cpm Index The Cpm index is defined as:
Where: USL = Upper specification limit LSL = Lower specification limit : = process mean T = target value F = process standard deviation Cpm is based on the Taguchi index, which places more emphasis on process centering on the target.
© QUALITY COUNCIL OF INDIANA CQE 2006
X-67 (1067)
X. STATISTICAL APPLICATIONS CAPABILITY / PERFORMANCE INDICES
Cpm Index Exercise Example: For a process with : = 12, F = 2, T = 10, USL = 16 and LSL = 4, determine Cpm:
© QUALITY COUNCIL OF INDIANA CQE 2006
X-67 (1068)
X. STATISTICAL APPLICATIONS CAPABILITY / PERFORMANCE INDICES
Process Performance Indices To determine process performance an estimation of sigma is necessary:
Fi is a measure of total data sigma and generally comes from a calculator or computer. The performance index is defined as:
The performance ratio is defined as:
Ppk is the ratio giving the smallest answer between:
© QUALITY COUNCIL OF INDIANA CQE 2006
X-69 (1069)
X. STATISTICAL APPLICATIONS QUESTIONS 10.1. Which of the following charts have upper control limits, but frequently have lower control limits of zero? a. b. c. d.
X-bar and individual charts c charts and u charts p charts and np charts R and sigma charts
10.5. The spread of individual observations from a normal process capability distribution may be expressed numerically as: a. 6 /d2 b. 2 x A2 c. /d2 d. D4 10.6. Pre-control starts a process specifically centered between: a. b. c. d.
Process limits Specification limits Normal distribution limits Three sigma control limits
Answers: 10.1. d, 10.5. a, 10.6. b
© QUALITY COUNCIL OF INDIANA CQE 2006
X-70 (1070)
X. STATISTICAL APPLICATIONS QUESTIONS 10.10.
An
and R chart was prepared for an operation using twenty
samples with five pieces in each sample; was found to be 33.6 and was 6.20. During production, a sample of five was taken and the pieces measured 36, 43, 37, 25, and 38. At the time, this sample was taken: a. b. c. d.
Both the average and range were within control limits Neither the average nor range were within control limits Only the average was outside control limits Only the range was outside control limits
10.13.
a. b. c. d.
The X-bar control limits will be tighter The supervisor obviously wants some variety in control chart usage Only one control chart will be required The X-bar and S values will come automatically from a weight checker
10.14.
a. b. c. d.
A quality engineer wants to chart the package weights on a highly automated food processing line. The recommended control chart is an X-bar - S chart and not the typical X-bar - R chart, in wide use throughout the facility. The most logical reason for this switch is which of the following?
Select the INCORRECT statement. If the ODs of a certain bushing are normally distributed with a mean of 2.00", then the proportion of bushings with ODs greater than 1.90" is:
Greater than the proportion with ODs less than 1.90" Greater than the proportion with ODs less than 2.20" Greater than 50% Greater than the proportion with ODs greater than the median
Answers: 10.10. d, 10.13. d, 10.14. b
© QUALITY COUNCIL OF INDIANA CQE 2006
X-71 (1071)
X. STATISTICAL APPLICATIONS QUESTIONS 10.17.
a. b. c. d.
Given = 51.0, = 4.0, n = 5; assuming statistical control, what proportion of the population will meet specifications of 50 ± 3.0?
87% 88% 91% 93%
10.20.
a. b. c. d.
and R chart be
The machine capability is wider than the specification The machine capability is equal to the specification The machine capability is somewhat smaller than the specification The machine capability is very small compared to the specification
10.18.
a. b. c. d.
In which one of the following would the use of an the most helpful as a tool to control a process:
An and R chart with n=5 has been plotted for some time and has demonstrated random variation. Upon review of the last 30 plot points, the expected number of runs around the center line on the chart is expected to be approximately which of the following?
4 9 12 16
Answers: 10.17. c, 10.18. a, 10.20. d
© QUALITY COUNCIL OF INDIANA CQE 2006
X-72 (1072)
X. STATISTICAL APPLICATIONS QUESTIONS 10.26.
a. b. c. d.
±1.04 ±0.52 ±1.28 ±0.84
10.28.
a. b. c. d.
One looks at a process and notes that the chart for averages has been in control. If the range suddenly and significantly increases, the mean will:
Usually increase Stay the same Always decrease Occasionally show out of control of either limit
10.31.
a. b. c. d.
The lengths of a certain bushing are normally distributed with mean . How many standard deviation units symmetrical about will include 80% of the lengths?
During variable control charting a trend of four consecutive points is noted on both the average and range charts. The average chart is increasing and the range chart is decreasing. One may make which of the following conclusions?
No conclusions may be made yet The nominal measurement is increasing The variability is decreasing The process is improving
Answers: 10.26. c, 10.28. d, 10.31. a
© QUALITY COUNCIL OF INDIANA CQE 2006
XI-1 (1073)
XI. ADVANCED STATISTICS
MOST PEOPLE WOULD RATHER LIVE WITH A PROBLEM THEY CAN'T SOLVE, THAN ACCEPT A SOLUTION THEY CAN'T UNDERSTAND. R. E. D. WOOLSEY AND H. S. SWANSON
XI-2 (1074)
© QUALITY COUNCIL OF INDIANA CQE 2006
XI. ADVANCED STATISTICS STATISTICAL DECISION MAKING
Advanced Statistics Advanced Statistics is presented in the following topic areas: C C C C
Statistical decision making Analysis of variance (ANOVA) Relationships between variables Design and analysis of experiments
Statistical Decision Making Statistical Decision Making is presented in the following topic areas: C Point estimates C Confidence intervals C Hypothesis testing
C Paired-comparison tests C Goodness-of-fit tests C Contingency tables
© QUALITY COUNCIL OF INDIANA CQE 2006
XI-2 (1075)
XI. ADVANCED STATISTICS STATISTICAL DECISION MAKING
Statistical Inference The objective of statistical inference is to draw conclusions about population characteristics based on the information contained in a sample. The steps involved in statistical inference are: C Precisely define the problem objective C Formulate a null and an alternate hypothesis C Decide if the problem will be evaluated by a one-tail or two-tail test C Select a test distribution and a critical value for the test statistic C Calculate a test statistic from the sample C Make a inference by comparing the calculated and the critical values C Report the findings
XI-3 (1076)
© QUALITY COUNCIL OF INDIANA CQE 2006
XI. ADVANCED STATISTICS STATISTICAL DECISION MAKING / POINT ESTIMATES
Point Estimate for Population Mean In analyzing sample values to arrive at population probabilities, two major estimators are used: point estimates and confidence intervals. A point estimate of the population mean, μ, is the sample mean, X ¯. ∑X n
μ ≈ X=
i=1
i
n
Example: Given the following tensile strength readings from 4 piano wire segments: 28.7, 27.9, 29.2, and 26.5 psi, calculate the point estimation of the population mean. n
μ ≈ X=
∑X
i=1
n
i
=
28.7 + 27.9 + 29.2 + 26.5 = 28.08 psi 4
28.08 psi is the point estimate for the population mean.
XI-3 (1077)
© QUALITY COUNCIL OF INDIANA CQE 2006
XI. ADVANCED STATISTICS STATISTICAL DECISION MAKING / POINT ESTIMATES
Point Estimate for Population Variance The sample variance, s2, is the best point estimate of the population variance, σ2. The sample standard deviation, s, is the best point estimate of the population standard deviation, σ.
∑ ( X - X) n
s2 =
i=1
i
s=
σ2 =
n-1
∑ ( Xi - X ) n
i=1
n-1
n
2
∑ (X - μ)
i=1
i
N n
2
σ=
2
∑ (X - μ)
i=1
i
N
2
© QUALITY COUNCIL OF INDIANA CQE 2006
XI-4 (1078)
XI. ADVANCED STATISTICS STATISTICAL DECISION MAKING / CONFIDENCE INTERVALS
Confidence Interval for the Mean Continuous Data - σ Known The confidence interval of the population mean, μ, when the population standard deviation, σ, is known, is calculated using the sample mean, X ¯ , the population standard deviation, σ, the sample size, n, and the normal distribution. X - Z α/2
σX σ ≤ μ ≤ X + Z α/2 X n n
From sample data one can calculate the interval within which the population mean, μ, is predicted to fall. Confidence intervals are always estimated for population parameters. A confidence interval is a twotail event and requires critical values based on an alpha/2 risk in each tail.
© QUALITY COUNCIL OF INDIANA CQE 2006
XI-4 (1079)
XI. ADVANCED STATISTICS STATISTICAL DECISION MAKING / CONFIDENCE INTERVALS
Continuous Data - σ Unknown The confidence interval of the population mean, μ, when the population standard deviation, σ, is unknown, is calculated using the sample mean, X ¯ , the sample standard deviation, s, the sample size, n, and the t distribution. X - t α/2, n-1
s s ≤ μ ≤ X + t α/2, n-1 n n
Example: The average of 25 samples is 18 with a sample standard deviation of 6. Calculate the 95% confidence interval for the population mean. X - t α/2, n-1
18 - 2.064
s s ≤ μ ≤ X + t α/2, n-1 n n 6 6 ≤ μ ≤ 18 + 2.064 25 25
15.52 ≤ μ ≤ 20.48
© QUALITY COUNCIL OF INDIANA CQE 2006
XI-5 (1080)
XI. ADVANCED STATISTICS STATISTICAL DECISION MAKING / CONFIDENCE INTERVALS
Confidence Interval for Proportion For large sample sizes, with np and n(1-p) greater than or equal to 5, the binomial distribution can be approximated by the normal distribution to calculate a confidence interval for population proportion. p s - Z α/2
ps (1 - ps ) p (1 - ps ) ≤ p ≤ p s + Z α/2 s n n
ps = sample proportion, p = population proportion, n = sample size
XI-6 (1081)
© QUALITY COUNCIL OF INDIANA CQE 2006
XI. ADVANCED STATISTICS STATISTICAL DECISION MAKING / CONFIDENCE INTERVALS
Confidence Interval for Variance The confidence interval or interval estimate for the population variance, σ2, is given by:
( n - 1) s
2
≤ σ
X
Χ α/2, n - 1 2
2
≤
( n - 1) s
2 X
Χ 1 - α/2, n - 1 2
s2 = sample variance n = sample size n - 1 = degrees of freedom
Confidence Interval for Standard Deviation The confidence interval for the population standard deviation, σ, is given by:
( n - 1) s Χ α/2, n - 1 2
2 X
≤ σ ≤
( n - 1) s
2 X
Χ 1 - α/2, n - 1 2
© QUALITY COUNCIL OF INDIANA CQE 2006
XI-7 (1082)
XI. ADVANCED STATISTICS STATISTICAL DECISION MAKING / HYPOTHESIS TESTING
Hypothesis Testing Hypothesis testing is a type of statistical inference in which a null hypothesis and alternative hypothesis are stated. The null hypothesis is a statement about the value of a population parameter such as the mean, and must contain the condition of equality. The alternative hypothesis is a statement that must be true if the null hypothesis is false. A null hypothesis can only be rejected, or fail to be rejected, it cannot be accepted because of a lack of evidence to reject it. As an example of hypothesis tests for a population mean, there are only three possible forms, where μ is the population mean and μ0 is a specified value: H0: μ = μ0 H1: μ =/ μ0
H0: μ _ < μ0 H1: μ > μ0
H0: μ _ > μ0 H1: μ < μ0
© QUALITY COUNCIL OF INDIANA CQE 2006
XI-7 (1083)
XI. ADVANCED STATISTICS STATISTICAL DECISION MAKING / HYPOTHESIS TESTING
Hypothesis Testing (Continued) The steps of hypothesis testing are: C State the null and alternative hypothesis C Specify the level of significance, α C Determine the critical values separating the reject and nonrejection areas C Determine the sampling distribution and test statistic C Determine if the test statistic is in the reject or nonrejection area C Conclude if the null hypothesis is rejected or failed to be rejected C State the statistical decision in terms of the original problem
© QUALITY COUNCIL OF INDIANA CQE 2006
XI-8 (1084)
XI. ADVANCED STATISTICS STATISTICAL DECISION MAKING / HYPOTHESIS TESTING
Types of Errors When formulating a conclusion regarding a population based on observations from a small sample, two types of errors are possible: C Type I error: This error results when the null hypothesis is rejected when it is, in fact, true. The probability of making a type I error is called α (alpha) or producer’s risk. C Type II error: This error results when the null hypothesis is not rejected when it should be rejected. This error is called the consumer’s risk and is denoted by the symbol β (beta). The degree of risk (α) is normally chosen by the concerned parties (α is often taken as 5%) in arriving at the critical value of the test statistic. Increasing the sample size can reduce both the α and β risks.
XI-8 (1085)
© QUALITY COUNCIL OF INDIANA CQE 2006
XI. ADVANCED STATISTICS STATISTICAL DECISION MAKING / HYPOTHESIS TESTING
Types of Errors (Continued) The types of errors are shown in the Figure below: Null Hypothesis True
The Decision Made
Fail to p = 1 - α Reject Correct H0 Decision Reject H0
p=α Type I Error Error Matrix
False p=β Type II Error p = 1- β Correct Decision
XI-9 (1086)
© QUALITY COUNCIL OF INDIANA CQE 2006
XI. ADVANCED STATISTICS STATISTICAL DECISION MAKING / HYPOTHESIS TESTING
One-Tail Test If a null hypothesis is established to test whether a sample value is smaller or larger than a population value, then the entire α risk is placed on one end of a distribution curve. This constitutes a one tail-test. H0: new _ < to present
H1: new > present
ENTIRE " = 5%
0 :0 = 35 HOURS
Determine if the true mean is within the α critical region.
XI-10 (1087)
© QUALITY COUNCIL OF INDIANA CQE 2006
XI. ADVANCED STATISTICS STATISTICAL DECISION MAKING / HYPOTHESIS TESTING
Two-Tail Test If a null hypothesis is established to test whether a population shift has occurred, in either direction, then a two-tail test is required. The allowable α error is generally divided into two equal parts. H0: levels are =
H1: levels are =/
" = 0.025 2
" = 0.025 2 -1.96
0 :0
+1.96
Determine if the true mean is within either the upper or lower α critical regions.
XI-11 (1088)
© QUALITY COUNCIL OF INDIANA CQE 2006
XI. ADVANCED STATISTICS STATISTICAL DECISION MAKING / HYPOTHESIS TESTING
Required Sample Size The sample size, n, needed for hypothesis testing depends on: C The desired type I (α) risk and type II (β) risk C The minimum value to be detected between the population means (μ - μ0) C The variation in the characteristic being measured (s or σ) The sample size equation for variable data is: Z 2α/2 σ 2 n= E2
n = Sample size Z = The appropriate Z value E = The desired mean interval σ = The population standard deviation For binomial data, use the following formula: n=
Z 2α/2 ( p )( 1 - p )
( Δp )
2
Z = The appropriate Z value p ¯ = Proportion rate Δp = The desired proportion interval
© QUALITY COUNCIL OF INDIANA CQE 2006
XI-12 (1089)
XI. ADVANCED STATISTICS STATISTICAL DECISION MAKING / HYPOTHESIS TESTING
Hypothesis Tests for Means Z Test When the population follows a normal distribution and the population standard deviation, σX, is known, then the hypothesis tests for comparing a population mean, μ, with a fixed value, μ0, are given by the following: H0: μ = μ0 H1: μ =/ μ0
H0: μ _ < μ0 H1: μ > μ0
H0: μ _ > μ0 H1: μ < μ0
The null hypothesis is denoted by H0 and the alternative hypothesis is denoted by H1. The test statistic is given by: Z=
X - μ0 X - μ0 = σX ⎛ σX ⎞ ⎜ ⎟ ⎝ n⎠
Where the sample average is X ¯ , the number of samples is n and the standard deviation of means is σX¯. If n > 30, the sample standard deviation, s, is often used as an estimate of the population standard deviation, σX.
XI-12 (1090)
© QUALITY COUNCIL OF INDIANA CQE 2006
XI. ADVANCED STATISTICS STATISTICAL DECISION MAKING / HYPOTHESIS TESTING
Hypothesis Tests for Means (Continued) Z Test (Continued) Example: The average vial height from an injection molding process has been 5.00" with a standard deviation of 0.12". An experiment is conducted using new material which yielded the following vial heights: 5.10", 4.90", 4.92", 4.87", 5.09", 4.89", 4.95", and 4.88". Can one state, with 95% confidence, that the new material is producing shorter vials? H0: μ _ > μ0 H0: μ _ > 5.00"
H1: μ < μ0 H1: μ < 5.00"
X ¯ = 4.95", n = 8, σX = 0.12". The test statistic is: Z=
X - μ0 4.95 - 5.00 = = -1.18 ⎛ σX ⎞ ⎛ 0.12 ⎞ ⎜ ⎟ ⎜ ⎟ ⎝ n⎠ ⎝ 8 ⎠
It is a left, one-tailed test and with a 95% confidence, the level of significance, α = 0.05. Z0.05 = -1.645. Since the test statistic, -1.18, does not fall in the reject region, the null hypothesis cannot be rejected. There is insufficient evidence to conclude that the vials made with the new material are shorter.
© QUALITY COUNCIL OF INDIANA CQE 2006
XI-13 (1091)
XI. ADVANCED STATISTICS STATISTICAL DECISION MAKING / HYPOTHESIS TESTING
Hypothesis Tests for Means (Continued) Student’s t Test The student’s t distribution is used for making inferences about a population mean when the population variance σ2 is unknown and the sample size n is small. A sample size of 30 is normally the crossover point between the t and Z tests. The test statistic formula is: t=
X - μ0 ⎛ sX ⎞ ⎜ ⎟ ⎝ n⎠
X ¯ = The sample mean μ0 = The target value or population mean sx = The sample standard deviation n = The number of test samples The null and alternative hypotheses are the same as were given for the Z test. The degrees of freedom is determined by the number of samples, n, and is simply: d.f. = n - 1
© QUALITY COUNCIL OF INDIANA CQE 2006
XI-14 (1092)
XI. ADVANCED STATISTICS STATISTICAL DECISION MAKING / HYPOTHESIS TESTING
Hypothesis Tests for Means (Continued) Student’s t Test (Continued) Example: The average daily yield of a chemical process has been 880 tons (μ = 880 tons). A new process has been evaluated for 25 days (n = 25) with a yield of 900 tons (X ¯ ) and sample standard deviation, s = 20 tons. Can one say, with 95% confidence, that the process has changed? H0: μ = μ0 H1: μ =/ μ0 H0: μ = 880 tons H1: μ =/ 880 tons The test statistic calculation is: t=
X - μ0 900 - 880 = = 5.0 ⎛ sX ⎞ ⎛ 20 ⎞ ⎜ ⎟ ⎜ ⎟ ⎝ n⎠ ⎝ 25 ⎠
With a 95% confidence, the level of significance, α = 0.05. Since it is a two-tailed test, α/2 is used to determine the critical values. The degrees of freedom, d.f. = n - 1 = 24. The critical values in a t distribution table, are t0.025 = -2.064 and t0.975 = 2.064. Since the test statistic, 5.0, falls in the right-hand reject (or critical) region, the null hypothesis is rejected. One concludes, with 95% confidence, that the process has changed.
