CONTENTS
Preface vii
1 Introduction 1
1.1 The Nature of Quality and the Role of Statistics . . . . . . . . . . 1
1.2 Modern Quality Philosophy and Business
Practice Improvement Strategies . . . . . . . . . . . . . . . . . . 3
1.2.1 Modern Quality Philosophy and a Six-Step
Process-Oriented Quality Assurance Cycle . . . . . . . . 4
1.2.2 The Modern Business Environment and General
Business Process Improvement . . . . . . . . . . . . . . . 7
1.2.3 Some Caveats . . . . . . . . . . . . . . . . . . . . . . . . 10
1.3 Logical Process Identification and Analysis . . . . . . . . . . . . 12
1.4 Elementary Principles of Quality Assurance
Data Collection . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
1.5 Simple Statistical Graphics and Quality
Assurance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
1.6 Chapter Summary . . . . . . . . . . . . . . . . . . . . . . . . . . 25
1.7 Chapter 1 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . 25
2 Statistics and Measurement 33
2.1 Basic Concepts in Metrology and Probability Modeling
of Measurement . . . . . . . . . . . . . . . . . . . . . . . . . . . 34
2.2 Elementary One- and Two-Sample Statistical Methods
and Measurement . . . . . . . . . . . . . . . . . . . . . . . . . . 40
2.2.1 One-SampleMethods and Measurement Error . . . . . . . 40
2.2.2 Two-Sample Methods and Measurement Error . . . . . . 45
2.3 Some Intermediate Statistical Methods
and Measurement . . . . . . . . . . . . . . . . . . . . . . . . . . 53
2.3.1 A Simple Method for Separating Process
and Measurement Variation . . . . . . . . . . . . . . . . 54
2.3.2 One-Way Random Effects Models and Associated
Inference . . . . . . . . . . . . . . . . . . . . . . . . . . 56
2.4 Gauge R&R Studies . . . . . . . . . . . . . . . . . . . . . . . . . 62
2.4.1 Two-Way Random Effects Models and Gauge
R&R Studies . . . . . . . . . . . . . . . . . . . . . . . . 62
2.4.2 Range-Based Estimation . . . . . . . . . . . . . . . . . . 65
2.4.3 ANOVA-Based Estimation . . . . . . . . . . . . . . . . . 68
2.5 Simple Linear Regression and Calibration
Studies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75
2.6 R&R Considerations for Go/No-Go Inspection . . . . . . . . . . 80
2.6.1 Some Simple Probability Modeling . . . . . . . . . . . . 81
2.6.2 Simple R&R Point Estimates for 0/1 Contexts . . . . . . . 82
2.6.3 Confidence Limits for Comparing Call Rates
for Two Operators . . . . . . . . . . . . . . . . . . . . . 84
2.7 Chapter Summary . . . . . . . . . . . . . . . . . . . . . . . . . . 87
2.8 Chapter 2 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . 87
3 Process Monitoring 107
3.1 Generalities About Shewhart Control Charting . . . . . . . . . . . 108
3.2 Shewhart Charts for Measurements/“Variables Data” . . . . . . . 113
3.2.1 Charts for Process Location . . . . . . . . . . . . . . . . 113
3.2.2 Charts for Process Spread . . . . . . . . . . . . . . . . . 119
3.2.3 What If n = 1? . . . . . . . . . . . . . . . . . . . . . . . 124
3.3 Shewhart Charts for Counts/“Attributes Data” . . . . . . . . . . . 128
3.3.1 Charts for Fraction Nonconforming . . . . . . . . . . . . 128
3.3.2 Charts for Mean Nonconformities per Unit . . . . . . . . 132
3.4 Patterns on Shewhart Charts and Special
Alarm Rules . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 136
3.5 The Average Run Length Concept . . . . . . . . . . . . . . . . . 144
3.6 Statistical Process Monitoring and Engineering Control . . . . . . 150
3.6.1 Discrete Time PID Control . . . . . . . . . . . . . . . . . 150
3.6.2 Comparisons and Contrasts . . . . . . . . . . . . . . . . 157
3.7 Chapter Summary . . . . . . . . . . . . . . . . . . . . . . . . . . 160
3.8 Chapter 3 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . 160
