STATISTICAL METHODS FOR QUALITY ASSURANCE Basics ...

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STATISTICAL METHODS FOR QUALITY ASSURANCE:

Basics, Measurement, Control, Capability, and Improvement

Stephen B. Vardeman and J. Marcus Jobe September 27, 2007

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Contents

Preface

v

1 Introduction

1

1.1 The Nature of Quality and the Role of Statistics . . . . . . . . . . . . 1

1.2 Modern Quality Philosophy and Business Practice Improvement Strate-

gies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

1.2.1 Modern Quality Philosophy and a Six-Step Process-Oriented

Quality Assurance Cycle . . . . . . . . . . . . . . . . . . . . 3

1.2.2 The Modern Business Environment and General Business Process

Improvement . . . . . . . . . . . . . . . . . . . . . . . . . . 7

1.2.3 Some Caveats . . . . . . . . . . . . . . . . . . . . . . . . . . 10

1.3 Logical Process Identi cation 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 Measure-

ment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33

2.2 Elementary One- and Two-Sample Statistical Methods and Measure-

ment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39

2.2.1 One-Sample Methods and Measurement Error . . . . . . . . . 39

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 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53

2.3.2 One-Way Random Effects Models and Associated Inference . 56

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2.4 Gauge R&R Studies . . . . . . . . . . . . . . . . . . . . . . . . . . . 63 2.4.1 Two-Way Random Effects Models and Gauge R&R Studies . 63 2.4.2 Range-Based Estimation . . . . . . . . . . . . . . . . . . . . 66 2.4.3 ANOVA-Based Estimation . . . . . . . . . . . . . . . . . . . 69

2.5 Simple Linear Regression and Calibration Studies . . . . . . . . . . . 76 2.6 Measurement Precision and the Ability to Detect a Change or Difference 82 2.7 R&R Considerations for Go/No-Go Inspection . . . . . . . . . . . . 91

2.7.1 Some Simple Probability Modeling . . . . . . . . . . . . . . 91 2.7.2 Simple R&R Point Estimates for 0/1 Contexts . . . . . . . . . 92 2.7.3 Application of Inference Methods for the Difference in Two

Binomial "p's" . . . . . . . . . . . . . . . . . . . . . . . . . 95 2.8 Chapter Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97 2.9 Chapter 2 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . 97

3 Process Monitoring

119

3.1 Generalities About Shewhart Control Charting . . . . . . . . . . . . . 119

3.2 Shewhart Charts for Measurements/"Variables Data" . . . . . . . . . 125

3.2.1 Charts for Process Location . . . . . . . . . . . . . . . . . . 125

3.2.2 Charts for Process Spread . . . . . . . . . . . . . . . . . . . 131

3.2.3 What if n = 1? . . . . . . . . . . . . . . . . . . . . . . . . . 136

3.3 Shewhart Charts for Counts/"Attributes Data" . . . . . . . . . . . . . 141

3.3.1 Charts for Fraction Nonconforming . . . . . . . . . . . . . . 141

3.3.2 Charts for Mean Nonconformities per Unit . . . . . . . . . . 145

3.4 Patterns on Shewhart Charts and Special Alarm Rules . . . . . . . . . 150

3.5 The Average Run Length Concept . . . . . . . . . . . . . . . . . . . 158

3.6 Statistical Process Monitoring and Engineering Control . . . . . . . . 164

3.6.1 Discrete Time PID Control . . . . . . . . . . . . . . . . . . . 164

3.6.2 Comparisons and Contrasts . . . . . . . . . . . . . . . . . . 171

3.7 Chapter Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . 174

3.8 Chapter 3 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . 174

A The First Appendix

205

Index

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