XI-17 (1093)
© QUALITY COUNCIL OF INDIANA CQE 2006
XI. ADVANCED STATISTICS STATISTICAL DECISION MAKING / HYPOTHESIS TESTING
t Distribution Table d.f.
t0.100
1 3.078 2 1.886 3 1.638 4 1.533 5 1.476 6 1.440 7 1.415 8 1.397 9 1.383 10 1.372 11 1.363 12 1.356 13 1.350 14 1.345 15 1.341 16 1.337 17 1.333 18 1.330 19 1.328 20 1.325 21 1.323 22 1.321 23 1.319 24 1.318 25 1.316 26 1.315 27 1.314 28 1.313 29 1.311 inf. 1.282 * One tail 5% α risk
t0.050*
t0.025**
t0.010
6.314 12.706 31.821 2.920 4.303 6.965 2.353 3.182 4.541 2.132 2.776 3.747 2.015 2.571 3.365 1.943 2.447 3.143 1.895 2.365 2.998 1.860 2.306 2.896 1.833 2.262 2.821 1.812 2.228 2.764 1.796 2.201 2.718 1.782 2.179 2.681 1.771 2.160 2.650 1.761 2.145 2.624 1.753 2.131 2.602 1.746 2.120 2.583 1.740 2.110 2.567 1.734 2.101 2.552 1.729 2.093 2.539 1.725 2.086 2.528 1.721 2.080 2.518 1.717 2.074 2.508 1.714 2.069 2.500 1.711 2.064 2.492 1.708 2.060 2.485 1.706 2.056 2.479 1.703 2.052 2.473 1.701 2.048 2.467 1.699 2.045 2.462 1.645 1.960 2.326 ** Two tail 5% α risk
t0.005
d.f.
63.657 9.925 5.841 4.604 4.032 3.707 3.499 3.355 3.250 3.169 3.106 3.055 3.012 2.977 2.947 2.921 2.898 2.878 2.861 2.845 2.831 2.819 2.807 2.797 2.787 2.779 2.771 2.763 2.756 2.576
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 inf.
© QUALITY COUNCIL OF INDIANA CQE 2006
XI-18 (1094)
XI. ADVANCED STATISTICS STATISTICAL DECISION MAKING / HYPOTHESIS TESTING
Hypothesis Tests for Proportions p Test When testing a claim about a population proportion, we may use a p test. When np < 5 or n(1-p) < 5, the binomial distribution is used to test hypotheses relating to proportion. If conditions that np _ > 5 and n(1-p) _ > 5 are met, then the binomial distribution of sample proportions can be approximated by a normal distribution. The hypothesis tests for comparing a sample proportion, p, with a fixed value, p0, are given by the following: H0: p = p0 H1: p =/ p0
H0: p _ < p0 H1: p > p0
H0: p _ > p0 H1: p < p0
The null hypothesis is denoted by H0 and the alternative hypothesis is denoted by H1. The test statistic is given by: Z=
x - np0
np0 ( 1 - p0 )
The number of successes is x and the number of samples is n. Z is compared with a critical value Zα or Zα/2, which is based on a significance level, α, for a onetailed test or α/2 for a two-tailed test.
© QUALITY COUNCIL OF INDIANA CQE 2006
XI-19 (1095)
XI. ADVANCED STATISTICS STATISTICAL DECISION MAKING / HYPOTHESIS TESTING
Hypothesis Tests for Variance Chi-square (Χ2) Test It was discussed earlier that standard deviation (or variance) is fundamental in making inferences regarding the population mean. In many practical situations, variance (σ2) assumes a position of greater importance than the population mean. The standardized test statistic is called the chi-square (Χ2) test. Population variances are distributed according to the chi-square distribution. Therefore, inferences about a single population variance will be based on chi-square. The chi-square test is widely used in two applications. Case I. Comparing variances when the variance of the population is known. Case II. Comparing frequencies of test outcomes when there is no defined population variance (attribute data).
XI-20 (1096)
© QUALITY COUNCIL OF INDIANA CQE 2006
XI. ADVANCED STATISTICS STATISTICAL DECISION MAKING / HYPOTHESIS TESTING
Hypothesis Tests for Variance (Cont.) Chi-square (Χ2) Test (Continued) When the population follows a normal distribution, the hypothesis tests for comparing a population variance, σX2 , with a fixed value, σ02, are given by the following: H0: σX2 = σ02 H1: σX2 =/ σ02
H0: σX2 _ < σ02 H1: σX2 > σ02
H0: σX2 _ > σ02 H1: σX2 < σ02
The null hypothesis is denoted by H0 and the alternative hypothesis is denoted by H1. The test statistic is given by: Χ = 2
( n - 1) s
2 X
σ0 2
Where the number of samples is n and the sample variance is sX2 . The test statistic, Χ2, is compared with a 2 which is based on a significance critical value Χα2 or Χα/2 level, α, for a one-tailed test or α/2 for a two-tailed test and the number of degrees of freedom, d.f. The degrees of freedom is determined by the number of samples, n, and is simply: d.f. = n - 1
XI-20 (1097)
© QUALITY COUNCIL OF INDIANA CQE 2006
XI. ADVANCED STATISTICS STATISTICAL DECISION MAKING / HYPOTHESIS TESTING
Hypothesis Tests for Variance (Cont.) Chi-square (Χ2) Test (Continued) If the H1 sign is =/, it is a two-tailed test. If the H1 sign is >, it is a right, one-tailed test, and if the H1 sign is <, it is a left, one-tailed test. The Χ2 distribution looks like: Left tail
f(Χ2)
Right tail
f(Χ2)
2 0 Χ1-α
0
Χα2
Chi-square Distribution Tail Areas
XI-21 (1098)
© QUALITY COUNCIL OF INDIANA CQE 2006
XI. ADVANCED STATISTICS STATISTICAL DECISION MAKING / HYPOTHESIS TESTING
Hypothesis Tests for Variance (Cont.) Chi-square (Χ2) Test (Continued)
Chi-square Case I. Population Variance Is Known. Example: The R & D department claims that the new steel alloy will show a four sigma tensile variation less than or equal to 60 psi 95 % of the time. An eight sample test yielded a standard deviation of 8 psi. Can a reduction in tensile strength variation be validated with 95 % confidence? The best range of variation expected is 60 psi. This translates to a sigma of 15 psi (an approximate 4 sigma spread covering 95.44 % of occurrences). H0: σX2 _ > σ02 or H1: σX2 < σ02 or
H0: σX2 _ > (15)2 H1: σX2 < (15)2
This is a left-tail test. Using d.f. = n - 1 = 7, the chisquare critical value for 95 % confidence is 2.17. Χ = 2
( n - 1) s σ0 2
2 X
=
( 8 - 1)( 8 psi ) ( 15 psi ) 2
2
= 1.99
Since 1.99 is to the left of 2.17, and is in the critical area, the null hypothesis must be rejected. The decreased variation in the new steel alloy tensile strength supports the R & D claim.
XI-22 (1099)
© QUALITY COUNCIL OF INDIANA CQE 2006
XI. ADVANCED STATISTICS STATISTICAL DECISION MAKING / HYPOTHESIS TESTING
Critical Values of the Chi-square (Χ2) Distribution X2.95
d.f. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 18 20 24 30 40 60 120
2 Χ0.99 0.00016 0.0201 0.115 0.297 0.554 0.872 1.24 1.65 2.09 2.56 3.05 3.57 4.11 4.66 5.23 5.81 7.01 8.26 10.86 14.95 22.16 37.48 86.92
2 Χ0.95 0.0039 0.1026 0.352 0.711 1.15 1.64 2.17 2.73 3.33 3.94 4.57 5.23 5.89 6.57 7.26 7.96 9.39 10.85 13.85 18.49 26.51 43.19 95.70
2 Χ0.90 0.0158 0.2107 0.584 1.064 1.61 2.20 2.83 3.49 4.17 4.87 5.58 6.30 7.04 7.79 8.55 9.31 10.86 12.44 15.66 20.60 29.05 46.46 100.62
2 Χ0.10 2.71 4.61 6.25 7.78 9.24 10.64 12.02 13.36 14.68 15.99 17.28 18.55 19.81 21.06 22.31 23.54 25.99 28.41 33.20 40.26 51.81 74.40 140.23
2 Χ0.05 3.84 5.99 7.81 9.49 11.07 12.59 14.07 15.51 16.92 18.31 19.68 21.03 22.36 23.68 25.00 26.30 28.87 31.41 36.42 43.77 55.76 79.08 146.57
X2.05
2 Χ0.01 6.63 9.21 11.34 13.28 15.09 16.81 18.48 20.09 21.67 23.21 24.73 26.22 27.69 29.14 30.58 32.00 34.81 37.57 42.98 50.89 63.69 88.38 158.95
XI-23 (1100)
© QUALITY COUNCIL OF INDIANA CQE 2006
XI. ADVANCED STATISTICS STATISTICAL DECISION MAKING / HYPOTHESIS TESTING
Hypothesis Tests for Variance (Cont.) Chi-square (Χ2) Test (Continued) Chi-square Case II. Comparing Observed and Expected Frequencies of Test Outcomes. (Attribute Data) This application of chi-square is called the contingency table or row and column analysis. The procedure is as follows: 1. State the null hypothesis:
hypothesis
and
alternative
Null hypothesis: There is no difference among the treatment probabilities. Alternative hypothesis: probabilities is different.
At least one of the
H0: p1 = p2 = p3 = ... = pn H1: p1 =/ p2 =/ p3 =/ ... =/ pn 2. The contingency table degrees of freedom = d.f. d.f. = (rows - 1)(columns - 1) = (r - 1)(c - 1)
XI-24 (1101)
© QUALITY COUNCIL OF INDIANA CQE 2006
XI. ADVANCED STATISTICS STATISTICAL DECISION MAKING / HYPOTHESIS TESTING
Hypothesis Tests for Variance (Cont.) Chi-square (Χ2) Test (Continued) 3. Determine the observed frequencies Oij for the various conditions being compared. 4. Calculate all row totals, Ri, column totals, Ci, and the grand total, N. c
R i = ∑ Oij j=1 r
C j = ∑ Oij i=1 r
c
i=1
j=1
N = ∑ Ri = ∑ Cj
5. Calculate the expected frequencies Eij for each condition, under the assumption that no difference exists among the processes. Eij =
R iC j N
6. Calculate the chi-square test statistic: Χ = 2
r
c
∑∑
i=1j=1
(O
ij
- Eij ) Eij
2
or
Χ = 2
∑
( O - E)
2
E
This is the most “famous” chi-square statistic.
© QUALITY COUNCIL OF INDIANA CQE 2006
XI-24 (1102)
XI. ADVANCED STATISTICS STATISTICAL DECISION MAKING / HYPOTHESIS TESTING
Hypothesis Tests for Variance (Cont.) Chi-square (Χ2) Test (Continued) 7. Note that although the alternative hypothesis has =/, the Χ2 critical value for this Case II test is always determined using the chi-square table with the entire level of significance, α, in the one-tail, right side, of the distribution. Determine the Χ2 critical value from a table using α and the degrees of freedom. 8. Compare the calculated test statistic and the critical value. If the calculated test statistic exceeds the critical value, then a significant difference exists, at a selected confidence level.
XI-25 (1103)
© QUALITY COUNCIL OF INDIANA CQE 2006
XI. ADVANCED STATISTICS STATISTICAL DECISION MAKING / HYPOTHESIS TESTING
Hypothesis Tests for Variance (Cont.) Chi-square (Χ2) Test (Continued) Example: An airport authority wanted to evaluate the ability of three X-ray inspectors to detect key items. A test was devised whereby transistor radios were placed in ninety pieces of luggage. Each inspector was exposed to exactly thirty of the preselected and “bugged” items in a random fashion. At a 95% confidence level, is there any significant difference in the abilities of the inspectors? Inspectors 1
2
3
Treatment Totals
Radios detected
27
25
22
74
Radios undetected
3
5
8
16
Sample total
30
30
30
90
Inspector Observed Results
© QUALITY COUNCIL OF INDIANA CQE 2006
XI-25 (1104)
XI. ADVANCED STATISTICS STATISTICAL DECISION MAKING / HYPOTHESIS TESTING
Hypothesis Tests for Variance (Cont.) Chi-square (Χ2) Test (Continued) Example continued: 1. Null hypothesis: There is no difference between the inspectors. H0: p1 = p2 = p3 Alternative hypothesis: At least one of the inspectors is different. H1: p1 =/ p2 =/ p3 2. Degrees of freedom = d.f. d.f. = (rows - 1)(columns - 1) = (r - 1)(c - 1) d.f. = (2 - 1)(3 - 1) = 2 3. Determine the observed frequencies Oij for the various conditions being compared. 4. Calculate all row totals, Ri, column totals, Ci, and the grand total, N. These are given in the previous Table.
XI-26 (1105)
© QUALITY COUNCIL OF INDIANA CQE 2006
XI. ADVANCED STATISTICS STATISTICAL DECISION MAKING / HYPOTHESIS TESTING
Hypothesis Tests for Variance (Cont.) Chi-square (Χ2) Test (Continued) Example continued: 5. Calculate the expected frequencies Eij for each condition, using the formula below, these are shown in the Table. Eij =
R iC j N
Inspectors 1
2
3
Treatment Totals
Radios detected
24.67
24.67
24.67
74
Radios undetected
5.33
5.33
5.33
16
30
30
30
90
Sample total
Inspector Expected Results 6. Calculate the chi-square test statistic: r
c
Χ2 = ∑ ∑
( Oij - Eij ) Eij
i=1j=1
Χ = 2
( 2.33 )
2
2
24.67 2 Χ = 2.89
+
( 0.33 )
2
24.67
+
( 2.67 )
2
24.67
+
( 2.33 ) 5.33
2
+
( 0.33 ) 5.33
2
+
( 2.67 ) 5.33
2
© QUALITY COUNCIL OF INDIANA CQE 2006
XI-26 (1106)
XI. ADVANCED STATISTICS STATISTICAL DECISION MAKING / HYPOTHESIS TESTING
Hypothesis Tests for Variance (Cont.) Chi-square (Χ2) Test (Continued) Example continued: 7. The critical value from the Table or the Appendix Table VI using d.f. = 2, α = 0.05, right-tail, is Χ2 = 5.99. There is only a 5% chance that the calculated value of Χ2 will exceed 5.99. 8. Compare the calculated test statistic and the critical value. Since the Χ2 calculated value of 2.89 is less than the critical value of 5.99, and this is a right-tail test, the null hypothesis cannot be rejected. There is insufficient evidence to say with 95% confidence that the abilities of the inspectors differ.
© QUALITY COUNCIL OF INDIANA CQE 2006
XI-27 (1107)
XI. ADVANCED STATISTICS STATISTICAL DECISION MAKING / HYPOTHESIS TESTING
Practical Significance vs Statistical Significance The hypothesis is tested to determine if a claim has significant statistical merit. Traditionally, levels of 5% or 1% are used for the critical significance values. If the calculated test statistic has a p-value below the critical level then it is deemed to be statistically significant. More stringent critical values may be required when catastrophic loss is involved. Less stringent critical values may be advantageous when there are no such risks. On occasion, some hypothesis is found to be statistically significant, but may not be worth the effort to implement. This could occur if a large sample was tested and the result is statistically significant, but would not have any practical significance.
