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

206

This is the preface. More here later.

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Preface

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1 CHAPTER

Introduction

This opening chapter rst introduces the subject of quality assurance and the relationship between it and the subject of statistics in Section 1.1. Then Section 1.2 provides context for the material of this book. Standard emphases in modern quality assurance are introduced and a six-step process-oriented quality assurance cycle is put forward as a framework for approaching projects in this eld. Some connections between modern quality assurance and popular business process improvement programs are discussed next. Some of the simplest quality assurance tools are then introduced in Sections 1.3 through 1.5 . There is a brief discussion of process mapping/analysis in Section 1.3,.discussion of some simple principles of quality assurance data collection follows in Section 1.4, and simple statistical graphics are considered in Section 1.5.

1.1 The Nature of Quality and the Role of Statistics

This book's title raises at least two basic questions: "What is `quality'?" and "What do `statistical methods' have to do with assuring it?"

Consider rst the word "quality." What does it mean to say that a particular good is a quality product? And what does it mean to call a particular service a quality service? In the case of manufactured goods (like automobiles and dishwashers), issues of reliability (the ability to function consistently and effectively across time), appropriateness of con guration, and t and nish of parts come to mind. In the realm of services (like telecommunications and transportation services) one thinks of consistency of availability and performance, esthetics, and convenience. And in evaluating the "quality" of both goods and services, there is an implicit understanding that these issues will be

2 Chapter 1. Introduction

balanced against corresponding costs to determine overall "value." Here is a popular de nition of quality that re ects some of these notions.

De nition 1 Quality in a good or service is tness for use. That tness includes aspects of both product design and conformance to the (ideal) design.

Quality of design has to do with appropriateness; the choice and con guration of features that de ne what a good or service is supposed to be like and is supposed to do. In many cases it is essentially a matter of matching product "species" to an arena of use. One needs different things in a vehicle driven on the dirt roads of the Baja peninsula than in one used on the German autobahn. Vehicle quality of design has to do with providing the "right" features at an appropriate price. With this understanding, there is no necessary contradiction between thinking of both a Rolls Royce and a Toyota economy car as quality vehicles. Similarly, both a particular fast food outlet and a particular four star restaurant might be thought of as quality eateries.

Quality of conformance has to do with living up to speci cations laid down in product design. It is concerned with small variation from what is speci ed or expected. Variation inevitably makes goods and services undesirable. Mechanical devices whose parts vary substantially from their ideal/design dimensions tend to be noisy, inef cient, prone to breakdown, and dif cult to service. They simply don't work well. In the service sector, variation from what is promised/expected is the principal source of customer dissatisfaction. A city bus system that runs on schedule every day that it is supposed to run can be seen as a quality transportation system. One that fails to do so cannot. And an otherwise elegant hotel that fails to ensure the spotless bathrooms its customers expect will soon be without those customers.

This book is concerned primarily with tools for assuring quality of conformance. This is not because quality of design is unimportant. Designing effective goods and services is a highly creative and important activity. But it is just not the primary topic of this text.

Then what does the subject of statistics have to do with the assurance of quality of conformance? To answer this question, it is helpful to have clearly in mind a de nition of statistics.

De nition 2 Statistics is the study of how best to

1. collect data,

2. summarize or describe data, and

3. draw conclusions or inferences based on data,

all in a framework that recognizes the reality and omnipresence of variation.

If quality of conformance has to do with small variation and one wishes to assure it, it will be necessary to measure, monitor, nd sources of, and seek ways to reduce variation. All of these require data (information on what is happening in a system producing a product) and therefore the tool of statistics. The intellectual framework

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