Statistical methods for quality improvement

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Statistical Methods for

Quality Improvement

i

WILEY SERIES IN PROBABILITY AND STATISTICS

Established by WALTER A SHEWHART and SAMUEL S WILKS

Editors: David J Balding, Noel A C Cressie, Garrett M Fitzmaurice,

Harvey Goldstein, Iain M Johnstone, Geert Molenberghs, David W Scott, Adrian F M Smith, Ruey S Tsay, Sanford Weisberg

Editors Emeriti: Vic Barnett, J Stuart Hunter, Joseph B Kadane, Jozef L Teugels

A complete list of the titles in this series appears at the end of this volume

ii

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Statistical Methods for

Copyright © 2011 by John Wiley & Sons, Inc All rights reserved.

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Library of Congress Cataloging-in-Publication Data

Ryan, Thomas P.,

1945-Statistical methods for quality improvement / Thomas P Ryan – 3rd ed.

p cm – (Wiley series in probability and statistics ; 840) Includes bibliographical references and index.

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Contents

PART I FUNDAMENTAL QUALITY IMPROVEMENT AND

STATISTICAL CONCEPTS

1.1 Quality and Productivity, 4

1.2 Quality Costs (or Does It?), 5

1.3 The Need for Statistical Methods, 5

1.4 Early Use of Statistical Methods for Improving Quality, 6

1.5 Influential Quality Experts, 7

vi CONTENTS2.8 The Seven Newer Tools, 28

2.8.1 Affinity Diagram, 282.8.2 Interrelationship Digraph, 292.8.3 Tree Diagram, 29

2.8.4 Prioritization Matrix, 292.8.5 Matrix Diagram, 302.8.6 Process Decision Program Chart, 302.8.7 Activity Network Diagram, 302.9 Software, 30

3.6.1 Normal Distribution, 553.6.2 t Distribution, 59

3.6.3 Exponential Distribution, 613.6.4 Lognormal Distribution, 623.6.5 Weibull Distribution, 643.6.6 Extreme Value Distribution, 643.6.7 Gamma Distribution, 643.6.8 Chi-Square Distribution, 653.6.9 Truncated Normal Distribution, 653.6.10 Bivariate and Multivariate Normal Distributions, 663.6.11 F Distribution, 67

3.6.12 Beta Distribution, 683.6.13 Uniform Distribution, 68

3.8.5.1 Probability Plots, 763.8.5.2 Likelihood Ratio Tests, 783.8.6 Bonferroni Intervals, 80

3.9 Enumerative Studies Versus Analytic Studies, 81

References, 81

Exercises, 83

PART II CONTROL CHARTS AND PROCESS CAPABILITY

4 Control Charts for Measurements With Subgrouping

4.1 Basic Control Chart Principles, 89

4.2 Real-Time Control Charting Versus Analysis of Past Data, 92

4.3 Control Charts: When to Use, Where to Use, How Many to Use, 944.4 Benefits from the Use of Control Charts, 94

4.7.7 Recomputing Control Limits, 1114.7.8 Applying Control Limits to Future Production, 1124.7.9 Combining an X - and an S-Chart, 113

4.7.10 Standards for Control Charts, 1134.7.11 Deleting Points, 114

4.7.12 Target Values, 114

viii CONTENTS4.8 Illustrative Example with Real Data, 114

4.9 Determining the Point of a Parameter Change, 116

4.10 Acceptance Sampling and Acceptance Control Chart, 117

4.10.1 Acceptance Control Chart, 119

4.10.1.1 Acceptance Chart with X Control Limits, 121

4.10.1.2 Acceptance Charts Versus Target Values, 1234.11 Modified Limits, 124

4.12 Difference Control Charts, 124

4.13 Other Charts, 126

4.14 Average Run Length (ARL), 127

4.14.1 Weakness of the ARL Measure, 1284.15 Determining the Subgroup Size, 129

4.15.1 Unequal Subgroup Sizes, 1304.16 Out-of-Control Action Plans, 131

4.17 Assumptions for the Charts in This Chapter, 132

4.17.1 Normality, 1324.17.2 Independence, 1364.18 Measurement Error, 140

4.18.1 Monitoring Measurement Systems, 1424.19 Software, 142

5 Control Charts for Measurements Without Subgrouping

5.1 Individual Observations Chart, 158

5.1.1 Control Limits for the X -Chart, 159

5.1.2 X-Chart Assumptions, 161

5.1.3 Illustrative Example: Random Data, 1625.1.4 Example with Particle Counts, 1635.1.5 Illustrative Example: Trended Data, 1645.1.6 Trended Real Data, 168

5.2 Transform the Data or Fit a Distribution?, 170

5.3 Moving Average Chart, 171

6.1 Charts for Nonconforming Units, 182

6.1.1 np-Chart, 182

6.1.2 p-Chart, 184

6.1.3 Stage 1 and Stage 2 Use of p-Charts and np-Charts, 185

6.1.4 Alternative Approaches, 1876.1.4.1 Arcsin Transformations, 1886.1.4.2 Q-Chart for Binomial Data, 192

6.1.4.3 Regression-Based Limits, 1936.1.4.4 ARL-Unbiased Charts, 1956.1.4.5 Unit and Group-Runs Chart, 1966.1.4.6 Monitoring a Multinomial Process, 1966.1.5 Using Software to Obtain Probability Limits for p- and np-Charts, 197