XI-27 (1108)
© QUALITY COUNCIL OF INDIANA CQE 2006
XI. ADVANCED STATISTICS STATISTICAL DECISION MAKING / HYPOTHESIS TESTING
Power of Test H0: μ = μ0 Consider a null hypothesis that a population has mean μo= 70.0 and σ¯X = 0.80. The 95% confidence limits are 70 ±(1.96)(0.8) = 71.57 and 68.43. One accepts the hypothesis μ = 70 if X ¯ s are between these limits. The alpha risk is that sample means will exceed those limits. What if μ shifts to 71, would it be detected? There is a risk that the null hypothesis would be accepted even if the shift occurred. This risk is termed β. Normal D Distribution, istribution,μμ==70 70
0.45 0.4 0.35 0.3
LCL
0.25
UCL
0.2 0.15 0.1
.025
.025
0.05 0 67
68
69
70 X
71
72
73
72
73
Normal Norm al Distribution, D istribution, μ μ==71 71
0.45
$
0.4 0.35 0.3 0.25 0.2 0.15 0.1 0.05 0 68
69
70
71 X
Illustration of Beta (β) Risk
74
XI-29 (1109)
© QUALITY COUNCIL OF INDIANA CQE 2006
XI. ADVANCED STATISTICS STATISTICAL DECISION MAKING / HYPOTHESIS TESTING
Power of Test H0: μ = μ0 (Continued) To construct a power curve, 1 - β is plotted against values of μ. A shift in a mean away from the null increase the probability of detection. In general, as alpha increases, beta decreases, and the power of 1 - β increases. A gain in power can be obtained by accepting a lower level of protection from the alpha error. Increasing the sample size makes it possible to decrease both alpha and beta, and increase power. 1 - β = Probability of rejecting the null hypothesis given that the null hypothesis is false. 1 0.9 0.8
1 - β
0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 67
68
69
70
μ
71
Power Curve, (1 - β) vs μ
72
73
XI-30 (1110)
© QUALITY COUNCIL OF INDIANA CQE 2006
XI. ADVANCED STATISTICS STATISTICAL DECISION MAKING / HYPOTHESIS TESTING
Normal Distribution Hypotheses Tests Large samples
Means
F 21
Fx - x =
X1 vs X 2
Normal
6 Z= X- : F/ n
X vs :
1
2
N1
+
61 - X 62 X F 6X - 6X 1
2 ( - 1) s2 X = (n
F2
Variances S12 vs S 22
F=
S12 S 22
6 t= X- : s/ n
X vs :
2
2
S2 =
F1 = F2
Means
((n1 - 1)s ) 12 + ((n2 - 1)s ) 22 n1 + n2 - 2
X1 vs X 2 S X6 - X62 = S 1 % 1 1 n 1 n2
df = n1 + n2 - 2
2
A = S12 / n 1
2
F1 … F2
B = S22 / n 2
S6x - 6x = A + B 1 2 Welch-Satterthwaite Approximation
df =
2
N2
S 12 vs F2
Small samples
Z=
F 22
(A + B)
2
A2 + B2 n1 - 1 n2 - 1
t=
61 - X 62 X SX6 1 - X6 2
XI-31 (1111)
© QUALITY COUNCIL OF INDIANA CQE 2006
XI. ADVANCED STATISTICS STATISTICAL DECISION MAKING / HYPOTHESIS TESTING
Attribute Hypotheses Tests (Continued) p vs :
Fp =
Z=
p p) 6 (1 - 6 n
p-6 p Fp
Binomial p1 vs p2
p= 6
Fp1&p2 =
Z =
1 1 p (1 - 6 6 p) + n1 n2
n1 + n2
F= c
Z=
c = no. of defects k = no. samples
2
X2 =
c1
k1
+
c2
2
k1 + k 2
k2
c1 + c 2
c - 6 c c
Poisson c vs c
Fp
1
n1 p1 + n2 p2
c vs :
p1 - p2
- ( c1 + c2)
-p
2
XI-32 (1112)
© QUALITY COUNCIL OF INDIANA CQE 2006
XI. ADVANCED STATISTICS STATISTICAL DECISION MAKING / PAIRED-COMPARISON TESTS
Paired-comparison Hypotheses Tests Two Mean, Equal Variance, t Test Tests the difference between two population means, μ1 and μ2, when σ1 and σ2 are unknown but considered equal, and are normally distributed. H0: μ1 = μ2 sp =
(n
1
H1: μ1 =/ μ2
- 1) s12 + ( n2 - 1) s22 n1 + n2 - 2
sp = pooled standard deviation d.f. = n1 + n2 - 2
t n +n -2 = 1
2
X1 - X 2 1 1 sp + n1 n2
XI-33 (1113)
© QUALITY COUNCIL OF INDIANA CQE 2006
XI. ADVANCED STATISTICS STATISTICAL DECISION MAKING / PAIRED-COMPARISON TESTS
Paired-comparison Tests (Continued) Two Mean, Unequal Variance, t Test Tests the difference between two population means, μ1 and μ2, when σ1 and σ2 are unknown, and are not considered to be equal. H0: μ1 = μ2
H1: μ1 =/ μ2 2
⎛ s12 s22 ⎞ ⎜n + n ⎟ ⎝ 1 2 ⎠ d.f. = 2 2 2 ⎛ s1 ⎞ ⎛ s22 ⎞ ⎜n ⎟ ⎜ ⎟ ⎝ 1 ⎠ + ⎝ n2 ⎠ ( n1 - 1) ( n2 - 1)
t d.f. =
X1 - X 2 s12 s22 + n1 n2
XI-34 (1114)
© QUALITY COUNCIL OF INDIANA CQE 2006
XI. ADVANCED STATISTICS STATISTICAL DECISION MAKING / PAIRED-COMPARISON TESTS
Paired-comparison Tests (Continued) Paired t Test Tests the difference between two population means, μ1 and μ2, when data is taken in pairs with the difference calculated for each pair, and the populations are normally distributed. Data from the samples are assumed to be related. H0: μ1 = μ2 t=
H1: μ1 =/ μ2 d ⎛ sd ⎞ ⎜ ⎟ ⎝ n⎠
Note that paired t tests using H0: μ1 _ < μ2 and H1: μ1 > μ2 or H0: μ1 _ > μ2 and H1: μ1 < μ2 may also be performed. The paired t test method with dependent samples, as compared to treating the data as two independent samples, will often show a more significant difference because the standard deviation (sd) includes no sample to sample variation. In general, the paired t test is a more sensitive test than the comparison of two independent samples.
© QUALITY COUNCIL OF INDIANA CQE 2006
XI-35 (1115)
XI. ADVANCED STATISTICS STATISTICAL DECISION MAKING / PAIRED-COMPARISON TESTS
Paired-comparison Tests (Continued) F Test The need for a statistical method of comparing two population variances is apparent. The F test, named in honor of Sir Ronald Fisher, is usually employed. If independent, random samples are drawn from two normal populations with equal variances, the ratio of (s1)2/(s2)2 creates a sampling distribution known as the F distribution. The hypotheses tests for comparing a population variance, σ12, with another population variance, σ22, are given by the following: H0: σ12 = σ22
H0: σ12 _ < σ22
H0: σ12 _ > σ22
H1: σ12 =/ σ22
H1: σ12 > σ22
H1: σ12 < σ22
The shape of the F distribution is non-symmetrical and will depend on the number of degrees of freedom associated with s12 and s22. The degrees of freedom are ν1 and ν2 respectively.
© QUALITY COUNCIL OF INDIANA CQE 2006
XI-35 (1116)
XI. ADVANCED STATISTICS STATISTICAL DECISION MAKING / PAIRED-COMPARISON TESTS
Paired-comparison Tests (Continued) F Test (Continued) The F statistic is the ratio of two sample variances (two chi-square distributions) and is given by the formula: s12 F= 2 s2
Where s12 and s22 are sample variances and ν1 is the d.f. in the numerator. Since the identification of the sample variances is arbitrary, it is customary to designate the larger sample variance as s12 and place it in the numerator.
XI-36 (1117)
© QUALITY COUNCIL OF INDIANA CQE 2006
XI. ADVANCED STATISTICS STATISTICAL DECISION MAKING / PAIRED-COMPARISON TESTS
Paired-comparison Tests (Continued) F Test (Continued)
f(F)
f (")
ν1
1
2
3
4
5
6
7
8
9
10
1
161.4
199.5
215.7
224.6
230.2
234.0
236.8
238.9
240.5
241.9
2
18.51
19.00
19.16
19.25
19.30
19.33
19.35
19.37
19.38
19.40
3
10.13
9.55
9.28
9.12
9.01
8.94
8.89
8.85
8.81
8.79
4
7.71
6.94
6.59
6.39
6.26
6.16
6.09
6.04
6.00
5.96
5
6.61
5.79
5.41
5.19
5.05
4.95
4.88
4.82
4.77
4.74
6
5.99
5.14
4.76
4.53
4.39
4.28
4.21
4.15
4.10
4.06
7
5.59
4.74
4.35
4.12
3.97
3.87
3.79
3.73
3.68
3.64
8
5.32
4.46
4.07
3.84
3.69
3.58
3.50
3.44
3.39
3.35
9
5.12
4.26
3.86
3.63
3.48
3.37
3.29
3.23
3.18
3.14
10
4.96
4.10
3.71
3.48
3.33
3.22
3.14
3.07
3.02
2.98
ν2
F Critical Values (α = 0.05)
XI-37 (1118)
© QUALITY COUNCIL OF INDIANA CQE 2006
XI. ADVANCED STATISTICS STATISTICAL DECISION MAKING / PAIRED-COMPARISON TESTS
Paired-comparison Tests (Continued) F Test (Continued) Example: A materials laboratory wants to know if there is an improvement in consistency of strength after aging for one year (assume a 95% confidence level). At Start
One Year Later
No. of tests
9
7
Product standard deviation (psi)
900
300
Solution: H0: σ12 _ < σ22 H1: σ12 > σ22 and ν1 = 8 ν2 = 6 One is concerned with an improvement in variation; therefore, a one-tail test is used, with the entire α risk in the right-tail. From the prior F Table, the critical value of F is 4.15. The null hypothesis rejection area is equal to or greater than 4.15.
( 900 ) s12 F= 2 = 2 = 9 s2 ( 300 ) 2
Since the calculated F value is in the critical region, the null hypothesis is rejected. There is sufficient evidence to indicate a reduced variance and more consistency of strength after aging for one year.
XI-38 (1119)
© QUALITY COUNCIL OF INDIANA CQE 2006
XI. ADVANCED STATISTICS STATISTICAL DECISION MAKING / PAIRED-COMPARISON TESTS
Summary of Inference Tests Type Z
Test Statistic X - μ0 X - μ0 = σX ⎛ σX ⎞ ⎜ ⎟ ⎝ n⎠
Z=
t=
t test
X - μ0 ⎛ sX ⎞ ⎜ ⎟ ⎝ n⎠
Two mean X1 - X 2 t n +n -2 = equal 1 1 sp + variance n1 n2 t test 1
2
d.f.
Application
N.A.
Single sample mean. Standard deviation of population is known.
n-1
Single sample mean. Standard deviation of population unknown.
2 sample means. Variances are unknown, but n1+n2-2 considered equal. ( n1 - 1) s12 + ( n2 - 1) s22 s = p
Two mean unequal variance t test
t d.f. =
X1 - X 2 s12 s22 + n1 n2
*
n1 + n2 - 2
2 sample means. Variances are unknown, but considered unequal. d.f. is determined from the WelchSatterthwaite approximation.
XI-38 (1120)
© QUALITY COUNCIL OF INDIANA CQE 2006
XI. ADVANCED STATISTICS STATISTICAL DECISION MAKING / PAIRED-COMPARISON TESTS
Summary of Inference Tests (Continued) Type
Test Statistic t=
Paired t test Χ2 σ2 known
Χ2
Χ = 2
Χ2 =
r
d ⎛ sd ⎞ ⎜ ⎟ ⎝ n⎠
( n - 1) s σ 20
c
∑∑
( Oij - Eij )
i=1j=1
F
2 X
s12 F= 2 s2
Eij
2
d.f.
Application
n-1
2 sample means. Data is taken in pairs. A different d is
n-1
Tests sample variance against known variance.
Compares observed and expected (r-1)(c-1) frequencies of test outcomes. n1 - 1 n2 - 1
Tests if two sample variances are equal.
XI-39 (1121)
© QUALITY COUNCIL OF INDIANA CQE 2006
XI. ADVANCED STATISTICS STATISTICAL DECISION MAKING / GOODNESS-OF-FIT TESTS
Goodness-of-fit Tests The chi-square goodness-of-fit (GOF) test can be applied to any univariate distribution with a cumulative distribution function. H0: The data follow a specified distribution H1: The data do not follow the specified distribution There observed frequency in each cell is Oi or fo and the expected or theoretical frequency, Ei or fe. Any cells which have an expected frequency of less than 5, are combined with an adjacent cell. Chi-square ( Χ2 ) is then summed across all cells: k
Χ2 = ∑
i=1
(O
- Ei ) i Ei
2
or
k
Χ2 = ∑
(f
o
i=1
- fe ) fe
2
k is the number of cells after combining. c is the number of estimated population parameters for the distribution plus 1. The calculated chi-square is then compared to the chi-square critical value for the following appropriate degrees of freedom. GOF Distribution Weibull (3 parameter) Normal Poisson Binomial Uniform
d.f. (k - c) k-4 k-3 k-2 k-2 k-1
XI-40 (1122)
© QUALITY COUNCIL OF INDIANA CQE 2006
XI. ADVANCED STATISTICS STATISTICAL DECISION MAKING / GOODNESS-OF-FIT TESTS
Uniform Distribution (GOF) Example: Is a game die honest and balanced, given the number of times each side has come up? A die was tossed 48 times with the following sample results: 1 spot 12 times, 2 spots 7 times, 3 spots 2 times 4 spots 7 times, 5 spots 12 times, 6 spots 8 times When a die is rolled, the expectation is that each side should come up an equal number of times. It is obvious there will be random departures from this theoretical expectation even if the die is honest. H0: The die outcomes follow a uniform distribution H1: The die outcomes do not follow a uniform distribution Spots 1 2 3 4 5 6 Total =
fe 8 8 8 8 8 8 48
fo 12 7 2 7 12 8 48
(fe - fo)2 /fe 2.000 0.125 4.500 0.125 2.000 0.000 8.750
XI-40 (1123)
© QUALITY COUNCIL OF INDIANA CQE 2006
XI. ADVANCED STATISTICS STATISTICAL DECISION MAKING / GOODNESS-OF-FIT TESTS
Uniform Distribution (GOF) (Cont.) Example continued: 2
Χ =
k
∑
i=1
( fo
- fe )
2
fe
= 8.750
The calculated chi-square is 8.75. The critical chisquare Χ20.05,5 = 11.07. The calculated chi-square does not exceed critical chi-square. Therefore, the hypothesis of an honest die following a uniform distribution cannot be rejected. The random departures from theoretical expectation could well be explained by chance cause. The student is encouraged to work through the following examples given in the CQE Primer for: C Normal distribution (GOF) C Poisson distribution (GOF) C Binomial distribution (GOF)
XI-46 (1124)
© QUALITY COUNCIL OF INDIANA CQE 2006
XI. ADVANCED STATISTICS STATISTICAL DECISION MAKING / CONTINGENCY TABLES
Contingency Tables A two-way classification table (rows and columns) containing original frequencies can be analyzed to determine whether the two variables (classifications) are independent or have significant association. A contingency coefficient (correlation) can be calculated. If the chi-square test shows a significant dependency, the contingency coefficient shows the strength of the correlation. Results obtained in samples do not always agree exactly with the theoretical expected results according to rules of probability. A measure of the difference found between observed and expected frequencies is supplied by the statistic chi-square, Χ2, where: k
Χ =∑ 2
i=1
(O
i
- Ei ) ( O1 - E1 ) + ( O2 - E2 ) + ... + ( On - En ) = Ei E1 E2 En 2
2
2
2
If Χ2 = 0 observed and theoretical frequencies agree exactly. If Χ2 > 0 they do not agree exactly. The larger the value of Χ2, the greater the discrepancy between observed and theoretical frequencies. The chi-square distribution is an appropriate reference distribution for critical values when the expected frequencies are at least equal to 5.
XI-47 (1125)
© QUALITY COUNCIL OF INDIANA CQE 2006
XI. ADVANCED STATISTICS STATISTICAL DECISION MAKING / CONTINGENCY TABLES
Contingency Tables (Continued) A contingency table example is shown in the CQE Primer. The methodology is exactly like that presented earlier for Chi-square Case II.
Coefficient of Contingency (C) The degree of relationship, association or dependence of the classifications in a contingency table is given by: C=
Χ2 Χ2 + N
Where N equals the grand frequency total. The maximum value of C is never greater than 1.0, and is dependent on the total number of rows and columns. The maximum coefficient of contingency is: Max C =
k-1 k
Where: k = min of (r, c) and r = rows, c = columns
© QUALITY COUNCIL OF INDIANA CQE 2006
XI-49 (1126)
XI. ADVANCED STATISTICS STATISTICAL DECISION MAKING / CONTINGENCY TABLES
Correlation of Attributes Contingency table classifications often describe characteristics of objects or individuals. Thus, they are often referred to as attributes and the degree of dependence, association or relationship is called correlation of attributes. For (k = r = c) tables, the correlation coefficient, φ, is defined as: φ=
Χ2 N ( k - 1)
The value of φ falls between 0 and 1. If the calculated value of chi-square is significant, then φ is significant. In the example given in the CQE Primer, rows and columns are not equal and the correlation calculation is not applied.
© QUALITY COUNCIL OF INDIANA CQE 2006
XI-50 (1127)
XI. ADVANCED STATISTICS ANALYSIS OF VARIANCE
Analysis of Variance (ANOVA) In many investigations (such as experimental trials), it is necessary to compare three or more population means simultaneously. The underlying assumptions in analysis of variance of means are: the variance is the same for all factor treatments or levels, the individual measurements within each treatment are normally distributed and the error term is considered a normally and independently distributed random effect. The variability of a set of measurements is proportional to the sum of squares of deviations used to calculate the variance: 2 X X ∑( ) Analysis of variance partitions the sum of squares of deviations of individual measurements from the grand mean (called the total sum of squares) into parts: the sum of squares of treatment means plus a remainder which is termed the experimental or random error. When an experimental variable is highly related to the response, its part of the total sum of the squares will be highly inflated. This condition is confirmed by comparing the variable sum of squares with that of the random error using an F test.
© QUALITY COUNCIL OF INDIANA CQE 2006
XI-50 (1128)
XI. ADVANCED STATISTICS ANALYSIS OF VARIANCE
A Comparison of Three or More Means An analysis of variance to detect a difference in three or more population means first requires obtaining the same summary statistics applied in the short cut formula for calculating variance of a set of data: ΣX2 is called the crude sum of squares (ΣX)2 / N is the CM (correction for the mean) ΣX2 - (ΣX)2 / N is termed SS (total sum of squares, or corrected SS) ΣX 2 - (ΣX)2 / N total sum of squares = σ 2 (variance) = N-1 total DF (degrees of freedom)
© QUALITY COUNCIL OF INDIANA CQE 2006
XI-51 (1129)
XI. ADVANCED STATISTICS ANALYSIS OF VARIANCE
Three or More Means (Continued) One-Way ANOVA In the one-way ANOVA, the total variation in the data has two parts: the variation among treatment means and the variation within treatments. ANOVA grand average = GM. The total SS is then: Total SS = ∑( Xi - GM)
2
Where X i is any individual measurement
Total SS = SST + SSE Where SST = treatment sum of squares and SSE is the experimental error sum of squares. SST = ∑nt ( Xt - GM)
SSE = ∑( Xt - Xt )
2
2
Sum of the squared deviations of each treatment average from the grand average or grand mean. Sum of the squared deviations of each individual observation within a treatment from the treatment average.
XI-51 (1130)
© QUALITY COUNCIL OF INDIANA CQE 2006
XI. ADVANCED STATISTICS ANALYSIS OF VARIANCE
Three or More Means (Continued) One-Way ANOVA (Continued) For the ANOVA calculations:
∑ ( TCM) = ∑
Each treatment total squared Number of observations in that treatment
SST = ∑( TCM) - CM
SSE = Total SS - SST
(always obtained by difference)
Total DF = N - 1
(total degrees of freedom)
TDF = t -1
(treatment DF = number of treatments minus 1)
EDF = (N-1) - (t - 1) = N - t
(error DF, always obtained by difference)
MST =
SST SST = TDF t-1
(mean square treatments)
MSE =
SSE SSE = EDF N-t
(mean square error)
XI-52 (1131)
© QUALITY COUNCIL OF INDIANA CQE 2006
XI. ADVANCED STATISTICS ANALYSIS OF VARIANCE
Three or More Means (Continued) One-Way ANOVA (Continued) To test the null hypothesis: H0: μ1 = μ2 = ... = μt F=
MST MSE
H1: At least one mean different
When F > Fα , reject H0
Example: The following coded results were obtained from a single factor randomized experiment, in which the outputs of three machines were compared. Determine if there is a significant difference in the results (α=0.05). Machines
Data
Sum
n
Avg
A
5, 7, 6, 7, 6
31
5
6.2
192.2
195
B
2, 0, 1, -2, 2
3
5
0.6
1.8
13
C
1, 0, -2, -3, 0
-4
5
-0.8
3.2
14
30
15
197.2
222
Total
TCM =
XI-52 (1132)
© QUALITY COUNCIL OF INDIANA CQE 2006
XI. ADVANCED STATISTICS ANALYSIS OF VARIANCE
Three or More Means (Continued) One-Way ANOVA (Continued) Example continued: N = 15 Total DF = N - 1 = 15 - 1 = 14 ∑ X = 30 GM = ∑ X N = 30 N = 2.0 ∑ X = 222 ( ∑ X ) = ( 30 ) = 60 CM = 2
2
2
N 15 2 Total SS = ∑ X - CM = 222 - 60 = 162 ∑ ( TCM ) = 197.2
SST = ∑ ( TCM ) - CM = 197.2 - 60 = 137 .2
and
SST = ∑ n t ( X t - GM ) = 5 ( 6.2 - 2 ) + 5 ( 0.6 - 2 ) + 5 ( 0.8 - 2 ) SST = 82.2 + 9.8 + 39.2 = 137.2 SSE = Total SS - SST = 162 - 137.2 = 24.8 2
2
2
2
The completed ANOVA table is: Source (of variation)
SS
Machines 137.2
DF
Mean Square
F
2
68.6
33.2
2.067
Error
24.8
12
Total
162
14
Fα ,ν
1 ,ν 2
F0.05,2,12 = 3.89
σe = 2.07 = 1.44
© QUALITY COUNCIL OF INDIANA CQE 2006
XI-53 (1133)
XI. ADVANCED STATISTICS ANALYSIS OF VARIANCE
Three or More Means (Continued) One-Way ANOVA (Continued) Example continued: Since the computed value of F (33.2) exceeds the critical value of F, the null hypothesis is rejected. Thus, there is evidence that a real difference exists among the machine means. σe is the pooled standard deviation of within treatments variation. It can also be considered the process capability sigma of individual measurements. It is the variation within measurements which would still remain if the difference among treatment means were eliminated.
