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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…mehr
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.
Produktdetails
- Produktdetails
- Verlag: Wiley
- Seitenzahl: 448
- Erscheinungstermin: 29. April 2019
- Englisch
- Abmessung: 246mm x 173mm x 25mm
- Gewicht: 839g
- ISBN-13: 9781118456033
- ISBN-10: 1118456033
- Artikelnr.: 51385310
- Verlag: Wiley
- Seitenzahl: 448
- Erscheinungstermin: 29. April 2019
- Englisch
- Abmessung: 246mm x 173mm x 25mm
- Gewicht: 839g
- ISBN-13: 9781118456033
- ISBN-10: 1118456033
- Artikelnr.: 51385310
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.
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
Sensitivity Rules 91 3.5.2 Runs-type Signaling Rules 95 3.5.2.1 Signaling
Indicators 97 3.6 Run-length Distribution in the Specified Parameter Case
(Case K) 110 3.6.1 Methods of Calculating the Run-length Distribution 110
3.6.1.1 The Exact Approach (for Shewhart and some Shewhart-type Charts) 110
3.6.1.2 The Markov Chain Approach 111 3.6.1.3 The Integral Equation
Approach 128 3.6.1.4 The Computer Simulations (the Monte Carlo) Approach
128 3.7 Parameter Estimation Problem and Its Effects on the Control Chart
Performance 131 3.8 Parametric Variables Control Charts in Case U 133 3.8.1
Shewhart Control Charts in Case U 133 3.8.1.1 Shewhart Control Charts for
the Mean in Case U 133 3.8.1.2 Shewhart Control Charts for the Standard
Deviation in Case U 134 3.8.2 CUSUM Chart for the Mean in Case U 137 3.8.3
EWMA Chart for the Mean in Case U 137 3.9 Types of Parametric Control
Charts in Case U: Illustrative Examples 138 3.9.1 Charts for the Mean 138
3.9.2 Charts for the Standard Deviation 141 3.9.2.1 Using the Estimator Sp
144 3.10 Run-length Distribution in the unknown Parameter Case (Case U) 153
3.10.1 Methods of Calculating the Run-length Distribution and Its
Properties: The Conditioning/Unconditioning Method 153 3.10.1.1 The
Shewhart Chart for the Mean in Case U 153 3.10.1.2 The Shewhart Chart for
the Variance in Case U 169 3.10.1.3 The CUSUM Chart for the Mean in Case U
170 3.10.1.4 The EWMA Chart for the Mean in Case U 171 3.11 Control Chart
Enhancements 172 3.11.1 Run-length Calculation for Runs-type Signaling
Rules in Case U 172 3.12 Phase I Control Charts 174 3.12.1 Phase I X-chart
174 3.13 Size of Phase I Data 176 3.14 Robustness of Parametric Control
Charts 177 Appendix 3.1 Some Derivations for the EWMA Control Chart 178
Appendix 3.2 Markov Chains 180 Appendix 3.3 Some Derivations for the
Shewhart Dispersion Charts 184 4 Nonparametric (Distribution-free)
Univariate Variables Control Charts 187 Chapter Overview 187 4.1
Introduction 187 4.2 Distribution-free Variables Control Charts in Case K
189 4.2.1 Shewhart Control Charts 189 4.2.1.1 Shewhart Control Charts Based
on Signs 189 4.2.1.2 Shewhart Control Charts Based on Signed-ranks 196
4.2.2 CUSUM Control Charts 202 4.2.2.1 CUSUM Control Charts Based on Signs
202 4.2.2.2 A CUSUM Sign Control Chart with Runs-type Signaling Rules 203
4.2.2.3 Methods of Calculating the Run-length Distribution 203 4.2.2.4
CUSUM Control Charts Based on Signed-ranks 205 4.2.3 EWMA Control Charts
208 4.2.3.1 EWMA Control Charts Based on Signs 208 4.2.3.2 EWMA Control
Charts Based on Signs with Runs-type Signaling Rules 210 4.2.3.3 Methods of
Calculating the Run-length Distribution 210 4.2.3.4 EWMA Control Charts
Based on Signed-ranks 214 4.2.3.5 An EWMA-SR control chart with runs-type
signaling rules 216 4.2.3.6 Methods of Calculating the Run-length
Distribution 216 4.3 Distribution-free Control Charts in Case K:
Illustrative Examples 219 4.3.1 Shewhart Control Charts 219 4.3.2 CUSUM
Control Charts 229 4.3.3 EWMA Control Charts 243 4.4 Distribution-free
Variables Control Charts in Case U 253 4.4.1 Shewhart Control Charts 254
4.4.1.1 Shewhart Control Charts Based on the Precedence Statistic 254
4.4.1.2 Shewhart Control Charts Based on the Mann-Whitney Test Statistic
275 4.4.2 CUSUM Control Charts 281 4.4.2.1 CUSUM Control Charts Based on
the Exceedance Statistic 281 4.4.2.2 CUSUM Control Charts Based on the