6.1.6 Variable Sample Size, 1986.1.7 Charts Based on the Geometric and Negative BinomialDistributions, 199

6.1.8 Overdispersion, 2016.2 Charts for Nonconformities, 202

6.2.1 c-Chart, 202

6.2.2 Transforming Poisson Data, 2046.2.3 Illustrative Example, 2046.2.4 Regression-Based Limits, 2086.2.5 Using Software to Obtain Probability Limits for

c-Charts, 211

6.2.6 u-Chart, 211

6.2.6.1 Regression-Based Limits, 2136.2.6.2 Using Computer Software to Obtain u-Chart

Probability Limits, 2146.2.7 Overdispersion, 215

6.2.8 D-Chart, 216

6.2.8.1 Probability-Type D-Chart Limits, 218

6.3 Summary, 218

x CONTENTSReferences, 218

Exercises, 221

7.1 Data Acquisition for Capability Indices, 225

7.1.1 Selection of Historical Data, 2267.2 Process Capability Indices, 227

7.2.1 C p, 2277.2.2 C pm, 2287.2.3 C pk, 2297.2.3.1 CPU and CPL as Process Capability Indices, 231

7.2.4 C pmk, 2317.2.5 Other Capability Indices, 2327.3 Estimating the Parameters in Process Capability Indices, 232

7.3.1 X-Chart, 233

7.3.2 X -Chart, 233

7.3.3 Case Study, 2347.4 Distributional Assumption for Capability Indices, 235

7.5 Confidence Intervals for Process Capability Indices, 236

7.5.1 Confidence Interval for C p, 2367.5.2 Confidence Interval for C pk, 2377.5.3 Confidence Interval for C pm, 2397.5.4 Confidence Interval for C pmk, 2397.5.5 Confidence Intervals Computed Using Data in Subgroups, 2397.5.6 Nonparametric Capability Indices and Confidence Limits, 2407.5.6.1 Robust Capability Indices, 241

7.5.6.2 Capability Indices Based on Fitted Distributions, 2427.5.6.3 Data Transformation, 242

7.5.6.4 Capability Indices Computed Using Resampling

Methods, 2437.6 Asymmetric Bilateral Tolerances, 243

7.6.1 Examples, 2447.7 Capability Indices That Are a Function of Percent Nonconforming, 2457.7.1 Examples, 246

7.8 Modified k Index, 250

7.9 Other Approaches, 251

7.10 Process Capability Plots, 251

8.2.2 Fast Initial Response CUSUM, 2718.2.3 Combined Shewhart–CUSUM Scheme, 2738.2.4 CUSUMs with Estimated Parameters, 2768.2.5 Computation of CUSUM ARLs, 2768.2.6 Robustness of CUSUM Procedures, 2778.2.7 CUSUM Procedures for Individual Observations, 2828.3 CUSUM Procedures for Controlling Process Variability, 283

8.4 Applications of CUSUM Procedures, 286

8.5 Generalized Likelihood Ratio Charts: Competitive Alternative to

CUSUM Charts, 2868.6 CUSUM Procedures for Nonconforming Units, 286

8.7 CUSUM Procedures for Nonconformity Data, 290

8.8 Exponentially Weighted Moving Average Charts, 294

8.8.1 EWMA Chart for Subgroup Averages, 2958.8.2 EWMA Misconceptions, 298

8.8.3 EWMA Chart for Individual Observations, 2988.8.4 Shewhart–EWMA Chart, 299

8.8.5 FIR–EWMA, 2998.8.6 Designing EWMA Charts with Estimated Parameters, 2998.8.7 EWMA Chart with Variable Sampling Intervals, 2998.8.8 EWMA Chart for Grouped Data, 300

8.8.9 EWMA Chart for Variances, 3008.8.10 EWMA for Attribute Data, 3008.9 Software, 301

8.10 Summary, 301

References, 301

Exercises, 306

9.2.4 Recomputing the UCL, 3209.2.5 Characteristics of Control Charts Based on T2, 3209.2.6 Determination of a Change in the Correlation Structure, 3229.2.7 Illustrative Example, 322

9.3 Multivariate Chart Versus Individual X -Charts, 326

9.4 Charts for Detecting Variability and Correlation Shifts, 327

9.4.1 Application to Table 9.2 Data, 3289.5 Charts Constructed Using Individual Observations, 330

9.5.1 Retrospective (Stage 1) Analysis, 3319.5.2 Stage 2 Analysis: Methods for Decomposing Q, 333

9.5.2.1 Illustrative Example, 3349.5.3 Other Methods, 335

9.5.4 Monitoring Multivariate Variability with Individual

Observations, 3359.6 When to Use Each Chart, 335

9.7 Actual Alpha Levels for Multiple Points, 336

9.8 Requisite Assumptions, 336

9.9 Effects of Parameter Estimation on ARLs, 337

9.10 Dimension-Reduction and Variable Selection Techniques, 337

9.11 Multivariate CUSUM Charts, 338

9.12 Multivariate EWMA Charts, 339

9.12.1 Design of a MEWMA Chart, 3419.12.2 Searching for Assignable Causes, 3429.12.3 Unequal Sample Sizes, 342

9.12.4 Self-Starting MEWMA Chart, 3429.12.5 Combinations of MEWMA Charts and Multivariate

Shewhart Charts, 3439.12.6 MEWMA Chart with Sequential Sampling, 3439.12.7 MEWMA Chart for Process Variability, 3439.13 Effect of Measurement Error, 343

9.14 Applications of Multivariate Charts, 344

9.15 Multivariate Process Capability Indices, 344

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9.16 Summary, 344Appendix, 345References, 345Exercises, 350

10.1 Pre-control, 35310.2 Short-Run SPC, 35610.3 Charts for Autocorrelated Data, 35910.3.1 Autocorrelated Attribute Data, 36310.4 Charts for Batch Processes, 364

10.5 Charts for Multiple-Stream Processes, 36410.6 Nonparametric Control Charts, 36510.7 Bayesian Control Chart Methods, 36610.8 Control Charts for Variance Components, 36710.9 Control Charts for Highly Censored Data, 36710.10 Neural Networks, 367

10.11 Economic Design of Control Charts, 36810.11.1 Economic-Statistical Design, 37010.12 Charts with Variable Sample Size and/or Variable SamplingInterval, 370

10.13 Users of Control Charts, 37110.13.1 Control Chart Nonmanufacturing Applications, 372

10.13.1.1 Health Care, 37210.13.1.2 Financial, 37310.13.1.3 Environmental, 37310.13.1.4 Clinical Laboratories, 37310.13.1.5 Analytical Laboratories, 37310.13.1.6 Civil Engineering, 37310.13.1.7 Education, 37310.13.1.8 Law Enforcement/Investigative Work, 37310.13.1.9 Lumber, 373