XI-53 (1134)
© QUALITY COUNCIL OF INDIANA CQE 2006
XI. ADVANCED STATISTICS ANALYSIS OF VARIANCE
Two-Way ANOVA The two-way analysis procedure is an extension of the patterns described in the one-way analysis. Recall that a one-way ANOVA has two components of variance: Treatments and experimental error. In the two-way ANOVA there are three components of variance: Factor A treatments, Factor B treatments, and experimental error.
Two Factor, Two-Way ANOVA Experiment Source
MS
Columns 872.44 (Matls)
2
436.22
20.8 F0.05,2,14 = 3.74
Rows 2005.6 (Instruct)
1
2005.6
95.6 F0.05,1,14 = 4.60
14
20.98
SIGtotal = 13.66
293.78
17 SIG total =
F
Fα ,ν ,ν
DF
Error
SS
1
2
SIGe = 13.66
ANOVA Table for the Two-Factor, Two-Way Example
© QUALITY COUNCIL OF INDIANA CQE 2006
XI-55 (1135)
XI. ADVANCED STATISTICS ANALYSIS OF VARIANCE
Two Factor, Two-Way ANOVA Experiment (Continued) The null hypotheses: Instructor and study material means do not differ. Col F = ColMS/EMS = 436.22/20.98 = 20.79. This is larger than critical F = 3.74. Therefore, the null hypothesis of equal material means is rejected. Row F = RowMS/EMS = 2005.56/20.98 = 95.59. This is larger than critical F = 4.60. Therefore, the null hypothesis of equal instructor means is rejected. The difference between total sigma (13.66) and error sigma (4.58) is due to the significant difference in instructor means and material means. If the instructor difference and study material differences were only due to chance cause, the sigma variation in the data would be equal to SIGe, the square root of the Error Mean Square.
XI-56 (1136)
© QUALITY COUNCIL OF INDIANA CQE 2006
XI. ADVANCED STATISTICS ANALYSIS OF VARIANCE
Two Factor ANOVA Experiment with Interaction In the previous materials/instructor example, the data was listed in six cells. That is, six experimental combinations. There were also 3 replications (students) in each cell (k = 3). When k is greater than 1 in a two factor ANOVA, there is the opportunity to analyze for a possible interaction between the two factors. Example continued: Examine the previous data for interaction effects. A similar analysis pattern is noted here. The data in each cell is summed, and that total is divided by the number of observations in that cell. CellSq =
( SumCell ) k
2
InterSqs =
∑ ( CellSq )
InterSS = InterSqs - CM - ColSS - Row SS InterSS = 81604 - 78672.22 - 872.44 - 2005.56 = 53.78 ErrorSS = TotSS - ColSS - RowSS - InterSS ErrorSS = 3171.78 - 872.44 - 2005.56 - 53.78 = 240
XI-57 (1137)
© QUALITY COUNCIL OF INDIANA CQE 2006
XI. ADVANCED STATISTICS ANALYSIS OF VARIANCE
Two Factor ANOVA, Interaction (Cont.) Example continued: The null hypothesis for the interaction effect is that there is no interaction. Source
SS
Columns 872.44 (Materials)
DF
MS
F
Fα ,ν ,ν 1
2
2
436.22 21.81 F0.05,2,12 = 3.89 2005.56 100.3 F0.05,1,12 = 4.75
Rows (Instruct)
2005.6
1
Interaction (Row/Col)
53.78
2
26.89
Error
240
12
20
17
1.34 F0.05,2,12 = 3.89
SIGe = 20 = 4.47 SIG total =
Total SS/(N-1) = 13.66
The interaction calculated F (1.34) is less than critical F (3.89). The null hypothesis of no interaction is not rejected.
© QUALITY COUNCIL OF INDIANA CQE 2006
XI-58 (1138)
XI. ADVANCED STATISTICS ANALYSIS OF VARIANCE
Components of Variance An analysis of variance can be extended with a determination of the COV (components of variance). The COV table uses the MS (mean square), F, and F (alpha) columns from the previous ANOVA table and adds columns for EMS (expected mean square), variance, adjusted variance and percent contribution to design data variation. The model for the ANOVA is: X ijk = μ + Mi + Ij + MIij + ε k(ij)
The model states that any measurement ( X ) represents the combined effect of the population mean ( μ ), the different materials ( M ), the different instructors ( I ), the materials/instructor interaction ( M/I ), and the experimental error ( ε ). I represents materials at 3 levels, j represents instructors at 2 levels, k represents cells with 3 replications.
XI-58 (1139)
© QUALITY COUNCIL OF INDIANA CQE 2006
XI. ADVANCED STATISTICS ANALYSIS OF VARIANCE
Components of Variance (Continued) Example continued: MS
F
F(α)
COV TABLE EMS
2 2 436.22 21.81 3.89 σe + 6σM
2005.6 100.3 4.75 26.89 20
σ2e + 9σI2
1.34 3.89 σ + 3σ 2
2
e
MI
σ2e
VAR
ADJ VAR
% CONTR
69.37
69.37
22.21
220.62 220.62
70.65
2.3
2.3
0.74
20
20
6.4
Totals 312.39
100
Effect Variance = (Effect MS - Error MS)/(Variance Coefficient) M Var = (436.22 - 20)/6 = 69.37 I Var = (2005.56 - 20)/9 = 220.62 M/I Var = (26.89 - 20)/3 = 2.30 Error Var = 20
Material differences are significant and contribute 22.21% of variation in the data. Instructor differences are significant and contribute 70.65% of variation in the data. The material/instructor interaction is not significant. Experimental error contributes only 6.40% of total variation.
XI-59 (1140)
© QUALITY COUNCIL OF INDIANA CQE 2006
XI. ADVANCED STATISTICS ANALYSIS OF VARIANCE
ANOVA Table for an A x B Factorial Experiment In a factorial experiment involving factor A at a levels and factor B at b levels, total sum of squares can be partitioned into: Total SS = SS(A) + SS (B) + SS(AB) + SSE ANOVA Table for an A x B Factorial Experiment Source
DF
(a-1) Factor A (b-1) Factor B Interaction AB (a-1)(b-1) (n-ab) Error Total
(n-1)
SS
MS
SS(A)/(a-1) SS(A) SS(B)/(b-1) SS(B) SS(AB) SS(AB)/(a-1)(b-1) SSE/(n-ab) SSE Total SS
XI-59 (1141)
© QUALITY COUNCIL OF INDIANA CQE 2006
XI. ADVANCED STATISTICS ANALYSIS OF VARIANCE
ANOVA Table for a Randomized Block Design The randomized block design implies the presence of two independent variables, “blocks” and “treatments.” The total sum of squares of the response measurements can be partitioned into three parts; the sum of the squares for the blocks, treatments, and error. ANOVA Table for a Randomized Block Design Source
DF
SS
MS
Blocks Treatments Error
b-1 t-1 (b-1)(t-1)
SSB SST SSE
MSB=SSB/(b-1) MST=SST/(t-1) MSE=SSE/(b-1)(t-1)
Total
bt-1
Total SS
© QUALITY COUNCIL OF INDIANA CQE 2006
XI-60 (1142)
XI. ADVANCED STATISTICS / RELATIONSHIPS BETWEEN VARIABLES / LINEAR REGRESSION
Relationships Between Variables Relationships between variables is presented in the following topic areas: C Linear regression C Simple linear correlation C Time-series analysis
XI-60 (1143)
© QUALITY COUNCIL OF INDIANA CQE 2006
XI. ADVANCED STATISTICS / RELATIONSHIPS BETWEEN VARIABLES / LINEAR REGRESSION
Linear Regression Consider the problem of predicting the CQE test results (Y) for students based upon an input variable (X), the amount of preparation time in hours. A total of ten students were sampled in this fabricated example. Student
Study Time (Hours)
Test Results 50 = 50%
1 2 3 4 5 6 7 8 9 10
60 40 50 65 35 40 50 30 45 55
67 61 73 80 60 55 62 50 61 70
An initial approach to the analysis of the data in the table above is to plot the points on a graph known as a scatter diagram. Observe that Y appears to increase as X increases.
XI-61 (1144)
© QUALITY COUNCIL OF INDIANA CQE 2006
XI. ADVANCED STATISTICS / RELATIONSHIPS BETWEEN VARIABLES / LINEAR REGRESSION
Linear Regression (Continued) 81 74 67 60 53
30
35
40
45
50
55
60
65
Study Time (Hours), X
The mathematical equation of a straight line is: Y = β0 + β1X Where β0 is the Y intercept and β1 is the slope of the line.
© QUALITY COUNCIL OF INDIANA CQE 2006
XI-61 (1145)
XI. ADVANCED STATISTICS / RELATIONSHIPS BETWEEN VARIABLES / LINEAR REGRESSION
Linear Regression (Continued) A random error is the difference between an observed value of Y and the mean value of Y for a given value of X. One assumes that for any given value of X the observed value of Y varies in a random manner and possesses a normal probability distribution. The probabilistic model for any particular observed value of Y is: ⎛ Mean value of Y for ⎞ Y= ⎜ ⎟ + ( random error ) ⎝ a given value of X ⎠ Y = β 0 + β1X + ε
Variation in Y as a Function of X
XI-62 (1146)
© QUALITY COUNCIL OF INDIANA CQE 2006
XI. ADVANCED STATISTICS / RELATIONSHIPS BETWEEN VARIABLES / LINEAR REGRESSION
The Method of Least Squares If one denotes the predicted value of Y obtained from l , the prediction equation is: the fitted line as Y l i = β + β X Y 0 1 i
Where: β and β represent estimates of the true β0 and β1. 0
1
81 74 67
l i = β + β X Y 0 1 i
60 53 30
35
40
45
50
55
60
65
Study Time (Hours), X
The principle of least squares is: Choose, as the best fitting line, the line that minimizes the sum of squares of the deviations of the observed values of Y from those predicted.
XI-63 (1147)
© QUALITY COUNCIL OF INDIANA CQE 2006
XI. ADVANCED STATISTICS / RELATIONSHIPS BETWEEN VARIABLES / LINEAR REGRESSION
The Method of Least Squares (Cont.) Expressed mathematically, to minimize the sum of squared errors given by: n
(
li SSE = ∑ Yi - Y i=1
)
2
Substituting for Yl one obtains the following expression: i
n
(
)
2
SSE = ∑⎡Yi - β 0 + β 1Xi ⎤ ⎦ i =1⎣
Sum of squared errors =
The least square estimator of β0 and β1 are calculated as 2 follows: n n n X X Yi ∑ i ∑ i i∑ n n 2 i=1 i=1 =1 SX = ∑ Xi S XY = ∑ Xi Yi i=1 i=1
( )
( )( )
n
2
S β 1 = XY SX
n
β 0 = Y - β 1 X
2
Once β and β have been computed, substitute their values into the equation of a line to obtain the least squares prediction equation, or regression line. 0
1
The prediction equation for
l Y
is:
l i = β + β X Y 0 1 i
Where: β and β represent estimates of the true β0 and β1. 0
1
XI-65 (1148)
© QUALITY COUNCIL OF INDIANA CQE 2006
XI. ADVANCED STATISTICS / RELATIONSHIPS BETWEEN VARIABLES / LINEAR REGRESSION
Least Squares Example Example: Obtain the least squares prediction line for the table data below:
Sum
Xi
Yi
X2i
XiYi
Y2i
60 40 50 65 35 40 50 30 45 55
67 61 73 80 60 55 62 50 61 70
3,600 1,600 2,500 4,225 1,225 1,600 2,500 900 2,025 3,025
4,020 2,440 3,650 5,200 2,100 2,200 3,100 1,500 2,745 3,850
4,489 3,721 5,329 6,400 3,600 3,025 3,844 2,500 3,721 4,900
470
639
23200
30805
41529
Data Table for the Study Time/Test Score Example
XI-66 (1149)
© QUALITY COUNCIL OF INDIANA CQE 2006
XI. ADVANCED STATISTICS / RELATIONSHIPS BETWEEN VARIABLES / LINEAR REGRESSION
Least Squares Example (Continued) Example continued:
S X2
S XY
X=
⎛ n ⎞ ⎜ Xi ⎟ n = Xi2 - ⎝ i = 1 ⎠ n i=1
∑
∑
2
= 23,200 -
( 470 )2 10
= 1,110
⎛ n ⎞⎛ n ⎞ X Y ⎜ ⎟ ⎜ ⎟ i i n i=1 i=1 ⎝ ⎠ ⎝ ⎠ = 30,805 - ( 470 ) ( 639 ) = 772 = Xi Yi n 10 i=1
∑
∑
470 = 47 10
∑
Y=
639 = 63.9 10
S 772 β 1 = XY = = 0.6955 SX 1,110 2
β 0 = Y - β 1 X = 63.9 - (0.6955)(47) = 31.2115 l = 31.2115 + 0.6955 X Y
One may now predict Y for a given value of X for example, if 60 hours of study time is allocated, the predicted test score would be: l = 31.2115 + (0.6955)(60) Y l = 72.9415 = 73% Y
XI-67 (1150)
© QUALITY COUNCIL OF INDIANA CQE 2006
XI. ADVANCED STATISTICS / RELATIONSHIPS BETWEEN VARIABLES / LINEAR REGRESSION
Calculating s2e, an Estimator of σ2ε The model for Y assumes that Y is related to X: Y = β 0 + β1X + ε
If the least squares line is used: l i = β + β X Y 0 1 i
A random error ε enters into the calculations of β0 and β1. The random errors affect the error of prediction. We estimate σε2 from SSE (sum of squares for error) based on (n - 2) degrees of freedom. σˆ 2ε =
SSE n-2
σˆ 2ε is sometimes shown as s2e
∑( n
SSE =
i=1
li Yi - Y
)
2
=
(
n
)
⎡ Y - β 0 + β 1X ⎤ ∑ i i ⎦ i=1⎣
SSE = S Y - β 1S XY = S Y 2
2
(S )
2
XY
SX
2
(- ∑ Y ) n
SY = 2
∑ ( Y - Y) = ∑ Y n
i=1
2
i
n
i=1
i
2
i=1
n
i
2
2
XI-68 (1151)
© QUALITY COUNCIL OF INDIANA CQE 2006
XI. ADVANCED STATISTICS / RELATIONSHIPS BETWEEN VARIABLES / LINEAR REGRESSION
Inferences Concerning the Slope β1 of a Line The null hypothesis and alternative hypothesis are: H0: β1 = 0
H1: β1 =/ 0
The test statistic is a t distribution with n - 2 degrees of freedom: t=
β1 - β1 sβ
sβ = 1
1
σˆ ε SX
2
Example: From the data in Study Time/Test Score example, determine if the slope results are significant at a 95% confidence level. t=
β 1 - β1 β - β1 0.6955 - 0 = 1 = = 5.18 sβ ⎛ σˆ ⎞ ⎛ 4.47 ⎞ ⎜ ε ⎟ ⎜ ⎟ ⎜ S ⎟ 1,110 ⎠ ⎝ X ⎠ ⎝ 1
2
For a 95% confidence level, determine the critical values of t with α = 0.025 in each tail, using n - 2 = 8 degrees of freedom: t0.025, 8 = -2.306 and t0.025, 8 = 2.306. Reject the null hypothesis if t > 2.306 or t < -2.306, depending on whether the slope is positive or negative. In this case, the null hypothesis is rejected and we conclude that β1 =/ 0 and there is a linear relationship between Y and X.
XI-69 (1152)
© QUALITY COUNCIL OF INDIANA CQE 2006
XI. ADVANCED STATISTICS / RELATIONSHIPS BETWEEN VARIABLES / LINEAR REGRESSION
Confidence Interval Estimate for the Slope β1 The confidence interval estimate for the slope β1 is given by: σˆ ε β 1 ± t α/2, n-2 SX
thus, 2
σˆ ε σˆ ε < β 1 < β 1 + t α/2, n-2 β 1 - t α/2, n-2 SX SX 2
2
XI-70 (1153)
© QUALITY COUNCIL OF INDIANA CQE 2006
XI. ADVANCED STATISTICS / RELATIONSHIPS BETWEEN VARIABLES / SIMPLE LINEAR CORRELATION
Simple Linear Correlation Correlation Coefficient The population linear correlation coefficient, ρ, measures the strength of the linear relationship between the paired X and Y values in a population. ρ is a population parameter. For the population, the Pearson product moment coefficient of correlation, ρX,Y is given by: ρ X,Y =
cov ( X, Y ) σXσ Y
Where cov means covariance. Note that -1 < ρ < +1 The sample linear correlation coefficient, r, measures the strength of the linear relationship between the paired X and Y values in a sample. r is a sample statistic. For a sample, the Pearson product moment coefficient of correlation, rXY is given by:
∑ ( X - X )( Y - Y ) n
rXY =
S XY = SX SY 2
2
i
∑ ( X - X) ∑ ( Y - Y) n
i=1
Note that -1 < r < +1
i
i=1
2
i
n
i=1
i
2
XI-71 (1154)
© QUALITY COUNCIL OF INDIANA CQE 2006
XI. ADVANCED STATISTICS / RELATIONSHIPS BETWEEN VARIABLES / SIMPLE LINEAR CORRELATION
Simple Linear Correlation (Continued) Correlation Coefficient (Continued) Example: Using the study time and test score data reviewed earlier, determine the correlation coefficient. rXY =
SXY = SX SY 2
2
772
( 1,110 )( 696.9 )
= 0.878
The coefficient of correlation r will assume exactly the same sign as β1 and will equal zero when β1 = 0. C A positive value for r implies that the line slopes upward to the right. C A negative value indicates that it slopes downward to the right. Note that r = 0 implies no linear correlation, not simply “no correlation.” If X is of any value in predicting Y, then SSE, can never be larger than: S Y = ∑ ( Yi - Y ) n
2
2
i=1
SSE = S Y - β 1S XY = SY 2
2
(S ) XY
SX
2
2
XI-71 (1155)
© QUALITY COUNCIL OF INDIANA CQE 2006
XI. ADVANCED STATISTICS / RELATIONSHIPS BETWEEN VARIABLES / SIMPLE LINEAR CORRELATION
Coefficient of Determination (R2) The coefficient of determination is R2. The square of the linear correlation coefficient is r2. It can be shown that: R2 = r2 S - SSE ( SXY ) SSE R =r = Y =1= SY SY SX SY
2
2
2
2
2
2
2
2
The coefficient of determination is the proportion of the explained variation divided by the total variation, when a linear regression is performed. r 2 lies in the interval of 0 < r2 < 1. r2 will equal +1 or -1 only when all the points fall exactly on the fitted line. Example: Using the data from the previous example, determine the coefficient of determination.
