Statistical process control : the Deming paradigm and beyond

455 Pages·2002·2.61 MB·English

by  James R Thompson, Jacek Koronacki

STATISTICAL PROCESS
CONTROL
The Deming Paradigm and Beyond
SECOND EDITION

STATISTICAL PROCESS
CONTROL
The Deming Paradigm and Beyond
SECOND EDITION
James R. Thompson
Jacek Koronacki
CHAPMAN & HALL/CRC
A CRC Press Company
Boca Raton London New York Washington, D.C.
C2425 disclaimer Page 1 Thursday, November 15, 2001 1:13 PM
Library of Congress Cataloging-in-Publication Data
Thompson, James R., 1938-
Statistical process control: the Deming paradigm and beyond / James R. Thompson, Jacek
Koronacki.—2nd ed.
p. cm.
Includes bibliographical references and index.
ISBN 1-58488-242-5 (alk. paper)
1. Process control—Statistical methods. 2. Production management—Quality control. I.
Koronacki, Jacek. II. Title.
TS156.8 .T55 2001
658.5′62′015195—dc21
2001043990

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Library of Congress Card Number 2001043990
Printed in the United States of America 1 2 3 4 5 6 7 8 9 0
Printed on acid-free paper
Contents
Preface to First Edition ix
Preface to Second Edition xix
1 Statistical Process Control: A Brief Overview 1
1.1. Introduction 1
1.2. Quality Control: Origins, Misperceptions 3
1.3. A Case Study in Statistical Process Control 6
1.4. If Humans Behaved Like Machines 9
1.5. Pareto’s Maxim 10
1.6. Deming’s Fourteen Points 14
1.7. QC Misconceptions, East and West 18
1.8. White Balls, Black Balls 20
1.9. The Basic Paradigm of Statistical Process Control 32
1.10. Basic Statistical Procedures in Statistical Process Control 33
1.11. Acceptance Sampling 39
1.12. The Case for Understanding Variation 41
1.13. Statistical Coda 45
References 47
Problems 48
2 Acceptance-Rejection SPC 53
2.1. Introduction 53
2.2. The Basic Test 55
2.3. Basic Test with Equal Lot Size 58
2.4. Testing with Unequal Lot Sizes 63
2.5. Testing with Open-Ended Count Data 67
Problems 71
3 The Development of Mean and Standard Deviation Control
Charts 75
3.1. Introduction 75
3.2. A Contaminated Production Process 77
3.3. Estimation of Parameters of the “Norm” Process 81
3.4. Robust Estimators for Uncontaminated Process Parameters 90
3.5. A Process with Mean Drift 95
v
3.6. A Process with Upward Drift in Variance 100
3.7. Charts for Individual Measurements 104
3.8. Process Capability 118
References 123
Problems 123
4 Sequential Approaches 129
4.1. Introduction 129
4.2. The Sequential Likelihood Ratio Test 129
4.3. CUSUM Test for Shift of the Mean 132
4.4. Shewhart CUSUM Chart 136
4.5. Performance of CUSUM Tests on Data with Mean Drift 138
4.6. Sequential Tests for Persistent Shift of the Mean 141
4.7. CUSUM Performance on Data with Upward Variance Drift 158
4.8. Acceptance-Rejection CUSUMs 162
References 165
Problems 166
5 Exploratory Techniques for Preliminary Analysis 171
5.1. Introduction 171
5.2. The Schematic Plot 172
5.3. Smoothing by Threes 177
5.4. Bootstrapping 186
5.5. Pareto and Ishikawa Diagrams 193
5.6. A Bayesian Pareto Analysis for System Optimization of the
Space Station 197
5.7. The Management and Planning Tools 206
References 219
Problems 220
6 Optimization Approaches 225
6.1. Introduction 225
6.2. A Simplex Algorithm for Optimization 228
6.3. Selection of Objective Function 237
6.4. Motivation for Linear Models 242
6.5. Multivariate Extensions 252
6.6. Least Squares 253
6.7. Model “Enrichment” 258
6.8. Testing for Model “Enrichment” 260
6.9. 2p Factorial Designs 266
vi
6.10. Some Rotatable Quadratic Designs 270
6.11. Saturated Designs 276
6.12. A Simulation Based Approach 278
References 281
Problems 282
7 Multivariate Approaches 289
7.1. Introduction 289
7.2. Likelihood Ratio Tests for Location 290
7.3. Compound and Projection Tests 302