10.13.1.10 Forest Operations, 37410.13.1.11 Athletic Performance, 37410.13.1.12 Animal Production Systems, 37410.14 Software for Control Charting, 374

Bibliography, 375Exercises, 384

11.3.1 Digidot Plot, 39111.4 Boxplot, 392

11.5 Normal Probability Plot, 39611.6 Plotting Three Variables, 39811.7 Displaying More Than Three Variables, 39911.8 Plots to Aid in Transforming Data, 39911.9 Summary, 401

References, 402Exercises, 404

12.1 Simple Linear Regression, 40712.2 Worth of the Prediction Equation, 41112.3 Assumptions, 413

12.4 Checking Assumptions Through Residual Plots, 41412.5 Confidence Intervals and Hypothesis Test, 41512.6 Prediction Interval for Y, 416

12.7 Regression Control Chart, 41712.8 Cause-Selecting Control Charts, 41912.9 Linear, Nonlinear, and Nonparametric Profiles, 42112.10 Inverse Regression, 423

12.11 Multiple Linear Regression, 42612.12 Issues in Multiple Regression, 42612.12.1 Variable Selection, 42712.12.2 Extrapolation, 42712.12.3 Multicollinear Data, 42712.12.4 Residual Plots, 42812.12.5 Regression Diagnostics, 42812.12.6 Transformations, 42912.13 Software For Regression, 42912.14 Summary, 429

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References, 430Exercises, 432

ANOVA, 45313.6 Regression Analysis of Data from Designed Experiments, 45513.7 ANOVA for Two Factors, 460

13.7.1 ANOVA with Two Factors: Factorial Designs, 461

13.7.1.1 Conditional Effects, 46313.7.2 Effect Estimates, 463

13.7.3 ANOVA Table for Unreplicated Two-Factor Design, 46413.7.4 Yates’s Algorithm, 467

13.8 The 23Design, 46913.9 Assessment of Effects Without a Residual Term, 47413.10 Residual Plot, 477

13.11 Separate Analyses Using Design Units and Uncoded Units, 47913.12 Two-Level Designs with More Than Three Factors, 48013.13 Three-Level Factorial Designs, 482

13.14 Mixed Factorials, 48313.15 Fractional Factorials, 48313.15.1 2k−1Designs, 484

13.15.2 2k−2Designs, 49013.15.3 More Highly Fractionated Two-Level Designs, 49213.15.4 Fractions of Three-Level Factorials, 492

13.15.5 Incomplete Mixed Factorials, 49313.15.6 Cautions, 493

xvi CONTENTS13.16 Other Topics in Experimental Design and Their Applications, 49313.16.1 Hard-to-Change Factors, 493

13.16.2 Split-Lot Designs, 49413.16.3 Mixture Designs, 49413.16.4 Response Surface Designs, 49413.16.5 Designs for Measurement System Evaluation, 49513.16.6 Fraction of Design Space Plots, 496

13.16.7 Computer-Aided Design and Expert Systems, 49613.16.8 Sequential Experimentation, 497

13.16.9 Supersaturated Designs and Analyses, 49713.16.10 Multiple Responses, 498

13.17 Summary, 500References, 500Exercises, 506

14 Contributions of Genichi Taguchi and Alternative Approaches 513

14.1 “Taguchi Methods”, 51314.2 Quality Engineering, 51414.3 Loss Functions, 51414.4 Distribution Not Centered at the Target, 51814.5 Loss Functions and Specification Limits, 51814.6 Asymmetric Loss Functions, 518

14.7 Signal-to-Noise Ratios and Alternatives, 52214.8 Experimental Designs for Stage One, 52414.9 Taguchi Methods of Design, 525

14.9.1 Inner Arrays and Outer Arrays, 52614.9.2 Orthogonal Arrays as Fractional Factorials, 52714.9.3 Other Orthogonal Arrays Versus Fractional

Factorials, 52914.9.4 Product Arrays Versus Combined Arrays, 53514.9.5 Application of Product Array, 541

14.9.5.1 Cautions, 55114.9.6 Desirable Robust Designs and Analyses, 551

14.9.6.1 Designs, 55214.9.6.2 Analyses, 55214.9.6.3 Experiment to Compare Product Array

and Combined Array, 55214.10 Determining Optimum Conditions, 553

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14.11 Summary, 558References, 560Exercises, 563

15.1 EVOP Illustrations, 56615.2 Three Variables, 57615.3 Simplex EVOP, 57815.4 Other EVOP Procedures, 58115.5 Miscellaneous Uses of EVOP, 58115.6 Summary, 582

Appendix, 58215.A Derivation of Formula for Estimatingσ, 582

References, 583Exercises, 584

16.1 ANOM for One-Way Classifications, 58816.2 ANOM for Attribute Data, 591

16.2.1 Proportions, 59116.2.2 Count Data, 59416.3 ANOM When Standards Are Given, 59416.3.1 Nonconforming Units, 59416.3.2 Nonconformities, 59516.3.3 Measurement Data, 59516.4 ANOM for Factorial Designs, 59616.4.1 Assumptions, 60016.4.2 An Alternative Way of Displaying Interaction Effects, 60016.5 ANOM When at Least One Factor Has More Than Two Levels, 60116.5.1 Main Effects, 601

16.5.2 Interaction Effects, 60516.6 Use of ANOM with Other Designs, 61016.7 Nonparametric ANOM, 610

16.8 Summary, 611Appendix, 611References, 611Exercises, 613

xviii CONTENTS

17 Using Combinations of Quality Improvement Tools 615

17.1 Control Charts and Design of Experiments, 61617.2 Control Charts and Calibration Experiments, 61617.3 Six Sigma Programs, 616

17.3.1 Components of a Six Sigma Program, 62117.3.2 Six Sigma Applications and Programs, 62217.3.3 Six Sigma Concept for Customer Satisfaction, 62217.3.4 Six Sigma Training, 623

17.3.5 Lean Six Sigma, 62317.3.6 Related Programs/Other Companies, 623

17.3.6.1 SEMATECH’s Qual Plan, 62417.3.6.2 AlliedSignal’s Operational Excellence

Program, 62417.4 Statistical Process Control and Engineering Process Control, 624References, 625

of profiles Section 12.9, a moderately long section, was added to cover this newmaterial.