(S )
( 772 ) r = = S S ( 1,110 )( 696.9 ) or r = ( 0.878 ) = 0.771 2
2
2
XY
X
2
2
Y
= 0.771
2
2
One can say that 77% of the variation in test scores can be explained by variation in study hours.
XI-72 (1156)
© QUALITY COUNCIL OF INDIANA CQE 2006
XI. ADVANCED STATISTICS / RELATIONSHIPS BETWEEN VARIABLES / SIMPLE LINEAR CORRELATION
Simple Linear Correlation (Continued) Correlation Example 25 24 23 22
MPG
21 AVERAGE 20 MPG
20 19 18 17 16
2000
3000
4000
CAR WEIGHT
Correlation Plot of Car Weight and MPG SST = ∑ D12 + D22 + . . . + D29 SSE = ∑ d12 + d22 + . . . + d29 r2 = 1 -
SSE SST - SSE = SST SST
XI-73 (1157)
© QUALITY COUNCIL OF INDIANA CQE 2006
XI. ADVANCED STATISTICS / RELATIONSHIPS BETWEEN VARIABLES / TIME-SERIES ANALYSIS
Time-Series Analysis Data can be presented in either summary (static) or time series (dynamic) fashion. Important elements of most processes can change over time. For many business activities, trend charts will show patterns that indicate if a process is running normally or whether desirable or undesirable changes are occurring. It should be noted that normal convention has time increasing across the page (from left to right) and the measurement value increasing up the page. UPWARD TREND
DOWNWARD TREND
PROCESS SHIFT
100
100
100
80
80
80
60
60
60
40
40
40
20
20
20
0
0 1
5
10
15
0 1
20
5
UNUSUAL VALUES
10
15
20
1
CYCLES 100
100
80
80
80
60
60
60
40
40
40
20
20
20
0 1
5
10
15
20
10
15
20
INCREASING VARIABILITY
100
0
5
0 1
5
10
15
20
1
Time-Series (Trend) Charts
5
10
15
20
© QUALITY COUNCIL OF INDIANA CQE 2006
XI-74 (1158)
XI. ADVANCED STATISTICS DESIGN OF EXPERIMENTS / INTRODUCTION
Design and Analysis of Experiments Design and analysis of experiments is presented in the following topic areas: C C C C C C C C
Introduction Terminology Planning experiments Simple experiments Block experiments Full-factorial experiments Fractional-factorial experiments Other experiments
© QUALITY COUNCIL OF INDIANA CQE 2006
XI-74 (1159)
XI. ADVANCED STATISTICS DESIGN OF EXPERIMENTS / INTRODUCTION
Introduction to DOE Many experiments focus on 1FAT (one factor at a time) at two or three levels and try to hold everything else constant (which is impossible to do in a complicated process). When Design of Experiments (DOE) is properly constructed, it can focus on a wide range of key input factors or variables and will determine the optimum levels of each of the factors. It should be recognized that the Pareto principle applies to the world of experimentation. That is, 20% of the potential input factors generally make 80% of the impact on the result. Changing just one factor at a time, has shortcomings: C Too many experiments are necessary C The optimum values may never be revealed C The factor interaction cannot be determined C Conclusions may be wrong or misleading C Non-statistical experiments are often inconclusive C Time and effort may be wasted
© QUALITY COUNCIL OF INDIANA CQE 2006
XI-75 (1160)
XI. ADVANCED STATISTICS DESIGN OF EXPERIMENTS / INTRODUCTION
Introduction to DOE (Continued) Design of experiments is a methodology of varying a number of input factors simultaneously in a carefully planned manner, such that their individual and combined effects on the output can be identified. Advantages of DOE include: C Many factors can be evaluated simultaneously C Noise factors cannot be controlled, but other input factors can be controlled to make the output insensitive to noise factors C In-depth, statistical knowledge is not necessary C Important factors can be distinguished C Since the designs are balanced, there is confidence in the conclusions drawn C If important factors are overlooked, the results will indicate that they were overlooked C Precise statistical analysis can be run using standard computer programs C Quality can be improved without increased costs
XI-76 (1161)
© QUALITY COUNCIL OF INDIANA CQE 2006
XI. ADVANCED STATISTICS DESIGN OF EXPERIMENTS / TERMINOLOGY
DOE Terminology The CQE Primer lists a number of DOE terms. The student is encouraged to review those definitions. Alias
An alias occurs when two factor effects are confounded with each other.
Balanced design
A fractional-factorial design in which an equal number of trials is conducted for each factor.
Block
A subdivision of the experiment into relatively homogenous experimental units.
Confounded When the effects of two factors are not separable. A
+ +
B
+ +
C
+ +
AB AC BC
+ +
+ +
+ +
A
Or
+ + -
B
+ + -
C
+ + -
A is confounded with BC B is confounded with AC C is confounded with AB
AB AC BC
+ +
+ +
+ +
© QUALITY COUNCIL OF INDIANA CQE 2006
XI-77 (1162)
XI. ADVANCED STATISTICS DESIGN OF EXPERIMENTS / TERMINOLOGY
DOE Terminology (Continued) Correlation A number between -1 and 1 that indicates coefficient the degree of linear relationship between two sets of numbers. Zero (0) indicates (r) no linear relationship. Curvature
Refers to non-straight-line behavior between one or more factors and the response. For example: Y = B0 + B1X1 + B11 (X1 C X1) + ε
Degrees of The term used is DOF, DF, d.f. or ν. The freedom number of measurements that are independently available for estimating a population parameter. EVOP
evolutionary operation, a term that describes the way sequential experimental designs can be adapted by learning from current results to predict future treatments. Small response improvements may be made via large sample sizes. The experimental risk is low because the trials are conducted in vicinity of an already satisfactory process.
XI-78 (1163)
© QUALITY COUNCIL OF INDIANA CQE 2006
XI. ADVANCED STATISTICS DESIGN OF EXPERIMENTS / TERMINOLOGY
DOE Terminology (Continued) Experiment A test undertaken to make an improvement in a process or to learn previously unknown information. First-order The equation below is is first-order in both X1 and X2. Y = B0 + B1X1 + B2X2 + ε Fractional factorial
Fewer experiments than the full design are conducted. Three-factor two-level, half-fractional designs examples are: A + +
B + +
C + + -
A + +
B + +
C + +
© QUALITY COUNCIL OF INDIANA CQE 2006
XI-79 (1164)
XI. ADVANCED STATISTICS DESIGN OF EXPERIMENTS / TERMINOLOGY
DOE Terminology (Continued) Full factorial
Experimental designs which contain all combinations of all levels of all factors. A two-level, three-factor full-factorial design is: A B C + + + + + + + + + + + +
Input factor An independent variable which may affect a (dependent) response variable and is included at different levels in the experiment. Inner array In Taguchi-style, fractional-factorial experiments, these are the factors that can be controlled in a process.
XI-79 (1165)
© QUALITY COUNCIL OF INDIANA CQE 2006
XI. ADVANCED STATISTICS DESIGN OF EXPERIMENTS / TERMINOLOGY
DOE Terminology (Continued) Interaction Occurs when the effect of one input factor on the output depends upon the level of another input factor. No Interaction
Interaction
No drugs
Have eaten Haven’t eaten 2 4 6 8 # Drinks
Level
Drugs 0
1 2 3 # Drinks
A given factor or a specific setting of an input factor. Four levels of a heat treatment may be 100EF, 120EF, 140EF and 160EF.
Main effect An estimate of the effect of a factor independent of any other factors. Mixture experiments
Experiments in which the variables are expressed as proportions of the whole and sum to 1.0.
© QUALITY COUNCIL OF INDIANA CQE 2006
XI-80 (1166)
XI. ADVANCED STATISTICS DESIGN OF EXPERIMENTS / TERMINOLOGY
DOE Terminology (Continued) Orthogonal A design is orthogonal if the main and interaction effects can be estimated without confounding the other main effects or interactions. Outer array In a Taguchi-style fractional-factorial experiment, these are the factors that cannot be controlled in a process. Qualitative Descriptors of category and/or order, but not of interval or origin. Quantitative
Descriptors of order and interval (interval scale) and possibly also of origin (ratio scale).
Randomized trials
Frees an experiment from the environment and eliminates biases.
Repeated trials
Trials conducted to estimate the trial-totrial experimental error. Also called replications.
Residual error (ε) or (E)
The difference between the observed and the predicted value for that result, based on an empirically determined model.
© QUALITY COUNCIL OF INDIANA CQE 2006
XI-81 (1167)
XI. ADVANCED STATISTICS DESIGN OF EXPERIMENTS / TERMINOLOGY
DOE Terminology (Continued) Residuals
The difference between experimental responses and predicted model values.
Resolution II
An experiment in which some of the main effects are confounded.
Resolution III A fractional-factorial design in which no main effects are confounded with each other but the main effects and two-factor interaction effects are confounded. Resolution IV A fractional factorial design in which the main effects and two factor interaction effects are not confounded, but the two factor effects may be confounded with each other. Resolution V
A fractional-factorial design in which no confounding of main effects and two factor interactions occurs.
Response surface methodology (RSM)
The graph of a system response plotted against one or more system factors. Response surface methodology employs experimental design to discover the “shape” of the response surface.
© QUALITY COUNCIL OF INDIANA CQE 2006
XI-82 (1168)
XI. ADVANCED STATISTICS DESIGN OF EXPERIMENTS / TERMINOLOGY
DOE Terminology (Continued) Response variable
The variable that shows the observed results of an experimental treatment. Also output or dependent variable.
Robust design
Associated with the application of Taguchi experimentation in which a response variable is considered immune to input variables that may be difficult or impossible to control.
Screening experiment
A technique to discover the most important factors in an experimental system. Most screening experiments employ two-level designs.
Sequential Experiments are done one after another, experiments not at the same time. Simplex design
A spatial design used to determine the most desirable variable combination (proportions) in a mixture.
Test coverage
The percentage of all possible combinations of input factors in an experimental test.
Treatments
The various factor levels that describe how an experiment is to be carried out.
XI-83 (1169)
© QUALITY COUNCIL OF INDIANA CQE 2006
XI. ADVANCED STATISTICS DESIGN OF EXPERIMENTS / TERMINOLOGY
Interactions An interaction occurs when the effect of one input factor on the output depends upon the level of another input factor. No interaction
Moderate interaction
Strong interaction
Very strong interaction
A LOW
A HIGH
L Factor B
H
L Factor B
H
L Factor B
H
H
L Factor B
Interactions can be readily examined with full-factorial experiments. Often, interactions are lost with fractionalfactorial experiments. The preferred DOE approach screens a large number of factors with highly fractional experiments. Interactions are then explored or additional levels examined once the suspected factors have been reduced.
XI-85 (1170)
© QUALITY COUNCIL OF INDIANA CQE 2006
XI. ADVANCED STATISTICS DESIGN OF EXPERIMENTS / TERMINOLOGY
Response Surfaces 3-D Response Surface
Matching Dome Contour 50 60 70 80
Additive
Additive
Comparison of 3-D and 2-D Response Surfaces Rising Ridge Stationary Ridge Saddle Minimax 60
60
X2
70
70 80
80
X2
70
50
90
50 70
70
X1
80
60
80
X2 90
90
50
X1
Contour Examples
80
60 50
X1
50
© QUALITY COUNCIL OF INDIANA CQE 2006
XI-86 (1171)
XI. ADVANCED STATISTICS DESIGN OF EXPERIMENTS / PLANNED EXPERIMENTS
DOE Applications Situations where experimental design can be effectively used include: C Choosing between alternatives C Selecting the key factors affecting a response C Response surface modeling to: C C C C C
Hit a target Reduce variability Maximize or minimize a response Make a process robust Seek multiple goals
© QUALITY COUNCIL OF INDIANA CQE 2006
XI-87 (1172)
XI. ADVANCED STATISTICS DESIGN OF EXPERIMENTS / PLANNED EXPERIMENTS
DOE Steps Getting good results from a DOE involves a number of steps: C Set objectives C Select process variables C Select an experimental design C Execute the design C Check that the data are consistent with the experimental assumptions C Analyze and interpret the results C Use/present the results
© QUALITY COUNCIL OF INDIANA CQE 2006
XI-88 (1173)
XI. ADVANCED STATISTICS DESIGN OF EXPERIMENTS / PLANNED EXPERIMENTS
A Typical DOE Checklist The following checklist will be helpful for many investigations. C Define the objective of the experiment C Learn many facts about the process C Brainstorm the key variables with knowledgeable people C Run “dabbling experiments” where necessary C Assign levels to each independent variable C Select, develop and review the DOE plan C Run the experiments in random order C Draw conclusions and verify them
The Iterative Approach to DOE Instead of performing one big experiment, it is more common to perform several smaller experiments, with each stage supplying a different kind of answer.
© QUALITY COUNCIL OF INDIANA CQE 2006
XI-89 (1174)
XI. ADVANCED STATISTICS DESIGN OF EXPERIMENTS / PLANNED EXPERIMENTS
Experimental Objectives Some experimental design objectives are: 1. Comparative objective 2. Screening objective 3. Response surface (method) objective 4. Optimizing responses when factors are proportions of a mixture objective 5. Optimal fitting of a regression model objective
© QUALITY COUNCIL OF INDIANA CQE 2006
XI-90 (1175)
XI. ADVANCED STATISTICS DESIGN OF EXPERIMENTS / PLANNED EXPERIMENTS
Select and Scale the Process Variables Process variables include both inputs and outputs - i.e. factors and responses. C C C C C
Include all important factors Be bold, but not foolish, in choosing factor levels Avoid impractical factor settings Include all relevant responses Avoid using combined measurement responses
When choosing the range of settings for input factors, it is wise to avoid extreme values. The most popular experimental designs are called twolevel designs.
XI-90 (1176)
© QUALITY COUNCIL OF INDIANA CQE 2006
XI. ADVANCED STATISTICS DESIGN OF EXPERIMENTS / PLANNED EXPERIMENTS
Design Guidelines Factors Comparative Objective
Screening Objective ____
Response Surface Objective ____
1
1-factor completely randomized design
2-4
Randomized block design
Full or fractionalfactorial
Central composite or Box-Behnken
5 or more
Randomized block design
Fractionalfactorial or PlackettBurman
Screen first to reduce number of factors
The choice of a design depends on the amount of resources available and the degree of control over making wrong decisions.
© QUALITY COUNCIL OF INDIANA CQE 2006
XI-91 (1177)
XI. ADVANCED STATISTICS DESIGN OF EXPERIMENTS / PLANNED EXPERIMENTS
Experimental Assumptions In all experimentation, one makes assumptions. Some of the engineering and mathematical assumptions an experimenter makes include: C Are the measurement systems capable for all responses? C Is the process stable? C Are the residuals (the difference between the model predictions and the actual observations) well behaved?
XI-92 (1178)
© QUALITY COUNCIL OF INDIANA CQE 2006
XI. ADVANCED STATISTICS DESIGN OF EXPERIMENTS / PLANNED EXPERIMENTS
Experimental Assumptions (Continued) Are the Residuals Well Behaved? Residuals can be thought of as elements of variation unexplained by the fitted model. Residuals are expected to be normally and independently distributed with a mean of 0 and some constant variance. These are the assumptions behind ANOVA and classical regression analysis.
,
,
X1
Residuals suggest the X1 model is properly specified.
,
X2
Residuals suggest that the variance increases with X2
X3
Residuals suggest the need for a quadratic term added to X3.
XI-93 (1179)
© QUALITY COUNCIL OF INDIANA CQE 2006
XI. ADVANCED STATISTICS DESIGN OF EXPERIMENTS / SIMPLE EXPERIMENTS
Evolutionary Operations EVOP emphasizes a conservative experimental strategy for continuous process improvement. Tests are centered on the best conditions from previous experiments. Small incremental changes are made so that little or no process scrap is generated. 91% E 69% B pH
83% B 79% A
71% A
94% E 96% D
88% C E 92%
A 63%
D 88%
B 87%
69% A A 70%
C 84%
Concentration
EVOP Experimentation
XI-94 (1180)
© QUALITY COUNCIL OF INDIANA CQE 2006
XI. ADVANCED STATISTICS DESIGN OF EXPERIMENTS / BLOCK DESIGNS
Randomized Block Plans One may be able to divide the experiment into blocks, or planned homogeneous groups. When each group in the experiment contains exactly one measurement on every treatment, the experimental plan is called a randomized block plan. A randomized incomplete block (tension response) design is shown below. Treatment Block (Days)
A
B
C
D
1
-5
Omitted
-18
-10
2
Omitted
-27
-14
-5
3
-4
-14
-23
Omitted
4
-1
-22
Omitted
-12
© QUALITY COUNCIL OF INDIANA CQE 2006
XI-95 (1181)
XI. ADVANCED STATISTICS DESIGN OF EXPERIMENTS / BLOCK DESIGNS
Latin Square Designs In Latin square designs a third variable, the experimental treatment, is applied to the source variables in a balanced fashion. The Latin square plan is restricted by two conditions: C The number of rows, columns and treatments must be the same. C There should be no interactions between row and column factors, since these cannot be measured. A Latin square design is essentially a fractional-factorial experiment.