4 Process Characterization and Capability Analysis 191
4.1 More Statistical Graphics for Process
Characterization . . . . . . . . . . . . . . . . . . . . . . . . . . . 192
4.1.1 Dot Plots and Stem-and-Leaf Diagrams . . . . . . . . . . 192
4.1.2 Quantiles and Box Plots . . . . . . . . . . . . . . . . . . 194
4.1.3 Q-Q Plots and Normal Probability Plots . . . . . . . . . . 198
4.2 Process Capability Measures and Their
Estimation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 207
4.3 Prediction and Tolerance Intervals . . . . . . . . . . . . . . . . . 213
4.3.1 Intervals for a Normal Process . . . . . . . . . . . . . . . 214
4.3.2 Intervals Based on Maximum and/or Minimum
Sample Values . . . . . . . . . . . . . . . . . . . . . . . 216
4.4 Probabilistic Tolerancing and Propagation
of Error . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 220
4.5 Chapter Summary . . . . . . . . . . . . . . . . . . . . . . . . . . 229
4.6 Chapter 4 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . 230
5 Experimental Design and Analysis for Process Improvement
Part 1: Basics 251
5.1 One-Way Methods . . . . . . . . . . . . . . . . . . . . . . . . . 252
5.1.1 The One-Way Normal Model and a Pooled Estimator
of Variance . . . . . . . . . . . . . . . . . . . . . . . . . 253
5.1.2 Confidence Intervals for Linear Combinations
of Means . . . . . . . . . . . . . . . . . . . . . . . . . . 257
5.2 Two-Way Factorials . . . . . . . . . . . . . . . . . . . . . . . . . 261
5.2.1 Graphical and Qualitative Analysis for Complete
Two-Way Factorial Data . . . . . . . . . . . . . . . . . . 262
5.2.2 Defining and Estimating Effects . . . . . . . . . . . . . . 266
5.2.3 Fitting and Checking Simplified Models for Balanced
Two-Way Factorial Data . . . . . . . . . . . . . . . . . . 274
5.3 2p Factorials . . . . . . . . . . . . . . . . . . . . . . . . . . . . 279
5.3.1 Notation and Defining Effects in p-Way Factorials . . . . 280
5.3.2 Judging the Detectability of 2p Factorial Effects
in Studies with Replication . . . . . . . . . . . . . . . . . 289
5.3.3 Judging the Detectability of 2p Factorial Effects
in Studies Lacking Replication . . . . . . . . . . . . . . . 292
5.3.4 The Yates Algorithm for Computing Fitted 2p Effects . . . 296
5.3.5 Fitting Simplified Models for Balanced 2p Data . . . . . . 297
5.4 Chapter Summary . . . . . . . . . . . . . . . . . . . . . . . . . . 301
5.5 Chapter 5 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . 302
6 Experimental Design and Analysis for Process Improvement
Part 2: Advanced Topics 333
6.1 2p−q Fractional Factorials . . . . . . . . . . . . . . . . . . . . . 334
6.1.1 Motivation and Preliminary Insights . . . . . . . . . . . . 334
6.1.2 Half-Fractions of 2p Factorials . . . . . . . . . . . . . . . 337
6.1.3 1/2q Fractions of 2p Factorials . . . . . . . . . . . . . . . 344
6.2 Response Surface Studies . . . . . . . . . . . . . . . . . . . . . . 354
6.2.1 Graphics for Understanding Fitted Response Functions . . 355
6.2.2 Using Quadratic Response Functions . . . . . . . . . . . 362
6.2.3 Analytical Interpretation of Quadratic Response
Functions . . . . . . . . . . . . . . . . . . . . . . . . . . 369
6.2.4 Response Optimization Strategies . . . . . . . . . . . . . 372
6.3 Qualitative Considerations in Experimenting for Quality
Improvement . . . . . . . . . . . . . . . . . . . . . . . . . . . . 378
6.3.1 “Classical” Issues . . . . . . . . . . . . . . . . . . . . . . 378
6.3.2 “Taguchi” Emphases . . . . . . . . . . . . . . . . . . . . 381
6.4 Chapter Summary . . . . . . . . . . . . . . . . . . . . . . . . . . 384
6.5 Chapter 6 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . 384
A Tables 407
Bibliography 421
Index 425