A major addition to the chapter on attribute control charts (Chapter 6) has beenthe sections on how to use software such as MINITAB R to obtain probabilitylimits for attribute charts, with this addition motivated by reader feedback Thatchapter also contains 15 new references

Two sections were added to the chapter on process capability indices,Chapter 7, in addition to 16 new references

Chapter 8, on alternatives to Shewhart charts, has been expanded considerably

to include sections on the effects of parameter estimation on the properties ofCUSUM and EWMA procedures, in addition to information on certain freewarethat can be used to aid in the design of CUSUM procedures Following therecommendation of a colleague, a section on generalized likelihood ratio charts(Section 8.5) has also been added, in addition to 28 new chapter references

An important, although brief, section on conditional effects was added toChapter 13, along with a section on fraction of design space plots and 31 newreferences Chapter 14 has one new section and four additional references Morematerial on Six Sigma programs and training has been added to Chapter 17, andthere is a new section on Lean Six Sigma, in addition to eight new references.There has been a moderate increase in the number of chapter exercises, in-cluding nine new exercises in Chapter 3, five in Chapter 4, a total of eleven inChapters 5–8, and five in Chapter 13

xix

xx PREFACE

For a one-semester college course, Chapters 4–10 could form the basis for acourse that covers control charts and process capability Instructors who wish tocover only basic concepts might use Chapters 1, 2, as much of 3 as is necessary,

4, 5, and 6, and selectively choose from Chapters 7, 8, and 10

The book might also be used in a special topics design of experiments course,with emphasis on Chapters 13 and 14, with Chapter 16 also covered and perhapsChapter 15 For reader convenience, the book’s data sets can be found online at:

ftp://ftp.wiley.com/public/sci tech med/quality improvement

I am indebted to the researchers who have made many important contributionssince the publication of the previous edition, and I am pleased to present their work

in addition to my own work I am also grateful for the feedback from instructorswho have taught from the first two editions and also appreciate the support of

my editor at Wiley, Susanne Steitz-Filler, and the work of the production people,especially Rosalyn Farkas

THOMASP RYAN

December 2010

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Preface to the Second Edition

There have been many developments in statistical process control (SPC) duringthe past ten years, and many of those developments have been incorporated intothis edition

In particular, major changes were made to the chapters on process capabilityand multivariate control charts as much material has been added with the resultthat these chapters are now considerably longer

Chapter 10 has also been considerably expanded and now includes sections onshort-run control charts, pre-control, autocorrelated data, nonparametric controlcharts, and various other topics that were not covered in the first edition.Chapter 13 on the design of experiments is noticeably longer, in part because

of the addition of material on robust design considerations Chapter 14 on Taguchimethods and alternatives while retaining the material from the first edition nowincludes considerable discussion and illustration of combined arrays and productarrays

Chapter 17 is a new chapter on using SPC tools together as is done in SixSigma programs These programs are also discussed in the chapter

Other significant additions include material on probability-type limits for tribute charts and cause-selecting (regression-type) control charts

at-In addition to new material, retained material from the first edition has beenextensively reorganized In particular, cumulative sum (CUSUM) and exponen-tially weighted moving average (EWMA) methods are now in a separate chapter,and are covered in considerable detail

The first edition has been used in college courses as well as in short courses.Chapters 4–10 of the second edition could form the basis for a course that coverscontrol charts and process capability Instructors who wish to cover only basicconcepts might cover Chapters 1, 2, as much of 3 as is necessary, 4, 5, and 6, andselectively choose from 7, 8 and 10

The book might also be used in a course on design of experiments, especially

a special topics course There are some topics in Chapters 13 and 14 that havenot been covered in experimental design texts, and evolutionary operation and

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xxii PREFACE TO THE SECOND EDITION

analysis of means (Chapters 15 and 16, respectively) are not covered to any extent

in design texts So an atypical design course could be put together using Chapters13–16 as a basis

I am indebted to the researchers who have made many important contributionsduring the past 10 years, and I am pleased to present their work, in addition to

of my editor at Wiley, Steve Quigley, and the work of the production people,especially Rosalyn Farkas

THOMASP RYAN

July 1999

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Preface to the First Edition

A moderate number of books have been written on the subject of statistical quality

control, which in recent years has also been referred to as statistical process control (SPC) These range from books that contain only the basic control charts

to books that also contain material on acceptance sampling and selected statisticalmethods such as regression and analysis of variance

Statistical Methods for Quality Improvement was written in recognition of the

fact that quality improvement requires the use of more than just control charts

In particular, it would be difficult to keep a particular process characteristic

“in control” without some knowledge of the factors affecting that characteristic.Consequently, Chapters 13–16 were written to provide insight into statisticallydesigned experiments and related topics

The first two chapters provide an overview of the use of statistics in qualityimprovement in the United States and Japan Chapter 3 presents statistical distri-butions that are needed for the rest of the book, and also reviews basic concepts inprobability and statistics Basic control chart principles are discussed in Chapter

4, and Chapters 5, 6, 8, and 9 contain the material on the various control charts.This material has several unique features In particular, there is some empha-sis on cumulative sum (CUSUM) procedures, and an entire chapter (Chapter 9)

is devoted to multivariate charts Chapter 7 discusses the commonly used cess capability indices and compares them The bibliography of control chartapplications at the end of Chapter 10 is another unique feature of the book.Quality improvement practitioners are beginning to recognize what can beaccomplished using statistical design of experiments, but progress has been slow.With this in mind, Chapter 13 was written to show what can be accomplishedusing experimental design principles

pro-In recent years there has been much interest and discussion regarding a set

of statistical and nonstatistical tools referred to as Taguchi methods These are

critically examined in Chapter 14 Evolutionary Operation is presented in Chapter15; Chapter 16 is an updated treatment of Analysis of Means The latter is a

xxiii

xxiv PREFACE TO THE FIRST EDITION

valuable tool that allows nonstatisticians, in particular, to analyze data fromdesigned experiments