XI-95 (1182)
© QUALITY COUNCIL OF INDIANA CQE 2006
XI. ADVANCED STATISTICS DESIGN OF EXPERIMENTS / BLOCK DESIGNS
Latin Square Designs (Continued) Consider the following 5 x 5 Latin square: Carburetor Type Car
I
II
III
IV
V
1
A
B
C
D
E
2
B
C
D
E
A
3
C
D
E
A
B
4
D
E
A
B
C
5
E
A
B
C
D
In the above design, five automobiles and five carburetors are used to evaluate gas mileage by five drivers (A, B, C, D, and E). Note that only 25 of the potential 125 combinations are tested. Thus, the resultant experiment is a one-fifth, fractional-factorial. Similar 3 x 3, 4 x 4, and 6 x 6 designs may be utilized.
XI-96 (1183)
© QUALITY COUNCIL OF INDIANA CQE 2006
XI. ADVANCED STATISTICS DESIGN OF EXPERIMENTS / BLOCK DESIGNS
Graeco-Latin Designs Graeco-Latin square designs are sometimes useful to eliminate more than two sources of variability in an experiment. A Graeco-Latin design is an extension of the Latin square design, but one extra blocking variable is added for a total of three blocking variables. Consider the following 4 X 4 Graeco-Latin Design: Carburetor Type Car
I
II
III
IV
Drivers
1
Aα
Bβ
Cγ
Dδ
A,B,C,D
2
Bδ
Aγ
Dβ
Cα
3
Cβ
Dα
Aδ
Bγ
Days
4
Dγ
Cδ
Bα
Aβ
α,β,γ,δ
XI-96 (1184)
© QUALITY COUNCIL OF INDIANA CQE 2006
XI. ADVANCED STATISTICS DESIGN OF EXPERIMENTS / BLOCK DESIGNS
Hyper-Graeco-Latin Designs A Hyper-Graeco-Latin square design permits the study of treatments with more than three blocking variables. Carburetor Type Car
I
II
III
IV
Drivers
Tires
1
AαMφ BβNΧ CγOΨ DδPΩ A,B,C,D M,N,O,P
2
BδNΩ AγMΨ DβPΧ CαOφ
3
CβOΧ DαPφ AδMΩ BγNΨ
Days
4 DγPΨ CδOΩ BαNφ AβMΧ α,β,γ,δ
Speeds φΧΨΩ
XI-97 (1185)
© QUALITY COUNCIL OF INDIANA CQE 2006
XI. ADVANCED STATISTICS DESIGN OF EXPERIMENTS / FULL-FACTORIAL EXPERIMENTS
Full-factorial Experiments Suppose that pressure, temperature and concentration are three key variables affecting the yield of a chemical process which is currently running at 64%. In order to find out the effect of all three factors and their interactions, conduct 2 3 = 8 experiments. This is called a full-factorial experiment. The low and high levels of input factors are noted below by (-) and (+). Exp. No.
Temp.
Press.
Conc.
% Yield
1
-
-
-
55
2
+
-
-
77
3
-
+
-
47
4
+
+
-
73
5
-
-
+
56
6
+
-
+
80
7
-
+
+
51
8
+
+
+
73
Average
64
Temperature: (-) = 120EC (+) = 150EC Pressure: (-) = 10 psi (+) = 14 psi Concentration: (-) = 10N (+) = 12N
XI-98 (1186)
© QUALITY COUNCIL OF INDIANA CQE 2006
XI. ADVANCED STATISTICS DESIGN OF EXPERIMENTS / FULL-FACTORIAL EXPERIMENTS
Full-factorial Experiments (Continued) The temperature effect =
The pressure effect =
( 77 + 73 + 80 + 73 ) - ( 55 + 47 + 56 + 51)
= 23.5
( 47 + 73 + 51 + 73 ) - ( 55 + 77 + 56 + 80 ) 4
The concentration effect =
T x P interaction =
4
( 56 + 80 + 51 + 73 ) - ( 55 + 77 + 47 + 73 ) 4
( 55 + 73 + 56 + 73 ) - ( 77 + 47 + 80 + 51) 4
=2
= 0.5
P x C interaction
=
( 55 + 77 + 51 + 73 ) - ( 47 + 73 + 56 + 80 )
T x C interaction
=
( 55 + 47 + 80 + 73 ) - ( 77 + 73 + 56 + 51)
T x P x C interaction =
( 77 + 47 + 56 + 73 ) - ( 55 + 73 + 80 + 51)
4
4
4
= -6
=0
= -0.5
= -1.5
XI-99 (1187)
© QUALITY COUNCIL OF INDIANA CQE 2006
XI. ADVANCED STATISTICS DESIGN OF EXPERIMENTS / FULL-FACTORIAL EXPERIMENTS
Full-factorial Experiments (Continued) Interactions EXP.
T
P
C
TXP
PXC
TXC
TXPXC YIELD
1
-
-
-
+
+
+
-
55
2
+
-
-
-
+
-
+
77
3
-
+
-
-
-
+
+
47
4
+
+
-
+
-
-
-
73
5
-
-
+
+
-
-
+
56
6
+
-
+
-
-
+
-
80
7
-
+
+
-
+
-
-
51
8
+
+
+
+
+
+
+
73
The best combination of factors is: high temperature, low pressure, and high concentration.
XI-100 (1188)
© QUALITY COUNCIL OF INDIANA CQE 2006
XI. ADVANCED STATISTICS DESIGN OF EXPERIMENTS / FULL-FACTORIAL EXPERIMENTS
Full-factorial Experiments (Continued) Comparison to a Fractional Factorial Design Consider the following fractional factorial experiment, in which only the main effects can be determined. Exp.
T
P
C
Yield
2
+
-
-
77
3
-
+
-
47
5
-
-
+
56
8
+
+
+
73
The temperature effect =
( 77 + 73 ) - ( 47 + 56 )
The pressure effect
=
( 47 + 73 ) - ( 77 + 56 )
The concentration effect =
( 56 + 73 ) - ( 47 + 77 )
2
2
2
= 23.5
= -6.5
= 2.5
The results are not identical, but, the same relative conclusions as to the effects of temperature, pressure, and concentration on the final yield can be drawn.
© QUALITY COUNCIL OF INDIANA CQE 2006
XI-101 (1189)
XI. ADVANCED STATISTICS / DESIGN OF EXPERIMENTS / FRACTIONAL-FACTORIAL EXPERIMENTS
Two-Level Fractional Factorial Example 1. Select a process 2. Identify the output factors of concern 3. Identify the input factors and levels to be investigated 4. Select a design (from a catalogue, Taguchi, selfcreated, etc.) 5. Conduct the experiment under the predetermined conditions 6. Collect the data (relative to the identified outputs) 7. Analyze the data and draw conclusions A example of a two-level, fractional factorial CQE Test Success is given in the CQE Primer. Please note that the values given were arbitrarily chosen for the purposes of the example, and are not based on factual data. The student is encouraged to work through this example.
XI-106 (1190)
© QUALITY COUNCIL OF INDIANA CQE 2006
XI. ADVANCED STATISTICS / DESIGN OF EXPERIMENTS / FRACTIONAL-FACTORIAL EXPERIMENTS
CQE Test Success (Continued) The significance of the CQE design results may be examined using the sum of squares and a scree plot. Note that SS =
( Δ value )
FACTOR
Δ
SS
G
23
66.1
C
20
50
A
13
21.2
D
5
3.1
B
0
0
E
0
0
F
0
0
2
8
SUM OF SQUARES SCREE PLOT
70 60 50 40 30 20 10 0 G
C
A
D FACTOR
B
E
F
XI-107 (1191)
© QUALITY COUNCIL OF INDIANA CQE 2006
XI. ADVANCED STATISTICS / DESIGN OF EXPERIMENTS / FRACTIONAL-FACTORIAL EXPERIMENTS
CQE Test Success (Continued) The scree plot indicates that factors D, B, E, and F are noise. The SS (sum of squares) for the error term is 3.1 (3.1 + 0 + 0 + 0). MSE (Mean Square Error) =
3.1 = 0.775 4
The maximum F table given in the CQE Primer accommodates screening designs for runs of 8, 12, 16, 20, and 24. p is the number of noise factors averaged to derive the MSE, and k is the number of factors. The maximum F ratio for factor G is:
66.1 = 85.29 0.775
The critical max-F value for k-1=7, p=4 and α=0.05 is 73. Thus, factor G is important at the 95% confidence level. The maximum F ratio for factor C is
50 = 65.42 0.775
The critical max-F value for k-1=7, p=4 and α=0.10 is 49. Thus, factor C is important at the 90% confidence level. The maximum F ratio for factor A is
21.1 = 27.22 0.775
The critical max-F values for k-1=7, p=4 and α=0.10 is 49. Therefore, factor A is not considered important.
© QUALITY COUNCIL OF INDIANA CQE 2006
XI-108 (1192)
XI. ADVANCED STATISTICS DESIGN OF EXPERIMENTS / OTHER DESIGNS
Plackett-Burman Designs Plackett-Burman designs are used for screening experiments. PB designs are very economical. The run number is a multiple of four rather than a power of 2. PB geometric designs are two-level designs with 4, 8, 16, 32, 64, and 128 runs and work best as screening designs. Each interaction effect is confounded with exactly one main effect. All other two-level PB designs (12, 20, 24, 28, etc.) are non-geometric designs. In these designs a two-factor interaction will be partially confounded with each of the other main effects in the study. Thus, the non-geometric designs are essentially “main-effect designs,” when there is reason to believe any interactions are of little practical importance. A PB design in 12 runs, for example, may be used to conduct an experiment containing up to 11 factors.
XI-108 (1193)
© QUALITY COUNCIL OF INDIANA CQE 2006
XI. ADVANCED STATISTICS DESIGN OF EXPERIMENTS / OTHER DESIGNS
Plackett-Burman Designs (Continued) Exp 1 2 3 4 5 6 7 8 9 10 11 12
X1 + + + + + +
X2 + + + + + + -
X3 + + + + + +
X4 + + + + + +
Factors X5 X6 X7 + + + + + + + + + + + + + + + + + + -
X8 + + + + + + -
X9 X10 X11 + + + + + + + + + + + + + + + + + + -
Plackett-Burman Non-Geometric Design (12 Runs/11 Factors) With a 20-run design, an experimenter can do a screening experiment for up to 19 factors. As many as 27 factors can be evaluated in a 28 run design.
XI-109 (1194)
© QUALITY COUNCIL OF INDIANA CQE 2006
XI. ADVANCED STATISTICS DESIGN OF EXPERIMENTS / OTHER DESIGNS
Three Factor, Three Level Experiments A 1/3 fractional-factorial design, three factors, three levels is shown below. Three level designs are always represented as 0, 1, and 2. CONCENTRATION
( 222 )
( 200 ) ( 122 ) ( 100 ) PRESSURE ( 022 ) ( 012 ) ( 000 )
( 001 )
( 002 )
TEMPERATURE
EXPER. CONC. PRESS. TEMP. 1 0 0 0 2 0 1 2 3 0 2 1 4 1 0 1 5 1 1 0 6 1 2 2 7 2 0 2 8 2 1 1 9 2 2 0
© QUALITY COUNCIL OF INDIANA CQE 2006
XI-110 (1195)
XI. ADVANCED STATISTICS DESIGN OF EXPERIMENTS / OTHER DESIGNS
Taguchi Designs The Taguchi philosophy emphasizes two tenets: (1) reduce the variation of a product or process which reduces the loss to society (2) use a proper development strategy to intentionally reduce variation
Orthogonal Arrays Degrees of Freedom Let d.f. = degrees of freedom Let k = number of factor levels For factor A, d.f.A = kA - 1 For factor B, d.f.B = kB - 1 For A x B interaction, d.f.AB = d.f.A x d.f.B d.f.min = Gd.f. all factors + Gd.f. all interactions of interest
XI-110 (1196)
© QUALITY COUNCIL OF INDIANA CQE 2006
XI. ADVANCED STATISTICS DESIGN OF EXPERIMENTS / OTHER DESIGNS
Taguchi Designs (Continued) Two - Level OAs OAs can be used to assign factors and interactions. The simplest OA is an L4 (four trial runs). Columns Trial
1
2
3
1
1
1
1
2
1
2
2
3
2
1
2
4
2
2
1
An L4 OA Design Factors A and B can be assigned to any two of the three columns. The remaining column is the interaction column. Assume a trial is conducted with two repeat runs for each trial. Assign factor A to column 1 and factor B to column 2. The interaction is then assigned to column 3.
XI-111 (1197)
© QUALITY COUNCIL OF INDIANA CQE 2006
XI. ADVANCED STATISTICS DESIGN OF EXPERIMENTS / OTHER DESIGNS
Taguchi Designs (Continued) Two - Level OAs (Continued) Column Trial 1
2
3
Raw Data (y1)
Simplified (Simplified)2 y1 - 40
(y1 - 40)2
1
1
1
1
44
47
4
7
16
49
2
1
2
2
43
45
3
5
9
25
3
2
1
2
41
42
1
2
1
4
4
2
2
1
48
49
8
9
64
81
Totals
39
249
Factor A GA1= 4+7+3+5 = 19 GA2= 1+2+8+9 = 20 Factor B GB1= 4+7+1+2 = 14 GB2= 3+5+8+9 = 25 A x B Interaction G31= 4+7+8+9 = 28 G32= 3 + 5 + 1 + 2 = 11 SST = ( 16 + 49 + 9 + 25 + 1 + 4 + 64 + 81) SS A =
( 20 - 19 )
2
= 0.125 SSB = 8 2 ( 28 - 11) SS3 = = 36.125 8 SSe = SST - SS A - SSB - SS3
( 25 - 14 ) 8
( 39 ) 8
2
= 58.875
2
= 15.125
SSe = 58.875 - 0.125 - 15.125 - 36.125 = 7.5
XI-112 (1198)
© QUALITY COUNCIL OF INDIANA CQE 2006
XI. ADVANCED STATISTICS DESIGN OF EXPERIMENTS / OTHER DESIGNS
Taguchi Designs (Continued) Linear Graphs & Triangular Tables 1
3
2
Column
2
3
1
3
2
2 L4 Linear Graph
1
L4 Triangular Table
The L4 linear graph shows that if the two factors are assigned to columns 1 and 2, the interaction will be in column 3. The L4 triangular table shows that if the two factors are put in columns 1 and 3, the other point of the triangle for the interaction is in column 2. If the two factors are put in columns 2 and 3, the interaction will be found in column 1.
XI-112 (1199)
© QUALITY COUNCIL OF INDIANA CQE 2006
XI. ADVANCED STATISTICS DESIGN OF EXPERIMENTS / OTHER DESIGNS
Taguchi Designs (Continued) Linear Graphs & Triangular Tables (Cont.) 1
2 3
3
5 7
2
5
1
4 6
Type A
6
4
7
Type B L8 Linear Graphs
The next level of linear graphs are for an L8 OA. The linear graphs in the Figure indicate that several factors can be assigned to different columns and several different interactions may be evaluated in different columns. If three factors (A, B and C) are assigned, the L8 linear graph indicates the assignment to columns 1, 2 and 4 located at the vertices in the type A triangle.
© QUALITY COUNCIL OF INDIANA CQE 2006
XI-113 (1200)
XI. ADVANCED STATISTICS DESIGN OF EXPERIMENTS / OTHER DESIGNS
Taguchi Designs (Continued) Linear Graphs & Triangular Tables (Cont.) Column Numbers 1 2 3 4 5 6
2 3
Column Numbers 3 4 5 6 2 5 4 7 1 6 7 4 7 6 5 1 2 3
7 6 5 4 3 2 1
Triangular Table The column assignment for the factors and their interactions are shown in the Table below. All main effects and all interactions can be estimated, which results in a high-resolution experiment. This is also a full-factorial experiment.
1 A
2 B
Column Number 3 4 5 6 7 AxB C AxC BxC AxBxC
Column Assignments for an L8 Linear Graph
© QUALITY COUNCIL OF INDIANA CQE 2006
XI-114 (1201)
XI. ADVANCED STATISTICS DESIGN OF EXPERIMENTS / OTHER DESIGNS
Taguchi Designs (Continued) Linear Graphs & Triangular Tables (Cont.) A number of Taguchi designs are available on the NIST website and other internet locations. Examples include: L4: L8: L9: L12: L16: L16b: L18: L25: L27: L32: L32b: L36: L50: L54: L64: L64b: L81:
3 Factors - 2 Levels 7 Factors - 2 Levels 4 Factors - 3 Levels 11 Factors - 2 Levels 15 Factors - 2 Levels 5 Factors - 4 Levels 1 Factor - 2 Levels and 7 Factors - 3 Levels 6 Factors - 5 Levels 13 Factors - 2 Levels 30 Factors - 2 Levels 1 Factor - 2 Levels and 9 Factors - 4 Levels 11 Factors - 2 Levels and 12 Factors - 3 Levels 1 Factor - 2 Levels and 11 Factors - 5 Levels 1 Factor - 2 Levels and 25 Factors - 3 Levels 31 Factors - 2 Levels 20 Factors - 4 Levels 40 Factors - 3 Levels
The above list represents the most common designs.
© QUALITY COUNCIL OF INDIANA CQE 2006
XI-115 (1202)
XI. ADVANCED STATISTICS DESIGN OF EXPERIMENTS / OTHER DESIGNS
Taguchi vs. Modern DOE Taguchi experiments are based on orthogonal arrays. They are usually identified with a name like, L8 to indicate an array with 8 runs. Modern experimental designs are also based on orthogonal arrays. They are identified with a superscript to indicate the number of variables. Thus, the design 23 also has eight runs. Both methods have different emphasis but are very similar. To rotate the table on the following page, use the commands: <Shift><+> clockwise rotation <Shift><->
counter clockwise rotation
Interactions
1 1 -1 1
1 -1 1 -1
-1 1 1 -1 -1 1 6
-1 -1 1
1 1 1
4 2 1
4
5
6
7
8
1
-1 1 -1 -1
3
-1
1
1
5
1
1
3
1
1
-1
-1 -1
-1 -1
1
1 -1 -1 -1 -1
2
1
-1 -1 -1 1
1
7
1
-1
-1
1
-1
1
1
-1
1
1
2
2
2
2
1
1
2
1
2
1
2
1
2
1
4
1
2
1
2
2
1
2
1
5
1
2
2
1
1
2
2
1
6
2
1
1
2
1
2
2
1
7
C B BC A AC AB ABC
2 2
2 2
2 1
2 1
1 2
1 2
1 1
1 1
3
Column no
Taguchi L8 Array
Run A B C AB AC BC ABC 1 2
Factor
Modern 23 Design
© QUALITY COUNCIL OF INDIANA CQE 2006
XI-115 (1203)
XI. ADVANCED STATISTICS DESIGN OF EXPERIMENTS / OTHER DESIGNS
Taguchi vs. Modern DOE (Cont.)
