Nonparametric Statistical Process Control

A unique approach to understanding the foundations of statistical quality control with a focus on the latest developments in nonparametric control charting methodologies

Statistical Process Control (SPC) methods have a long and successful history and have revolutionized many facets of industrial production around the world. This book addresses recent developments in statistical process control bringing the modern use of computers and simulations along with theory within the reach of both the researchers and practitioners. The emphasis is on the burgeoning field of nonparametric SPC (NSPC) and the many new methodologies developed by researchers worldwide that are revolutionizing SPC.

Over the last several years research in SPC, particularly on control charts, has seen phenomenal growth. Control charts are no longer confined to manufacturing and are now applied for process control and monitoring in a wide array of applications, from education, to environmental monitoring, to disease mapping, to crime prevention. This book addresses quality control methodology, especially control charts, from a statistician's viewpoint, striking a careful balance between theory and practice. Although the focus is on the newer nonparametric control charts, the reader is first introduced to the main classes of the parametric control charts and the associated theory, so that the proper foundational background can be laid.

• Reviews basic SPC theory and terminology, the different types of control charts, control chart design, sample size, sampling frequency, control limits, and more

• Focuses on the distribution-free (nonparametric) charts for the cases in which the underlying process distribution is unknown

• Provides guidance on control chart selection, choosing control limits and other quality related matters, along with all relevant formulas and tables

• Uses computer simulations and graphics to illustrate concepts and explore the latest research in SPC

Offering a uniquely balanced presentation of both theory and practice, Nonparametric Methods for Statistical Quality Control is a vital resource for students, interested practitioners, researchers, and anyone with an appropriate background in statistics interested in learning about the foundations of SPC and latest developments in NSPC.

Auteur

SUBHABRATA CHAKRABORTI, PHD is Professor of Statistics and Morrow Faculty Excellence Fellow at the University of Alabama, Tuscaloosa, AL , USA. He is a Fellow of the American Statistical Association and an elected member of the International Statistical Institute. Professor Chakraborti has contributed in a number of research areas, including censored data analysis and income inference. His current research interests include development of statistical methods in general and nonparametric methods in particular for statistical process control. He has been a Fulbright Senior Scholar to South Africa and a visiting professor in several countries, including India, Holland and Brazil. Cited for his mentoring and collaborative work with students and scholars from around the world, Professor Chakraborti has presented seminars, delivered keynote/plenary addresses and conducted research workshops at various conferences. MARIEN ALET GRAHAM, PHD is a senior lecturer at the Department of Science, Mathematics and Technology Education at the University of Pretoria, Pretoria, South Africa. She holds an Y1 rating from the South African National Research Foundation (NRF). Her current research interests are in Statistical Process Control, Nonparametric Statistics and Statistical Education. She has published several articles in international peer review journals and presented her work at various conferences.

Texte du rabat
A UNIQUE APPROACH TO UNDERSTANDING THE FOUNDATIONS OF STATISTICAL QUALITY CONTROL WITH A FOCUS ON NONPARAMETRIC CONTROL CHARTING METHODOLOGIES Statistical Process Control (SPC) methods have a long and successful history in industrial statistics and have revolutionized many facets of industrial production around the world. This book addresses recent developments in SPC bringing the modern use of computers and simulations along with the theory within the reach of both the researchers and practitioners. The emphasis is on the burgeoning field of nonparametric SPC (NSPC) and the many new methodologies developed by researchers worldwide. Over the last several years, research in SPC, particularly on control charts, has seen phenomenal growth. Control charts are no longer confined to manufacturing and are now applied for process control and monitoring in a wide array of applications, from education, to environmental monitoring, to disease mapping, to crime prevention. This book treats quality control methodology, especially control charts, from a statistician's viewpoint, striking a careful balance between theory and practice. Although the focus is on the newer nonparametric control charts, the reader is first introduced to the main classes of the parametric control charts and the associated theory, so that the proper foundational background can be laid. Offering a uniquely balanced presentation of both theory and practice, Nonparametric Statistical Process Control is a vital resource for students, interested practitioners, researchers, and anyone with an appropriate background in statistics interested in learning about the foundations of SPC and latest developments in NSPC.

Contenu
About the Authors xiii

Preface xv

About the companion website xix

1 Background/Review of Statistical Concepts 1

Chapter Overview 1

1.1 Basic Probability 1

1.2 Random Variables and Their Distributions 3

1.3 Random Sample 12

1.4 Statistical Inference 16

1.5 Role of the Computer 22

2 Basics of Statistical Process Control 23

Chapter Overview 23

2.1 Basic Concepts 23

2.1.1 Types of Variability 23

2.1.2 The Control Chart 25

2.1.3 Construction of Control Charts 29

2.1.4 Variables and Attributes Control Charts 30

2.1.5 Sample Size or Subgroup Size 31

2.1.6 Rational Subgrouping 31

2.1.7 Nonparametric or Distribution-free 34

2.1.8 Monitoring Process Location and/or Process Scale 36

2.1.9 Case K and Case U 37

2.1.10 Control Charts and Hypothesis Testing 37

2.1.11 General Steps in Designing a Control Chart 39

2.1.12 Measures of Control Chart Performance 39

2.1.12.1 False Alarm Probability (FAP) 41

2.1.12.2 False Alarm Rate (FAR) 43

2.1.12.3 The Average Run-length (ARL) 43

2.1.12.4 Standard Deviation of Run-length (SDRL) 44

2.1.12.5 Percentiles of Run-length 44

2.1.12.6 Average Number of Samples to Signal (ANSS) 48

2.1.12.7 Average Number of Observations to Signal (ANOS) 48

2.1.12.8 Average Time to Signal (ATS) 48

2.1.12.9 Number of Individual Items Inspected (I) 49

2.1.13 Operating Characteristic Curves (OC-curves) 50

2.1.14 Design of Control Charts 51

2.1.14.1 Sample Size, Sampling Frequency, and Variable Sample Sizes 51

2.1.14.2 Variable Control Limits 54

2.1.14.3 Standardized Control Limits 56

2.1.15 Size of a Shift 57

2.1.16 Choice of Control Limits 59

2.1.16.1 k-sigma Limits 59

2.1.16.2 Probability Limits 60

3 Parametric Univariate Variables Control Charts 63

Chapter Overview 63

3.1 Introduction 64

3.2 Parametric Variables Control Charts in Case K 64

3.2.1 Shewhart Control Charts 65

3.2.2 CUSUM Control Charts 67

3.2.3 EWMA Control Charts 72

3.3 Types of Parametric Variables Charts in Case K: Illustrative Examples 77

3.3.1 Shewhart Control Charts 77

3.3.1.1 Shewhart Control Charts for Monitoring Process Mean 77

3.3.1.2 Shewhart Control Charts for Monitoring Process Variation 79

3.3.2 CUSUM Control Charts 84

3.3.3 EWMA Control Charts 87

3.4 Shewhart, EWMA, and CUSUM Charts: Which to Use When 90

3.5 Control Chart Enhancements 91

3.5.1…