In general, there has been a conscious attempt to bring the reader up to date

in regard to the various topics that are presented in each chapter There was also

a concerted effort to use simple heuristics and intuitive reasoning, rather thanrelying heavily upon mathematical and statistical formalism and symbolism Thecontrol chart material, in particular, has also been written under the assumptionthat a sizable percentage of readers will have access to a computer for controlcharting

Chapters 4–10 could be used for a one-semester course devoted exclusively tocontrol charts, and Chapters 13–16 could from the core for a course on design ofexperiments Short-course instructors will also find ample material from which

to pick and choose

A book of this type is the end product of the combined efforts of manypeople, even though the book has only one author The architects of many of thestatistical tools presented herein have indirectly contributed greatly to the quality

of the book In particular, Jim Lucas’s work on cumulative sum procedures ispresented in detail for the first time in a statistics book, and the same can be saidfor Frank Alt’s work on multivariate charts I have also contributed some newcontrol chart procedures, which hopefully will be viewed as improvements onthe standard procedures

Much of the material in the book has been presented in industrial short coursesand college courses; the feedback from some of the participants has been valu-able There are also a number of colleagues who have read parts of the manuscriptand have made helpful suggestions Those deserving particular mention areJohannes Ledolter, Frank Alt, Jon Cryer, and Jim Lucas The contributions of theeditorial reviewers are also appreciated, as is the work of Joy Klammer who typedmost of the manuscript Permission from MINITAB, INC to use MINITAB forgenerating certain tables is also gratefully acknowledged, as is permission fromSQC SYSTEMS, INC to use SQCS in producing many of the control chartsand CUSUM tabulations that are contained in the book Permission from var-ious publications to reproduce certain materials is also appreciated, as are theefforts of the editorial and production people at Wiley, especially Isabel Steinand Shirley Thomas Lastly, I am very much indebted to my editor, Bea Shube,whose patience and steadfast support made writing the book a less arduous taskthan it could have been, particularly during trying times

THOMASP RYAN

Iowa City, Iowa

October 1988

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PA RT I

Fundamental Quality Improvement and

Statistical Concepts

1

PA RT I I

Control Charts and Process Capability

87

385

C H A P T E R 1

Introduction

This is a book about using statistical methods to improve quality It is not a bookabout Total Quality Management (TQM), Total Quality Assurance (TQA), just-in-time (JIT) manufacturing, benchmarking, QS-9000, or the ISO 9000 series Inother words, the scope of the book is essentially restricted to statistical techniques

Although standards such as QS-9000 and ISO 9000 are potentially useful, they are oriented toward the documentation of quality problems, not the identification

or eradication of problems Furthermore, many people feel that companies tend

to believe that all they need to do is acquire ISO 9000 certification, thus satisfyingonly a minimum requirement

Statistical techniques, on the other hand, are useful for identifying troublespots and their causes, as well as predicting major problems before they occur.Then it is up to the appropriate personnel to take the proper corrective action

The emphasis is on quality improvement, not quality control On July 1, 1997

the American Society for Quality Control (ASQC) became simply the AmericanSociety for Quality (ASQ) The best choice for a new name is arguable, assome would undoubtedly prefer American Society for Quality Improvement (thechoice of the late Bill Hunter, former professor of statistics at the University

of Wisconsin) Nevertheless, the name change reflects an appropriate movement

away from quality control George Box has emphasized that systems are not

stationary and that improvements should constantly be sought In defending hisstatement in Box (1997a) that there are “not truths, only major steps in a never-ending (and diverging) process that helped predict natural phenomena,” Box(1997b) pointed out that “Orville and Wilber Wright undoubtedly had profoundknowledge about the design of flying machines” in 1903, but their plane looksprimitive now

What is quality? How do we know when we have it? Can we have too muchquality? The “fitness for use” criterion is usually given in defining quality

Statistical Methods for Quality Improvement, Third Edition Thomas P Ryan.

© 2011 John Wiley & Sons, Inc Published 2011 by John Wiley & Sons, Inc.

3

a quality standard However, if another automaker builds its cars in such a waythat they will probably be trouble free for 7 years, the quality standard is likely toshift upward This is what happened in the Western world some years ago as themarketplace discovered that Japanese products, in particular, are of high quality.

A company will know that it is producing high-quality products if thoseproducts satisfy the demands of the marketplace

We could possibly have too much quality What if we could build a car thatwould last for 50 years Would anyone want to drive the same car for 50 yearseven if he or she lived long enough to do so? Obviously, styles and tastes change.This is particularly true for high technology products that might be obsolete after

a year or two How long should a personal computer be built to last?

In statistical terms, quality is largely determined by the amount of variability inwhat is being measured Assume that the target for producing certain invoices is

15 days, with anything less than, say, 10 days being almost physically impossible

If records for a 6-month period showed that all invoices of this type were processedwithin 17 days, this invoice-processing operation would seem to be of highquality

In general, the objective should be to reduce variability and to “hit the target”

if target values exist for process characteristics The latter objective has beeninfluenced by Genichi Taguchi (see Chapter 14) who has defined quality as the

“cost to society.”

1.1 QUALITY AND PRODUCTIVITY

One impediment to achieving high quality has been the misconception of somemanagers that there is an inverse relationship between productivity and quality.Specifically, it has been believed (by some) that steps taken to improve qualitywill simultaneously cause a reduction in productivity

This issue has been addressed by a number of authors including Fuller (1986)who related that managers at Hewlett–Packard began to realize many years agothat productivity rose measurably when nonconformities (i.e., product defects)were reduced This increase was partly attributable to a reduction in rework thatresulted from the reduction of nonconformities Other significant gains resultedfrom the elimination of problems such as the late delivery of materials Thesevarious problems contribute to what the author terms “complexity” in the work-place, and he discusses ways to eliminate complexity so as to free the workerfor productive tasks Other examples of increased productivity resulting fromimproved quality can be found in Chapter 1 of Deming (1982)

1.3 THE NEED FOR STATISTICAL METHODS 5

1.2 QUALITY COSTS (OR DOES IT?)

It is often stated that “quality doesn’t cost, it pays.” Although Crosby (1979) saidthat quality is free (the title of his book) and reiterated this in Crosby (1996),companies such as Motorola and General Electric, which launched massive train-ing programs a few decades ago, would undoubtedly disagree The large amount

of money that GE committed to a particular training program, Six Sigma, was

discussed in, for example, the January 13, 1997 issue of the Wall Street Journal.