XI-117 (1204)
© QUALITY COUNCIL OF INDIANA CQE 2006
XI. ADVANCED STATISTICS QUESTIONS 11.2. When finding a confidence interval for mean μ, based on a sample size of n: a. b. c. d.
Increasing n increases the interval Having to use Sx instead of n decreases the interval The larger the interval, the better the estimate of μ Increasing n decreases the interval
11.4. Determine whether the following two types of rockets have significantly different variances at the 5% level. Assume that the larger variance goes in the numerator.
a. b. c. d.
Rocket A
Rocket B
61 readings 1,347 miles2
31 readings 2,237 miles2
Significant difference because Fcalc < F table No significant difference because Fcalc < F table Significant difference because Fcalc > F table No significant difference because Fcalc > F table
11.7. Given the data below is normally distributed, and the population standard deviation is 3.1, what is the 90% confidence interval for the mean? 22, 23, 19, 17, 29, 25 a. b. c. d.
20.88 - 24.12 20.42 - 24.59 21.65 - 23.35 17.4 - 27.60
Answers: 2. d, 4. b, 7. b
© QUALITY COUNCIL OF INDIANA CQE 2006
XI-118 (1205)
XI. ADVANCED STATISTICS QUESTIONS 11.12.
A designed experiment has been conducted at three levels (A, B, and C) yielding the following "coded" data: A 6 3 5 2
B 5 9 1
C 3 4 2
As a major step in the analysis, the degrees of freedom for the "error" sum of squares is determined to be: a. b. c. d.
7 9 6 3
11.13. a. b. c. d.
Random order of performance Sequential procedure of conjecture, to design, and then to analysis Hidden replication Large number of possible combinations of factors
11.18.
a. b. c. d.
The power of efficiency in designed experiments lies in the:
A 2-level 5-factor experiment is being conducted to optimize the reliability of an electronic control module. A half replicate of the standard full-factorial experiment is proposed. The number of treatment combinations will be:
10 16 25 32
Answers: 12. a, 13. c, 18. b
© QUALITY COUNCIL OF INDIANA CQE 2006
XI-119 (1206)
XI. ADVANCED STATISTICS QUESTIONS 11.23. a. b. c. d.
Which of the following is NOT true in regards to blocking?
A block is a dummy factor which doesn't interact with real factors A blocking factor has 2 levels A block is a subdivision of the experiment Blocks are used to compensate when run randomization is restricted
11.29.
The difference between setting alpha equal to 0.05, and alpha equal to 0.01, in hypothesis testing is:
a. With alpha equal to 0.05, one is more willing to risk a type I error b. With alpha equal to 0.05, one is more willing to risk a type II error c. Alpha equal to 0.05 is a more "conservative" test of the null hypothesis (H0) d. With alpha equal to 0.05, one is less willing to risk a type I error 11.31. a. b. c. d.
A basic L4 Taguchi design is most similar to:
A two-factor, two-level, full-factorial A three-factor, two-level, one-half fractional-factorial A three-factor, two-level, full-factorial A test of a single variable at 4 levels
Answers: 23. b, 29. a, 31. b
© QUALITY COUNCIL OF INDIANA CQE 2006
XI-120 (1207)
XI. ADVANCED STATISTICS QUESTIONS 11.33. a. b. c. d.
The number of treatments must equal 4 or 5 Interest is centered determining interactions The design is a full-factorial Each treatment appears once per row and per column
11.35. a. b. c. d.
Which of the following is a valid null hypothesis?
p > 1/8 mu < 98 The mean of population A is not equal to the mean of population B mu = 110
11.36.
a. b. c. d.
Which of the following characteristics apply to the Latin square design?
An experiment is being run with 8 factors. Two of the factors are temperature and pressure. The levels for temperature are 25, 50, and 75. The levels for pressure are 14, 28, 42, and 56. How many degrees of freedom are required to determine the effect of the interaction between temperature and pressure?
1 2 4 6
Answers: 33. a, 35. d, 36. d
© QUALITY COUNCIL OF INDIANA CQE 2006
XII-1 (1208)
XII. APPENDIX
INDEX LEARNING TURNS NO STUDENT PALE, YET HOLDS THE EEL OF SCIENCE BY THE TAIL. ALEXANDER POPE
XII-2 (1209)
© QUALITY COUNCIL OF INDIANA CQE 2006
XII. APPENDIX
Table I - Standard Normal Table 0
Z
Z
X.X0
X.X1
X.X2
X.X3
X.X4
X.X5
X.X6
X.X7
X.X8
X.X9
0.0 0.1 0.2 0.3 0.4
0.5000 0.4602 0.4207 0.3821 0.3446
0.4960 0.4562 0.4168 0.3783 0.3409
0.4920 0.4522 0.4129 0.3745 0.3372
0.4880 0.4483 0.4090 0.3707 0.3336
0.4840 0.4443 0.4052 0.3669 0.3300
0.4801 0.4404 0.4013 0.3632 0.3264
0.4761 0.4364 0.3974 0.3594 0.3228
0.4721 0.4325 0.3936 0.3557 0.3192
0.4681 0.4286 0.3897 0.3520 0.3156
0.4641 0.4247 0.3859 0.3483 0.3121
0.5 0.6 0.7 0.8 0.9
0.3085 0.2743 0.2420 0.2119 0.1841
0.3050 0.2709 0.2389 0.2090 0.1814
0.3015 0.2676 0.2358 0.2061 0.1788
0.2981 0.2643 0.2327 0.2033 0.1762
0.2946 0.2611 0.2297 0.2005 0.1736
0.2912 0.2578 0.2266 0.1977 0.1711
0.2877 0.2546 0.2236 0.1949 0.1685
0.2843 0.2514 0.2206 0.1922 0.1660
0.2810 0.2483 0.2177 0.1894 0.1635
0.2776 0.2451 0.2148 0.1867 0.1611
1.0 1.1 1.2 1.3 1.4
0.1587 0.1357 0.1151 0.0968 0.0808
0.1562 0.1335 0.1131 0.0951 0.0793
0.1539 0.1314 0.1112 0.0934 0.0778
0.1515 0.1292 0.1093 0.0918 0.0764
0.1492 0.1271 0.1075 0.0901 0.0749
0.1469 0.1251 0.1056 0.0885 0.0735
0.1446 0.1230 0.1038 0.0869 0.0721
0.1423 0.1210 0.1020 0.0853 0.0708
0.1401 0.1190 0.1003 0.0838 0.0694
0.1379 0.1170 0.0985 0.0823 0.0681
1.5 1.6 1.7 1.8 1.9
0.0668 0.0548 0.0446 0.0359 0.0287
0.0655 0.0537 0.0436 0.0351 0.0281
0.0643 0.0526 0.0427 0.0344 0.0274
0.0630 0.0516 0.0418 0.0336 0.0268
0.0618 0.0505 0.0409 0.0329 0.0262
0.0606 0.0495 0.0401 0.0322 0.0256
0.0594 0.0485 0.0392 0.0314 0.0250
0.0582 0.0475 0.0384 0.0307 0.0244
0.0571 0.0465 0.0375 0.0301 0.0239
0.0559 0.0455 0.0367 0.0294 0.0233
2.0 2.1 2.2 2.3 2.4
0.0228 0.0179 0.0139 0.0107 0.0082
0.0222 0.0174 0.0136 0.0104 0.0080
0.0217 0.0170 0.0132 0.0102 0.0078
0.0212 0.0166 0.0129 0.0099 0.0075
0.0207 0.0162 0.0125 0.0096 0.0073
0.0202 0.0158 0.0122 0.0094 0.0071
0.0197 0.0154 0.0119 0.0091 0.0069
0.0192 0.0150 0.0116 0.0089 0.0068
0.0188 0.0146 0.0113 0.0087 0.0066
0.0183 0.0143 0.0110 0.0084 0.0064
2.5 2.6 2.7 2.8 2.9 3.0
0.0062 0.0047 0.0035 0.0026 0.0019 0.00135
0.0060 0.0045 0.0034 0.0025 0.0018
0.0059 0.0044 0.0033 0.0024 0.0018
0.0057 0.0043 0.0032 0.0023 0.0017
0.0055 0.0041 0.0031 0.0023 0.0016
0.0054 0.0040 0.0030 0.0022 0.0016
0.0052 0.0039 0.0029 0.0021 0.0015
0.0051 0.0038 0.0028 0.0021 0.0015
0.0049 0.0037 0.0027 0.0020 0.0014
0.0048 0.0036 0.0026 0.0019 0.0014
XII-3 (1210)
© QUALITY COUNCIL OF INDIANA CQE 2006
XII. APPENDIX
Table II - Six Sigma Failure Rates With a 1.5 σ Process Shift Z
ppm
Z
1.0
697,672.15
3.6
1.1
660,082.92
1.2
With No Process Shift
ppm
Z
ppm
Z
ppm
17,864.53
1.0
317,310.52
3.6
318.29
3.7
13,903.50
1.1
271,332.20
3.7
215.66
621,378.38
3.8
10,724.14
1.2
230,139.46
3.8
144.74
1.3
581,814.88
3.9
8,197.56
1.3
193,601.10
3.9
96.23
1.4
541,693.78
4.0
6,209.70
1.4
161,513.42
4.0
63.37
1.5
501,349.97
4.1
4,661.23
1.5
133,614.46
4.1
41.34
1.6
461,139.78
4.2
3,467.03
1.6
109,598.58
4.2
26.71
1.7
421,427.51
4.3
2,555.19
1.7
89,130.86
4.3
17.09
1.8
382,572.13
4.4
1,865.88
1.8
71,860.53
4.4
10.83
1.9
344,915.28
4.5
1,349.97
1.9
57,432.99
4.5
6.80
2.0
308,770.21
4.6
967.67
2.0
45,500.12
4.6
4.23
2.1
274,412.21
4.7
687.20
2.1
35,728.71
4.7
2.60
2.2
242,071.41
4.8
483.48
2.2
27,806.80
4.8
1.59
2.3
211,927.71
4.9
336.98
2.3
21,448.16
4.9
0.960
2.4
184,108.21
5.0
232.67
2.4
16,395.06
5.0
0.574
2.5
158,686.95
5.1
159.15
2.5
12,419.36
5.1
0.340
2.6
135,686.77
5.2
107.83
2.6
9,322.44
5.2
0.200
2.7
115,083.09
5.3
72.37
2.7
6,934.05
5.3
0.116
2.8
96,809.10
5.4
48.12
2.8
5,110.38
5.4
0.067
2.9
80,762.13
5.5
31.69
2.9
3,731.76
5.5
0.038
3.0
66,810.63
5.6
20.67
3.0
2,699.93
5.6
0.021
3.1
54,801.40
5.7
13.35
3.1
1,935.34
5.7
0.012
3.2
44,566.73
5.8
8.55
3.2
1,374.40
5.8
0.007
3.3
35,931.06
5.9
5.42
3.3
966.97
5.9
0.004
3.4
28,716.97
6.0
3.40
3.4
673.96
6.0
0.002
3.5
22,750.35
6.1
2.11
3.5
465.35
6.1
0.001
XII-4 (1211)
© QUALITY COUNCIL OF INDIANA CQE 2006
XII. APPENDIX
Table III - Poisson Distribution Probability of r or fewer occurrences of an event that has an average number of occurrences equal to np. r 0
1
2
3
4
5
6
7
0.02 0.04 0.06 0.08 0.10
0.980 0.961 0.942 0.923 0.905
1.000 0.999 0.998 0.997 0.995
1.000 1.000 1.000 1.000
0.15 0.20 0.25 0.30
0.861 0.819 0.779 0.741
0.990 0.982 0.974 0.963
0.999 0.999 0.998 0.996
1.000 1.000 1.000 1.000
0.35 0.40 0.45 0.50
0.705 0.670 0.638 0.607
0.951 0.938 0.925 0.910
0.994 0.992 0.989 0.986
1.000 0.999 0.999 0.998
1.000 1.000 1.000
0.55 0.60 0.65 0.70 0.75
0.577 0.549 0.522 0.497 0.472
0.894 0.878 0.861 0.844 0.827
0.982 0.977 0.972 0.966 0.959
0.998 0.997 0.996 0.994 0.993
1.000 1.000 0.999 0.999 0.999
1.000 1.000 1.000
0.80 0.85 0.90 0.95 1.00
0.449 0.427 0.407 0.387 0.368
0.809 0.791 0.772 0.754 0.736
0.953 0.945 0.937 0.929 0.920
0.991 0.989 0.987 0.984 0.981
0.999 0.998 0.998 0.997 0.996
1.000 1.000 1.000 1.000 0.999
1.000
1.1 1.2 1.3 1.4 1.5
0.333 0.301 0.273 0.247 0.223
0.699 0.663 0.627 0.592 0.558
0.900 0.879 0.857 0.833 0.809
0.974 0.966 0.957 0.946 0.934
0.995 0.992 0.989 0.986 0.981
0.999 0.998 0.998 0.997 0.996
1.000 1.000 1.000 0.999 0.999
1.000 1.000
1.6 1.7 1.8 1.9 2.0
0.202 0.183 0.165 0.150 0.135
0.525 0.493 0.463 0.434 0.406
0.783 0.757 0.731 0.704 0.677
0.921 0.907 0.891 0.875 0.857
0.976 0.970 0.964 0.956 0.947
0.994 0.992 0.990 0.987 0.983
0.999 0.998 0.997 0.997 0.995
1.000 1.000 0.999 0.999 0.999
8
np
1.000 1.000 1.000
9
XII-5 (1212)
© QUALITY COUNCIL OF INDIANA CQE 2006
XII. APPENDIX
Table III - Poisson Distribution (Cont.) r 0
1
2
3
4
5
6
7
8
9
2.2 2.4 2.6 2.8 3.0
0.111 0.091 0.074 0.061 0.050
0.355 0.308 0.267 0.231 0.199
0.623 0.570 0.518 0.469 0.423
0.819 0.779 0.736 0.692 0.647
0.928 0.904 0.877 0.848 0.815
0.975 0.964 0.951 0.935 0.916
0.993 0.988 0.983 0.976 0.966
0.998 0.997 0.995 0.992 0.988
1.000 0.999 0.999 0.998 0.996
1.000 1.000 0.999 0.999
3.2 3.4 3.6 3.8 4.0
0.041 0.033 0.027 0.022 0.018
0.171 0.147 0.126 0.107 0.092
0.380 0.340 0.303 0.269 0.238
0.603 0.558 0.515 0.473 0.433
0.781 0.744 0.706 0.668 0.629
0.895 0.871 0.844 0.816 0.785
0.955 0.942 0.927 0.909 0.889
0.983 0.977 0.969 0.960 0.949
0.994 0.992 0.988 0.984 0.979
0.998 0.997 0.996 0.994 0.992
4.2 4.4 4.6 4.8 5.0
0.015 0.012 0.010 0.008 0.007
0.078 0.066 0.056 0.048 0.040
0.210 0.185 0.163 0.143 0.125
0.395 0.359 0.326 0.294 0.265
0.590 0.551 0.513 0.476 0.440
0.753 0.720 0.686 0.651 0.616
0.867 0.844 0.818 0.791 0.762
0.936 0.921 0.905 0.887 0.867
0.972 0.964 0.955 0.944 0.932
0.989 0.985 0.980 0.975 0.968
5.2 5.4 5.6 5.8 6.0
0.006 0.005 0.004 0.003 0.002
0.034 0.029 0.024 0.021 0.017
0.109 0.095 0.082 0.072 0.062
0.238 0.213 0.191 0.170 0.151
0.406 0.373 0.342 0.313 0.285
0.581 0.546 0.512 0.478 0.446
0.732 0.702 0.670 0.638 0.606
0.845 0.822 0.797 0.771 0.744
0.918 0.903 0.886 0.867 0.847
0.960 0.951 0.941 0.929 0.916
10
11
12
13
14
15
16
2.8 3.0 3.2 3.4 3.6 3.8 4.0
1.000 1.000 1.000 0.999 0.999 0.998 0.997
1.000 1.000 0.999 0.999
1.000 1.000
4.2 4.4 4.6 4.8 5.0
0.996 0.994 0.992 0.990 0.986
0.999 0.998 0.997 0.996 0.995
1.000 0.999 0.999 0.999 0.998
1.000 1.000 1.000 0.999
1.000
5.2 5.4 5.6 5.8 6.0
0.982 0.977 0.972 0.965 0.957
0.993 0.990 0.988 0.984 0.980
0.997 0.996 0.995 0.993 0.991
0.999 0.999 0.998 0.997 0.996
1.000 1.000 0.999 0.999 0.999
1.000 1.000 0.999
1.000
np
XII-6 (1213)
© QUALITY COUNCIL OF INDIANA CQE 2006
XII. APPENDIX
Table III - Poisson Distribution (Cont.) r 0
1
2
3
4
5
6
7
8
9
6.2 6.4 6.6 6.8 7.0
0.002 0.002 0.001 0.001 0.001
0.015 0.012 0.010 0.009 0.007
0.054 0.046 0.040 0.034 0.030
0.134 0.119 0.105 0.093 0.082
0.259 0.235 0.213 0.192 0.173
0.414 0.384 0.355 0.327 0.301
0.574 0.542 0.511 0.480 0.450
0.716 0.687 0.658 0.628 0.599
0.826 0.803 0.780 0.755 0.729
0.902 0.886 0.869 0.850 0.830
7.2 7.4 7.6 7.8
0.001 0.001 0.001 0.000
