This is page i Printer: Opaque this STATISTICAL METHODS FOR QUALITY ASSURANCE: Basics, Measurement, Control, Capability, and Improvement Stephen B. Vardeman and J. Marcus Jobe September 27, 2007 ii This is page iii Printer: Opaque this 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 Identication 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 iv 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 page v Printer: Opaque this Preface This is the preface. More here later. vi This is page 1 Printer: Opaque this CHAPTER 1 Introduction This opening chapter rst introduces the subject of quality assurance and the relation- ship 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 relia- bility (the ability to function consistently and effectively across time), appropriateness of conguration, and t and nish of parts come to mind. In the realm of services (like telecommunications and transportation services) one thinks of consistency of avail- ability 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 denition of quality that reects some of these notions. Denition 1 Quality in a good or service is tness for use. That tness includes as- pects of both product design and conformance to the (ideal) design. Quality of design has to do with appropriateness; the choice and conguration of features that dene 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 specications laid down in product design. It is concerned with small variation from what is specied 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 difcult 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 denition of statistics. Denition 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 Chapter 1. Introduction 3 of the subject of statistics, emphasizing as it does the concept of variation, makes it a natural for application in the world of quality assurance. We will see that both simple and also somewhat more advanced methods of statistics have their uses in the quest to produce quality goods and services. Section 1.1 Exercises 1. "Quality" and "statistics" are related. Briey explain this relationship, using the denitions of both words. 2. Why is variation in manufactured parts undesirable? Why is variation undesir- able in a service industry? 3. If a product or service is designed appropriately, does that alone guarantee qual- ity? Why or why not? 4. If a product or service conforms to design specications, does that alone guar- antee quality? Why or why not? 1.2 Modern Quality Philosophy and Business Practice Improvement Strategies The global business environment is ercely competitive. No company can afford to "stand still" if it hopes to stay in business. Every healthy company has explicit strate- gies for constantly improving its business processes and products. Over the past several decades, there has been a blurring of distinctions between "quality improvement" and "general business practice improvement." (Formerly, the rst of these was typically thought of as narrowly focused on characteristics of manu- factured goods.) So there is now much overlap in emphases, language, and methodolo- gies between the areas. The best strategies in both arenas must in the end boil down to good methodical/scientic data-based problem solving. In this section we rst provide a discussion of some elements of modern quality philosophy and an intellectual framework around which we have organized the topics of this book (and that can serve as a road map for approaching quality improvement projects). We then provide some additional discussion and critique of the modern gen- eral business environment and its better known process improvement strategies. 1.2.1 Modern Quality Philosophy and a Six-Step Process-Oriented Quality Assurance Cycle Modern quality assurance methods and philosophy are focused not (primarily) on prod- ucts, but rather on the processes used to produce them.