Wall Street has recognized Six Sigma companies as companies that operate ciently, have greater customer satisfaction, and so on Six Sigma is discussed indetail in Chapter 17

effi-What is the real cost of a quality improvement program? That cost is impossible

to determine precisely, since it would depend in part on the quality costs for agiven time period without such a program as well as the costs of the programfor the same time period Obviously, we cannot both have a program and nothave a program at the same point in time, so the quality costs that would bepresent if the program were not in effect would have to be estimated from pastdata

Such a comparison would not give the complete picture, however Any view ofquality costs that does not include the effect that a quality improvement programwill have on sales and customers’ perceptions is a myopic view of the subject.Should a supplier consider the cost of a statistical quality control program beforedeciding whether or not to institute such a program? The supplier may not havemuch choice if it is to remain a supplier As a less extreme example, consider anindustry that consists of 10 companies If two of these companies implement astatistical quality improvement program and, as a result, the public soon perceivestheir products to be of higher quality than their competitors’ products, should theircompetitors consider the cost of such a program before following suit? Definitelynot, unless they can adequately predict the amount of lost sales and weigh thatagainst the cost of the program

1.3 THE NEED FOR STATISTICAL METHODS

Generally, statistical techniques are needed to determine if abnormal variationhas occurred in whatever is being monitored, to determine changes in the val-ues of process parameters, and to identify factors that are influencing processcharacteristics Methods for achieving each of these objectives are discussed insubsequent chapters Statistics is generally comparable to medicine in the sensethat there are many subareas in statistics, just as there are many medical spe-cialties Quality “illnesses” generally can be cured and quality optimized onlythrough the sagacious use of combinations of statistical techniques, as discussed

in Chapter 17

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1.4 EARLY USE OF STATISTICAL METHODS

FOR IMPROVING QUALITY

Although statistical methods have been underutilized and underappreciated inquality control/improvement programs for decades, such methods are extremelyimportant Occasionally their importance may even be overstated In discussingthe potential impact of statistical methods, Hoerl (1994) pointed out that Ishikawa(1985, pp 14–15) stated the following: “One might even speculate that the secondworld war was won by quality control and by the utilization of modern statistics.Certain statistical methods researched and utilized by the Allied powers were soeffective that they were classified as military secrets until the surrender of NaziGermany.” Although such a conclusion is clearly arguable, statistical methodsdid clearly play a role in World War II See Grant and Lang (1991) for a detailedaccount of the use of statistical quality control methods in World War II in theUnited States and shortly thereafter

Shortly after the war, The American Society for Quality Control was formed

in 1946; it published the journal Industrial Quality Control, the first issue of

which had appeared in July 1944 In 1969 the journal was essentially split into

two publications—the Journal of Quality Technology and Quality Progress The

former contains technical articles whereas the latter contains less technical

ar-ticles and also has news items The early issues of Industrial Quality Control

contained many interesting articles on how statistical procedures were being

used in firms in various industries, whereas articles in the Journal of Quality Technology are oriented more toward the proper use of existing procedures as well as the introduction of new procedures Publication of Quality Engineering

began in 1988, with case studies featured in addition to statistical methodology.The Annual Quality Congress has been held every year since the inception of

ASQC, and the proceedings of the meeting are published as the ASQ Annual Quality Transactions.

Other excellent sources of information include the Fall Technical Conference,which is jointly sponsored by ASQ and the American Statistical Association(ASA), the annual Quality and Productivity Research Conference, and the AnnualMeetings of ASA, which are referred to as the Joint Statistical Meetings (JSM).There are also various “applied” statistics journals, which contain important

articles relevant to industry, including Technometrics, published jointly by ASQ and ASA, Quality and Reliability Engineering International, IIE Transactions, Applied Statistics (Journal of The Royal Statistical Society, Series C), and The Statistician (Journal of The Royal Statistical Society, Series D) The latter two

are British publications

Readers interested in the historical development of statistical quality control

in Great Britain are referred to Pearson (1935, 1973) An enlightening look at theearly days of quality control practices in the United States, as seen through theeyes of Joseph M Juran, can be found in Juran (1997) See also Juran (1991)

1.5 INFLUENTIAL QUALITY EXPERTS 7

1.5 INFLUENTIAL QUALITY EXPERTS

Walter A Shewhart (1891–1967) came first As discussed more fully in Chapter 2,

he invented the idea of a control chart, with certain standard charts now commonlyreferred to as “Shewhart charts.” Shewhart (1931) is still cited by many writers

as an authoritative source on process control The book was reprinted in 1980 byASQC Shewhart (1939) was Shewhart’s other well-known book

W Edwards Deming (1900–1993) was such a prominent statistician and ity and productivity consultant that his passing was noted on the front page ofleading newspapers Ironically, he was about 80 years old before he started re-ceiving much attention in the United States, and this was essentially a very slowreaction to his accomplishments in helping the Japanese progress from havingpoor quality products prior to 1950 to later being able to manufacture products

qual-of superior quality

His “14 points for management” for achieving quality have frequently beencited, and also changed somewhat over the years It has been claimed that thereare as many as eight versions One version is as follows

1 Create a constancy of purpose.

2 Adopt a new philosophy.

3 Cease dependence on inspection.

4 Work constantly to improve the system.

5 Break down barriers between departments.

6 Do not award business to suppliers solely on the basis of price.

7 Drive out fear.

8 Eliminate numerical goals, targets, and slogans.

9 Eliminate work standards and substitute leadership.

10 Institute a program of training and education for all employees.

11 Institute modern training methods.

12 Remove the barriers that make it difficult for employees to do their jobs.

13 Institute and practice modern methods of supervision.

14 Create a management climate that will facilitate the attainment of these

objectives

Although these 14 points are typically applied in industrial settings, they can bemodified slightly and applied in other settings For an application that is certainlyfar removed from manufacturing, Guenther (1997) gave a closely related list of