0.006 0.005 0.004 0.004
0.025 0.022 0.019 0.016
0.072 0.063 0.055 0.048
0.156 0.140 0.125 0.112
0.276 0.253 0.231 0.210
0.420 0.392 0.365 0.338
0.569 0.539 0.510 0.481
0.703 0.676 0.648 0.620
0.810 0.788 0.765 0.741
8.0 8.5 9.0 9.5 10.0
0.000 0.000 0.000 0.000 0.000
0.003 0.002 0.001 0.001 0.000
0.014 0.009 0.006 0.004 0.003
0.042 0.030 0.021 0.015 0.010
0.100 0.074 0.055 0.040 0.029
0.191 0.150 0.116 0.089 0.067
0.313 0.256 0.207 0.165 0.130
0.453 0.386 0.324 0.269 0.220
0.593 0.523 0.456 0.393 0.333
0.717 0.653 0.587 0.522 0.458
10
11
12
13
14
15
16
17
18
19
6.2 6.4 6.6 6.8 7.0
0.949 0.939 0.927 0.915 0.901
0.975 0.969 0.963 0.955 0.947
0.989 0.986 0.982 0.978 0.973
0.995 0.994 0.992 0.990 0.987
0.998 0.997 0.997 0.996 0.994
0.999 0.999 0.999 0.998 0.998
1.000 1.000 0.999 0.999 0.999
1.000 1.000 1.000
7.2 7.4 7.6 7.8
0.887 0.871 0.854 0.835
0.937 0.926 0.915 0.902
0.967 0.961 0.954 0.945
0.984 0.980 0.976 0.971
0.993 0.991 0.989 0.986
0.997 0.996 0.995 0.993
0.999 0.998 0.998 0.997
0.999 0.999 0.999 0.999
1.000 1.000 1.000 1.000
8.0 8.5 9.0 9.5 10.0
0.816 0.763 0.706 0.645 0.583
0.888 0.849 0.803 0.752 0.697
0.936 0.909 0.876 0.836 0.792
0.966 0.949 0.926 0.898 0.864
0.983 0.973 0.959 0.940 0.917
0.992 0.986 0.978 0.967 0.951
0.996 0.993 0.989 0.982 0.973
0.998 0.997 0.995 0.991 0.986
0.999 0.999 0.998 0.996 0.993
20
21
22
1.000 1.000 0.999 0.998
1.000 0.999
1.000
np
8.5 9.0 9.5 10.0
1.000 0.999 0.999 0.998 0.997
XII-7 (1214)
© QUALITY COUNCIL OF INDIANA CQE 2006
XII. APPENDIX
Table IV - Binomial Distribution Probability of r or fewer occurrences of an event in n trials p (the probability of occurrence on each trial) n
r
0.05
0.10
0.15
0.20
0.25
0.30
0.35
0.40
0.45
0.50
2
0 1
0.9025 0.9975
0.8100 0.9900
0.7225 0.9775
0.6400 0.9600
0.5625 0.9375
0.4900 0.9100
0.4225 0.8775
0.3600 0.8400
0.3025 0.7975
0.2500 0.7500
3
0 1 2
0.8574 0.9928 0.9999
0.7290 0.9720 0.9990
0.6141 0.9392 0.9966
0.5120 0.8960 0.9920
0.4219 0.8438 0.9844
0.3430 0.7840 0.9730
0.2746 0.7182 0.9571
0.2160 0.6480 0.9360
0.1664 0.5748 0.9089
0.1250 0.5000 0.8750
4
0 1 2 3
0.8145 0.9860 0.9995 1.0000
0.6561 0.9477 0.9963 0.9999
0.5220 0.8905 0.9880 0.9995
0.4096 0.8192 0.9728 0.9984
0.3164 0.7383 0.9492 0.9961
0.2401 0.6517 0.9163 0.9919
0.1785 0.5630 0.8735 0.9850
0.1296 0.4752 0.8208 0.9744
0.0915 0.3910 0.7585 0.9590
0.0625 0.3125 0.6875 0.9375
5
0 1 2 3 4
0.7738 0.9774 0.9988 1.0000 1.0000
0.5905 0.9185 0.9914 0.9995 1.0000
0.4437 0.8352 0.9734 0.9978 0.9999
0.3277 0.7373 0.9421 0.9933 0.9997
0.2373 0.6328 0.8965 0.9844 0.9990
0.1681 0.5282 0.8369 0.9692 0.9976
0.1160 0.4284 0.7648 0.9460 0.9947
0.0778 0.3370 0.6826 0.9130 0.9898
0.0503 0.2562 0.5931 0.8688 0.9815
0.0312 0.1875 0.5000 0.8125 0.9688
6
0 1 2 3 4 5
0.7351 0.9672 0.9978 0.9999 1.0000 1.0000
0.5314 0.8857 0.9842 0.9987 0.9999 1.0000
0.3771 0.7765 0.9527 0.9941 0.9996 1.0000
0.2621 0.6554 0.9011 0.9830 0.9984 0.9999
0.1780 0.5339 0.8306 0.9624 0.9954 0.9998
0.1176 0.4202 0.7443 0.9295 0.9891 0.9993
0.0754 0.3191 0.6471 0.8826 0.9777 0.9982
0.0467 0.2333 0.5443 0.8208 0.9590 0.9959
0.0277 0.1636 0.4415 0.7447 0.9308 0.9917
0.0156 0.1094 0.3438 0.6562 0.8906 0.9844
7
0 1 2 3 4 5 6
0.6983 0.9556 0.9962 0.9998 1.0000 1.0000 1.0000
0.4783 0.8503 0.9743 0.9973 0.9998 1.0000 1.0000
0.3206 0.7166 0.9262 0.9879 0.9988 0.9999 1.0000
0.2097 0.5767 0.8520 0.9667 0.9953 0.9996 1.0000
0.1335 0.4449 0.7564 0.9294 0.9871 0.9987 0.9999
0.0824 0.3294 0.6471 0.8740 0.9712 0.9962 0.9998
0.0490 0.2338 0.5323 0.8002 0.9444 0.9910 0.9994
0.0280 0.1586 0.4199 0.7102 0.9037 0.9812 0.9984
0.0152 0.1024 0.3164 0.6083 0.8471 0.9643 0.9963
0.0078 0.0625 0.2266 0.5000 0.7734 0.9375 0.9922
8
0 1 2 3 4 5 6 7
0.6634 0.9428 0.9942 0.9996 1.0000 1.0000 1.0000 1.0000
0.4305 0.8131 0.9619 0.9950 0.9996 1.0000 1.0000 1.0000
0.2725 0.6572 0.8948 0.9786 0.9971 0.9998 1.0000 1.0000
0.1678 0.5033 0.7969 0.9437 0.9896 0.9988 0.9999 1.0000
0.1001 0.3671 0.6785 0.8862 0.9727 0.9958 0.9996 1.0000
0.0576 0.2553 0.5518 0.8059 0.9420 0.9887 0.9987 0.9999
0.0319 0.1691 0.4278 0.7064 0.8939 0.9747 0.9964 0.9998
0.0168 0.1064 0.3154 0.5941 0.8263 0.9502 0.9915 0.9993
0.0084 0.0632 0.2201 0.4770 0.7396 0.9115 0.9819 0.9983
0.0039 0.0352 0.1445 0.3633 0.6367 0.8555 0.9648 0.9961
9
0 1 2 3 4 5 6 7 8
0.6302 0.9288 0.9916 0.9994 1.0000 1.0000 1.0000 1.0000 1.0000
0.3874 0.7748 0.9470 0.9917 0.9991 0.9999 1.0000 1.0000 1.0000
0.2316 0.5995 0.8591 0.9661 0.9944 0.9994 1.0000 1.0000 1.0000
0.1342 0.4362 0.7382 0.9144 0.9804 0.9969 0.9997 1.0000 1.0000
0.0751 0.3003 0.6007 0.8343 0.9511 0.9900 0.9987 0.9999 1.0000
0.0404 0.1960 0.4628 0.7297 0.9012 0.9747 0.9957 0.9996 1.0000
0.0207 0.1211 0.3373 0.6089 0.8283 0.9464 0.9888 0.9986 0.9999
0.0101 0.0705 0.2318 0.4826 0.7334 0.9006 0.9750 0.9962 0.9997
0.0046 0.0385 0.1495 0.3614 0.6214 0.8342 0.9502 0.9909 0.9992
0.0020 0.0195 0.0898 0.2539 0.5000 0.7461 0.9102 0.9805 0.9980
10 0 1 2 3 4 5 6 7 8 9
0.5987 0.9139 0.9885 0.9990 0.9999 1.0000 1.0000 1.0000 1.0000 1.0000
0.3487 0.7361 0.9298 0.9872 0.9984 0.9999 1.0000 1.0000 1.0000 1.0000
0.1969 0.5443 0.8202 0.9500 0.9901 0.9986 0.9999 1.0000 1.0000 1.0000
0.1074 0.3758 0.6778 0.8791 0.9672 0.9936 0.9991 0.9999 1.0000 1.0000
0.0563 0.2440 0.5256 0.7759 0.9219 0.9803 0.9965 0.9996 1.0000 1.0000
0.0282 0.1493 0.3828 0.6496 0.8497 0.9527 0.9894 0.9984 0.9999 1.0000
0.0135 0.0860 0.2616 0.5138 0.7515 0.9051 0.9740 0.9952 0.9995 1.0000
0.0060 0.0464 0.1673 0.3823 0.6331 0.8338 0.9452 0.9877 0.9983 0.9999
0.0025 0.0232 0.0996 0.2660 0.5044 0.7384 0.8980 0.9726 0.9955 0.9997
0.0010 0.0107 0.0547 0.1719 0.3770 0.6230 0.8281 0.9453 0.9893 0.9990
XII-8 (1215)
© QUALITY COUNCIL OF INDIANA CQE 2006
XII. APPENDIX
Table V - t Distribution tα d.f.
t.100
t.050*
t.025**
t.010
t.005
d.f.
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 inf.
3.078 1.886 1.638 1.533 1.476 1.440 1.415 1.397 1.383 1.372 1.363 1.356 1.350 1.345 1.341 1.337 1.333 1.330 1.328 1.325 1.323 1.321 1.319 1.318 1.316 1.315 1.314 1.313 1.311 1.282
6.314 2.920 2.353 2.132 2.015 1.943 1.895 1.860 1.833 1.812 1.796 1.782 1.771 1.761 1.753 1.746 1.740 1.734 1.729 1.725 1.721 1.717 1.714 1.711 1.708 1.706 1.703 1.701 1.699 1.645
12.706 4.303 3.182 2.776 2.571 2.447 2.365 2.306 2.262 2.228 2.201 2.179 2.160 2.145 2.131 2.120 2.110 2.101 2.093 2.086 2.080 2.074 2.069 2.064 2.060 2.056 2.052 2.048 2.045 1.960
31.821 6.965 4.541 3.747 3.365 3.143 2.998 2.896 2.821 2.764 2.718 2.681 2.650 2.624 2.602 2.583 2.567 2.552 2.539 2.528 2.518 2.508 2.500 2.492 2.485 2.479 2.473 2.467 2.462 2.326
63.657 9.925 5.841 4.604 4.032 3.707 3.499 3.355 3.250 3.169 3.106 3.055 3.012 2.977 2.947 2.921 2.898 2.878 2.861 2.845 2.831 2.819 2.807 2.797 2.787 2.779 2.771 2.763 2.756 2.576
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 inf.
* one tail 5% α risk
** two tail 5% α risk
XII-9 (1216)
© QUALITY COUNCIL OF INDIANA CQE 2006
XII. APPENDIX
Table VI - Critical Values of the Chi-Square (X2) Distribution
X2
0 .95
X2
0.0 5
DF
X20.99
X20.95
X20.90
X20.10
X20.05
X20.01
1
0.00016
0.0039
0.0158
2.71
3.84
6.63
2
0.0201
0.1026
0.2107
4.61
5.99
9.21
3
0.115
0.352
0.584
6.25
7.81
11.34
4
0.297
0.711
1.064
7.78
9.49
13.28
5
0.554
1.15
1.61
9.24
11.07
15.09
6
0.872
1.64
2.20
10.64
12.59
16.81
7
1.24
2.17
2.83
12.02
14.07
18.48
8
1.65
2.73
3.49
13.36
15.51
20.09
9
2.09
3.33
4.17
14.68
16.92
21.67
10
2.56
3.94
4.87
15.99
18.31
23.21
11
3.05
4.57
5.58
17.28
19.68
24.73
12
3.57
5.23
6.30
18.55
21.03
26.22
13
4.11
5.89
7.04
19.81
22.36
27.69
14
4.66
6.57
7.79
21.06
23.68
29.14
15
5.23
7.26
8.55
22.31
25.00
30.58
16
5.81
7.96
9.31
23.54
26.30
32.00
18
7.01
9.39
10.86
25.99
28.87
34.81
20
8.26
10.85
12.44
28.41
31.41
37.57
24
10.86
13.85
15.66
33.20
36.42
42.98
30
14.95
18.49
20.60
40.26
43.77
50.89
40
22.16
26.51
29.05
51.81
55.76
63.69
60
37.48
43.19
46.46
74.40
79.08
88.38
120
86.92
95.70
100.62
140.23
146.57
158.95
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© QUALITY COUNCIL OF INDIANA CQE 2006
XII. APPENDIX
Table VII - Distribution of F f(F )
F Table α = 0.05
" F "
ν1(DF) ν2(DF)
1
2
3
4
5
6
7
8
9
1
161.4
199.5
215.7
224.6
230.2 234.0
236.8
238.9 240.5 241.9 243.9 245.9
2
18.51
19.00
19.16
19.25
19.30 19.33
19.35
19.37 19.38 19.40 19.41 19.43
3
10.13
9.55
9.28
9.12
9.01
8.94
8.89
8.85
8.81
8.79
8.74
8.70
4
7.71
6.94
6.59
6.39
6.26
6.16
6.09
6.04
6.00
5.96
5.91
5.86
5
6.61
5.79
5.41
5.19
5.05
4.95
4.88
4.82
4.77
4.74
4.68
4.62
6
5.99
5.14
4.76
4.53
4.39
4.28
4.21
4.15
4.10
4.06
4.00
3.94
7
5.59
4.74
4.35
4.12
3.97
3.87
3.79
3.73
3.68
3.64
3.57
3.51
8
5.32
4.46
4.07
3.84
3.69
3.58
3.50
3.44
3.39
3.35
3.28
3.22
9
5.12
4.26
3.86
3.63
3.48
3.37
3.29
3.23
3.18
3.14
3.07
3.01
10
4.96
4.10
3.71
3.48
3.33
3.22
3.14
3.07
3.02
2.98
2.91
2.85
11
4.84
3.98
3.59
3.36
3.20
3.09
3.01
2.95
2.90
2.85
2.79
2.72
12
4.75
3.89
3.49
3.26
3.11
3.00
2.91
2.85
2.80
2.75
2.69
2.62
13
4.67
3.81
3.41
3.18
3.03
2.92
2.83
2.77
2.71
2.67
2.60
2.53
14
4.60
3.74
3.34
3.11
2.96
2.85
2.76
2.70
2.65
2.60
2.53
2.46
15
4.54
3.68
3.29
3.06
2.90
2.79
2.71
2.64
2.59
2.54
2.48
2.40
ν1(DF) ν2(DF)
20
30
40
50
60
4
20
2.12
2.04
1.99
1.96
1.95
1.84
30
1.93
1.84
1.79
1.76
1.74
1.62
40
1.84
1.74
1.69
1.66
1.64
1.51
50
1.78
1.69
1.63
1.60
1.58
1.44
60
1.75
1.65
1.59
1.56
1.53
1.39
4
1.57
1.46
1.39
1.35
1.32
1.00
10
12
15
XII-11 (1218)
© QUALITY COUNCIL OF INDIANA CQE 2006
XII. APPENDIX
Table VIII - Distribution of F
f(F )
F Table α = 0.025
" F "
ν1(DF) ν2(DF)
1
2
3
4
5
6
7
8
9
10
12
15
1
647.8 799.5
864.2
899.6
921.8
937.1
948.2
956.7
963.3
968.6
976.7
984.9
2
38.51 39.00
39.17
39.25
39.30
39.33
39.36
39.37
39.39
39.40 39.41
39.43
3
17.44 16.04
15.44
15.10
14.88
14.73
14.62
14.54
14.47
14.42 14.34
14.25
4
12.22 10.65
9.98
9.60
9.36
9.20
9.07
8.98
8.90
8.84
8.75
8.66
5
10.01
8.43
7.76
7.39
7.15
6.98
6.85
6.76
6.68
6.62
6.52
6.43
6
8.81
7.26
6.60
6.23
5.99
5.82
5.70
5.60
5.52
5.46
5.37
5.27
7
8.07
6.54
5.89
5.52
5.29
5.12
4.99
4.90
4.82
4.76
4.67
4.57
8
7.57
6.06
5.42
5.05
4.82
4.65
4.53
4.43
4.36
4.30
4.20
4.10
9
7.21
5.71
5.08
4.72
4.48
4.32
4.20
4.10
4.03
3.96
3.87
3.77
10
6.94
5.46
4.83
4.47
4.24
4.07
3.95
3.85
3.78
3.72
3.62
3.52
11
6.72
5.26
4.63
4.28
4.04
3.88
3.76
3.66
3.59
3.53
3.43
3.33
12
6.55
5.10
4.47
4.12
3.89
3.73
3.61
3.51
3.44
3.37
3.28
3.18
13
6.41
4.97
4.35
4.00
3.77
3.60
3.48
3.39
3.31
3.25
3.15
3.05
14
6.30
4.86
4.24
3.89
3.66
3.50
3.38
3.29
3.21
3.15
3.05
2.95
15
6.20
4.77
4.15
3.80
3.58
3.41
3.29
3.20
3.12
3.06
2.96
2.86
ν1(DF) ν2(DF)
20
30
40
50
60
4
20
2.46
2.35
2.29
2.25
2.22
2.09
30
2.20
2.07
2.01
1.97
1.94
1.79
40
2.07
1.94
1.88
1.83
1.80
1.64
50
1.99
1.87
1.80
1.76
1.72
1.55
60
1.94
1.82
1.74
1.70
1.67
1.48
4
1.71
1.57
1.48
1.43
1.39
1.00
XII-12 (1219)
© QUALITY COUNCIL OF INDIANA CQE 2006
XII. APPENDIX
Table IX - Control Chart Factors CHART FOR AVERAGES Sample Observations
Control limit Factors
CHART FOR STANDARD DEVIATIONS Center Line Factors
Control Limit Factors
CHART FOR RANGES Center Line Factors
Control Limit Factors
n
A2
A3
C4
B3
B4
d2
D3
D4
2
1.880
2.659
0.7979
0
3.267
1.128
0
3.267
3
1.023
1.954
0.8862
0
2.568
1.693
0
2.574
4
0.729
1.628
0.9213
0
2.266
2.059
0
2.282
5
0.577
1.427
0.9400
0
2.089
2.326
0
2.114
6
0.483
1.287
0.9515
0.030
1.970
2.534
0
2.004
7
0.419
1.182
0.9594
0.118
1.882
2.704
0.076
1.924
8
0.373
1.099
0.9650
0.185
1.815
2.847
0.136
1.864
9
0.337
1.032
0.9693
0.239
1.761
2.970
0.184
1.816
10
0.308
0.975
0.9727
0.284
1.716
3.078
0.223
1.777
15
0.223
0.789
0.9823
0.428
1.572
3.472
0.347
1.653
20
0.180
0.680
0.9869
0.510
1.490
3.735
0.415
1.585
25
0.153
0.606
0.9896
0.565
1.435
3.931
0.459
1.541
Approximate capability
Approximate capability
© QUALITY COUNCIL OF INDIANA CQE 2006
XII. APPENDIX INDEX
Index The CQE Primer contains the following: C
Author/Name Index
C
Subject Index
C
Letter answers for questions given in the Primer
XII-13 (1220)