7.4. A Robust Estimate of “In Control” Location 305
7.5. A Rank Test for Location Slippage 308
7.6. A Rank Test for Change in Scale and/or Location 312
References 316
Problems 317
Appendix A: A Brief Introduction to Linear Algebra 321
A.1. Introduction 321
A.2. Elementary Arithmetic 323
A.3. Linear Independence of Vectors 327
A.4. Determinants 328
A.5. Inverses 331
A.6. Definiteness of a Matrix 333
A.7. Eigenvalues and Eigenvectors 333
A.8. Matrix Square Root 337
A.9. Gram-Schmidt Orthogonalization 338
Appendix B: A Brief Introduction to Stochastics 339
B.1. Introduction 339
B.2. Conditional Probability 344
B.3. Random Variables 346
B.4. Discrete Probability Distributions 351
B.5. More on Random Variables 356
B.6. Continuous Probability Distributions 360
B.7. Laws of Large Numbers 370
B.8. Moment-Generating Functions 372
B.9. Central Limit Theorem 376
B.10. Conditional Density Functions 377
B.11. Random Vectors 378
vii
B.12. Poisson Process 387
B.13. Statistical Inference 388
B.14. Bayesian Statistics 411
References 420
Appendix C: Statistical Tables 421
C.1. Table of the Normal Distribution 422
C.2. Table of the Chi-Square Distribution 423
C.3. Table of Student’s t Distribution 424
C.4. Table of the F Distribution with α=.05 425
C.5. Table of the F Distribution with α=.01 426
Index 427
viii
Preface to the First Edition
“Mayyouliveininterestingtimes”canbeacurseifonelivesinasociety
perceived to be so perfect that improvement can only be marginal and
not worth the trauma of change. If, on the other hand, one lives in
a society that is based on constant improvement, living in “interesting
times” presents opportunity. For good or ill, it is clear that people these
days live in very interesting times indeed. The struggle between the
West and the Communist World is over. Yet, with the triumph of the
Western system, there comes the challenge of seeing what happens now
that the political and military conflict is ended. Enormous residues of
intellectual energy are now freed to be focused on peacetime pursuits.
Itisinterestingtonotethatoneofthebasicoptimizationpostulatesof
statistical process control(SPC)wasdevelopedbyVilfredoPareto(1848-
1923),whowastrainedasanengineerbutisbestknownforhiseconomic
and sociological works. According to Pareto’s Maxim, the many failures
in a system are the result of a small number of causes. General malaise
is seldom the root problem. It follows that in order to improve a system,
skilled investigators are required to find and correct the causes of the
“Pareto glitches.”
We are, in this book, concerned about the orderly process of optimiza-
tion which is the nuts and bolts of statistical process control. But a few
words about the social theory of Pareto are in order, since this theory
gives insight to the important part SPC is likely to play in the post Cold
War world.
Paretoperceivedtheinevitabilityofelitesincontrolofsociety. Extrap-
olating from Pareto’s works, particularly the massive Mind and Society,
the American political scientist, James Burnham, writing in the late
1930s and early 1940s, observed the presence of such elites in Fascist,
Communist and Bourgeois Capitalist societies. These elites were based
on the expertise to seize and maintain power, rather than on excellence
in the arts, sciences and technology. Burnham pointed out that Pareto
hadstartedoutwithviewssimilartothoseofhisfather,whohadresisted
BourboncontrolofItalyinfavorofaJeffersonianrepublic. Inearlymid-
dleage,Pareto’spointofviewhadchangedfundamentallyfromakindof
Scottish Enlightenment optimism to one of cynicism when he noted the
great mistake of Aristotle. Aristotle assumed that once human beings
hadunderstoodtheAristoteleanlogicsystem, everybodywouldembrace
ix