14 points for parenting

There is one point of clarification that should be made When Deming arguedagainst target values, he was arguing against targets for production quotas, nottarget values for process characteristics The use of target values for process

Deming was constantly berating American management, believing that about90% of quality problems were caused by management Deming’s views on theshortcomings of American management can be found in many places, includingChapter 2 of Deming (1986) In general, Deming claimed that management(1) emphasizes short-term thinking and quarterly profits rather than long-termstrategies, (2) is inadequately trained and does not possess an in-depth knowledge

of the company, and (3) is looking for quick results

Deming has also been given credit for the PDCA (Plan–Do–Check–Act) cycle,although in his later years his preference was that it be called the PDSA cycle,with “Study” replacing “Check.” This has been termed “Deming’s Wheel,” butDeming referred to it as Shewhart’s cycle The cycle consists of planning astudy, performing the study, checking or studying the results, and acting in ac-cordance with what was learned from the study See, for example, Cryer andMiller (1994) and Johnson (2002) for additional information on the PDCAcycle

Several books have been written about Deming; one of the best-known bookswas written by Mary Walton, a journalist (Walton, 1986) See also Walton (1990),which is a book of case studies, and Voehl (1995) The latter is an edited volumethat contains chapters written by some prominent people in the field of qualityimprovement

Joseph M Juran (1904–2008) is another prominent quality figure, one who,like Deming, had an extremely long life He is mentioned only briefly here,however, because his contributions have been to quality management rather than

to the use of statistical methods for achieving quality improvement His quality

control handbook, which appropriately enough was renamed Juran’s Quality Control Handbook when the fourth edition came out in 1988, does contain a few chapters on statistical techniques, however The name was changed to Juran’s Quality Handbook for the fifth edition (which has 1872 pages), with A Blanton

Godfrey as co-editor The first edition was published in 1951 and has been used

as a reference book by countless quality practitioners

Eugene L Grant (1897–1996) has not been accorded the status of other ity pioneers, but nevertheless deserves to be mentioned with the others in thissection In Struebing (1996), Juran is quoted as saying “His contribution tostatistical methodology was much greater than (W Edwards) Deming’s Eventhough his impact on quality was profound and he was much more instrumen-tal in advancing quality than Deming, the media—which overstated Deming’scontribution—didn’t publicize Grant’s contributions.” Grant has been described

qual-as a quiet worker who did not seek to extol his accomplishments He wqual-as a careeracademic who was on the faculty of Stanford University from 1930 until he retired

in 1962 In the field of quality improvement, he was best known for his classic

1.6 SUMMARY 9

book Statistical Quality Control, first published in 1946 Recent editions of the

book have been co-authored by Richard S Leavenworth The seventh edition waspublished in 1996 A very large number of copies of the book were sold throughthe various editions, but some observers felt that his teaching of statistical qualitycontrol during World War II contributed at least as much to the increase in the use

of quality techniques as has his well-known book The Eugene L Grant Awardwas named in his honor and is given annually by the American Society for Quality

to an individual who has “demonstrated outstanding leadership in the ment and presentation of a meritorious educational program in quality control.”Harold F Dodge (1893–1976) is known for his contributions to acceptancesampling, especially the Dodge–Romig Sampling Inspection Tables Althoughacceptance sampling is covered only briefly in this book (in Section 4.10),Dodge’s contributions were noteworthy as he originated several types of ac-ceptance sampling plans and served as a consultant to the Secretary of Warduring World War II He was employed in the Quality Assurance Department atBell Laboratories from 1917 to 1958 and finished his career as a professor ofapplied mathematical statistics at the Statistics Center at Rutgers University from

develop-1958 until 1970

George E P Box (1919– ) is not generally listed as a quality leader or

“guru,” but his contributions to statistical methods for improving quality arewell known His quality-related book, Box, Luce˜no, and del Carmen Paniagua-Quinones (2009), extols the authors’ ideas and suggested approaches for im-proving quality The primary message of that book is that control charts andengineering process control should be used in tandem This idea is discussed inChapter 17 of this book He is the author of several other books, the best known

of which is Box, Hunter, and Hunter (2005) Box also had a column entitled

George’s Corner during the early years of the journal Quality Engineering He

was named an Honorary Member of ASQ by the ASQ Board of Directors in 1997

in recognition of his contributions to quality improvement

There are, of course, many other quality leaders, but they won’t be listed herefor fear of leaving someone out Some indication of the influence of researchers

on the state of the art of statistical quality control is given by the references thatare listed in the following chapters, and also by the number of pages on whichsuch researchers are mentioned, as shown in the book’s Subject Index

The quality leaders who were profiled in this chapter, while having differingareas of expertise, do have one obvious thing in common, as, except for Shewhart,they’ve had an extremely long life

1.6 SUMMARY

Statistical methods should be used to identify unusual variation and to aid inpinpointing the causes of such variation, whether it be for a manufacturing

Box, G E P (1997a) The generation of knowledge and quality Quality Progress, 30(1),

47–50.

Box, G E P (1997b) Author’s reply Quality Progress, 30(5), 8.

Box, G E P., A Luce˜no, and M del Carmen Paniagua-Quinones (2009) Statistical Control

by Monitoring and Feedback Adjustment, 2nd ed Hoboken, NJ: Wiley.

Box, G E P., J S Hunter, and W G Hunter (2005) Statistics for Experimenters, 2nd ed.

Cryer, J D and R B Miller (1994) Statistics for Business: Data Analysis and Modeling,

2nd ed Belmont, CA: Duxbury.

Deming, W E (1982) Quality, Productivity, and Competitive Position Cambridge, MA:

Massachusetts Institute of Technology, Center for Advanced Engineering Study.

Deming, W E (1986) Out of the Crisis Cambridge, MA: Massachusetts Institute of

Technol-ogy, Center for Advanced Engineering Study.

Fuller, F T (1986) Eliminating complexity from work: improving productivity by enhancing quality Report No 17, Center for Quality and Productivity Improvement, University of Wisconsin–Madison.

Grant, E L and T E Lang (1991) Statistical quality control in the World War II years Quality

Progress, 24(12), 31–36.

Grant, E L and R S Leavenworth (1996) Statistical Quality Control, 7th ed New York:

McGraw-Hill.

Guenther, M (1997) Letter to the Editor Quality Progress, 30(10), 12–14.

Hoerl, R (1994) Enhancing the bottom line impact of statistical methods W J Youden

Memorial Address given at the 38th Annual Fall Technical Conference Chemical and

Process Industries Division Newsletter, American Society for Quality Control, Winter

1994, pp 1–9.

Ishikawa, K (1985) What Is Total Quality Control? The Japanese Way Englewood Cliffs,

NJ: Prentice-Hall.

Johnson, C N (2002) The benefits of PDCA Quality Progress, May, 120.

Juran, J M (1991) World War II and the quality movement Quality Progress, 24(12),

19–24.

Juran, J M (1997) Early SQC: a historical supplement Quality Progress, 30(9), 73–81.

REFERENCES 11

Juran, J M and A Blanton Godfrey (eds.) (2000) Juran’s Quality Handbook, 5th ed New

York: McGraw-Hill.

Pearson, E S (1935) The Application of Statistical Methods to Industrial Standardization.

London: British Standards Association.

Pearson, E S (1973) Some historical reflections on the introduction of statistical methods in

industry The Statistician, 22(3), 165–179.

Shewhart, W A (1931) Economic Control of Quality of Manufactured Product New York:

Van Nostrand (Reprinted in 1980 by the American Society for Quality Control.)

Shewhart, W A (1939) Statistical Method from the Viewpoint of Quality Control Washington,

DC: The Graduate School, The Department of Agriculture (editorial assistance by W Edwards Deming).

Struebing, L (1996) Eugene L Grant: 1897–1996 Quality Progress, 29(11), 81–83.

Voehl, F (ed.) (1995) Deming: The Way We Knew Him Delray Beach, FL: St Lucie Press Walton, M (1986) The Deming Management Method New York: Dodd and Mead.

Walton, M (1990) Deming Management at Work New York: G P Putnam.

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C H A P T E R 2

Basic Tools for Improving Quality

There are various statistical and nonstatistical tools that have been used sively in quality improvement work In particular, there are seven simple toolsthat have often been referred to as “the seven basic tools,” with the late KaoruIshikawa generally associated with the term In particular, see Ishikawa (1976).The tools are:

7 Defect concentration diagram

The first four of these are statistical/graphical techniques They are introducedhere and some are covered in greater detail in subsequent chapters The last threetools are discussed only in this chapter It is important to realize that althoughmany gains have been made using just these seven tools, there are other tools,such as experimental designs (see Chapter 13), that should additionally be used.See also the “seven newer tools” that are discussed in Section 2.8

2.1 HISTOGRAM

A histogram is a bar chart that shows the relative frequencies of observations in

each of several classes For example, Figure 2.1 is a histogram that might represent

Statistical Methods for Quality Improvement, Third Edition Thomas P Ryan.

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13

14 BASIC TOOLS FOR IMPROVING QUALITY

Class Boundary

119.5 109.5 99.5 89.5 79.5 69.5 59.5 49.5

16 14 12 10 8 6 4 2 0

Figure 2.1 Histogram.

quality control data that have been grouped into seven classes, such as values of

a process characteristic that have been obtained over time A histogram is thus apictorial display of the way the data are distributed over the various classes Assuch, it can indicate, in particular, whether the data are distributed symmetrically

or asymmetrically over the classes This can be very useful information, as manycontrol charts are based on the implicit assumption of a particular symmetricdistribution, a normal distribution, for whatever is being charted (A normaldistribution is covered, along with other distributions, in Chapter 3.)

If we have a set of, say, 100 numerical values that were all obtained at thesame time, we should address the question of determining a meaningful way

to portray the data graphically so as to provide some insight into the processthat generated the numbers Assume that the 100 numbers are those given inTable 2.1 Such a table, by itself, tells us very little By looking at Table 2.1, wecan determine the largest value and the smallest value, and that is about all.One or more good graphical displays of the data will tell us much more,however A commonly used starting point in summarizing data is to put thedata into classes and then to construct a histogram from the data that have beenthus grouped This is what is generally covered in the first week or two in

an introductory statistics course We will construct a histogram for the data inTable 2.1, but our choice of a histogram as the first graphical tool to illustrateshould not be interpreted as an indication that a histogram is superior to othergraphical tools It isn’t There are alternative displays, some of which are pre-sented in Chapter 11, that have clear advantages over the histogram, particularly

then constructed and displayed as in Figure 2.2.

Table 2.2 Frequency Distribution for the Data in Table 2.1

16 BASIC TOOLS FOR IMPROVING QUALITY

Class Boundaries

89.5 79.5 69.5 59.5 49.5 39.5 29.5 19.5

Figure 2.2 Histogram of the data in Table 2.1.

It can be observed that the histogram is simply a bar chart in which the height

of each of the seven rectangles corresponds to the frequency of the class thatthe rectangle represents Notice that the values along the horizontal axis of thehistogram do not correspond to the values of the class intervals in Table 2.2

That is because these are class boundaries, which are defined as the average of

adjacent class limits (e.g., 29.5 is the average of 29 and 30) To illustrate their use,

we might think of the data in Table 2.1 as being rounded to the nearest integer sothat values between 29.0 and 29.5 would be rounded down to 29 and thus appear

in the first class, whereas values above 29.5 and less than 39.5 would be put in thesecond class Also, if the class limits had been used to construct the histogram,there would have been gaps between the rectangles because there is a one-unitgap between 29 and 30, 39 and 40, and so on If the classes are of equal width,which is generally desirable, the rectangles will then be of equal width

In this example the number of classes was implicitly determined from theselection of what seemed to be logical class intervals The use of the latter isdesirable whenever possible, but it is not always possible What should we havedone if there had been only 30 values rather than 100, but the largest and smallestvalues were still 21 and 87, respectively? If we tried to spread 30 values over 7classes, we might have some empty classes, and/or the shape of the histogramcould be rather flat We should keep in mind that one of the main reasonsfor constructing a histogram is to provide some insight into the shape of thedistribution of population values from which the sample values were obtained