Wilcoxon Rank-sum Statistic 285 4.4.3 EWMA Control Charts 287 4.4.3.1 EWMA
Control Charts Based on the Exceedance Statistic 287 4.4.3.2 EWMA Control
Charts Based on the Wilcoxon Rank-sum Statistic 290 4.5 Distribution-free
Control Charts in Case U: Illustrative Examples 293 4.5.1 Shewhart Control
Charts 293 4.5.2 CUSUM Control Charts 295 4.5.3 EWMA Control Charts 302 4.6
Effects of Parameter Estimation 307 4.7 Size of Phase I Data 307 4.8
Control Chart Enhancements 308 4.8.1 Sensitivity and Runs-type Signaling
Rules 308 Appendix 4.1 Shewhart Control Charts 311 Appendix 4.1.1 The
Shewhart-Prec Control Chart 311 Appendix 4.2 CUSUM Control Charts 312
Appendix 4.2.1 The CUSUM-EX Control Chart 312 Appendix 4.2.2 The CUSUM-rank
Control Chart 314 Appendix 4.3 EWMA Control Charts 317 Appendix 4.3.1 The
EWMA-SN Control Chart 317 Appendix 4.3.2 The EWMA-SR Control Chart 318
Appendix 4.3.3 The EWMA-EX Control Chart 319 Appendix 4.3.4 The EWMA-rank
Control Chart 323 5 Miscellaneous Univariate Distribution-free
(Nonparametric) Variables Control Charts 325 Chapter Overview 325 5.1
Introduction 325 5.2 Other Univariate Distribution-free (Nonparametric)
Variables Control Charts 326 5.2.1 Phase I Control Charts 326 5.2.1.1
Introduction 326 5.2.1.2 Phase I Control Charts for Location 331 5.2.2
Special Cases of Precedence Charts 343 5.2.2.1 The Min Chart 343 5.2.2.2
The CUMIN Chart 346 5.2.3 Control Charts Based on Bootstrapping 348 5.2.3.1
Methodology 351 5.2.4 Change-point Models 353 5.2.5 Some Adaptive Charts
357 5.2.5.1 Introduction 357 5.2.5.2 Variable Sampling Interval (VSI) and
Variable Sample Size (VSS) Charts 358 5.2.5.3 Other Adaptive Schemes 359
5.2.5.4 Properties and Performance Measures of Adaptive Charts 360 5.2.5.5
Adaptive Nonparametric Control Charts 362 Appendix A Tables 369 Appendix B
Programmes 381 References 413 Index 425
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
Sensitivity Rules 91 3.5.2 Runs-type Signaling Rules 95 3.5.2.1 Signaling
Indicators 97 3.6 Run-length Distribution in the Specified Parameter Case
(Case K) 110 3.6.1 Methods of Calculating the Run-length Distribution 110
3.6.1.1 The Exact Approach (for Shewhart and some Shewhart-type Charts) 110
3.6.1.2 The Markov Chain Approach 111 3.6.1.3 The Integral Equation
Approach 128 3.6.1.4 The Computer Simulations (the Monte Carlo) Approach
128 3.7 Parameter Estimation Problem and Its Effects on the Control Chart
Performance 131 3.8 Parametric Variables Control Charts in Case U 133 3.8.1
Shewhart Control Charts in Case U 133 3.8.1.1 Shewhart Control Charts for
the Mean in Case U 133 3.8.1.2 Shewhart Control Charts for the Standard
Deviation in Case U 134 3.8.2 CUSUM Chart for the Mean in Case U 137 3.8.3
EWMA Chart for the Mean in Case U 137 3.9 Types of Parametric Control
Charts in Case U: Illustrative Examples 138 3.9.1 Charts for the Mean 138
3.9.2 Charts for the Standard Deviation 141 3.9.2.1 Using the Estimator Sp
144 3.10 Run-length Distribution in the unknown Parameter Case (Case U) 153
3.10.1 Methods of Calculating the Run-length Distribution and Its
Properties: The Conditioning/Unconditioning Method 153 3.10.1.1 The
Shewhart Chart for the Mean in Case U 153 3.10.1.2 The Shewhart Chart for
the Variance in Case U 169 3.10.1.3 The CUSUM Chart for the Mean in Case U
170 3.10.1.4 The EWMA Chart for the Mean in Case U 171 3.11 Control Chart
Enhancements 172 3.11.1 Run-length Calculation for Runs-type Signaling
Rules in Case U 172 3.12 Phase I Control Charts 174 3.12.1 Phase I X-chart
174 3.13 Size of Phase I Data 176 3.14 Robustness of Parametric Control
Charts 177 Appendix 3.1 Some Derivations for the EWMA Control Chart 178
Appendix 3.2 Markov Chains 180 Appendix 3.3 Some Derivations for the
Shewhart Dispersion Charts 184 4 Nonparametric (Distribution-free)
Univariate Variables Control Charts 187 Chapter Overview 187 4.1
Introduction 187 4.2 Distribution-free Variables Control Charts in Case K
189 4.2.1 Shewhart Control Charts 189 4.2.1.1 Shewhart Control Charts Based
on Signs 189 4.2.1.2 Shewhart Control Charts Based on Signed-ranks 196
4.2.2 CUSUM Control Charts 202 4.2.2.1 CUSUM Control Charts Based on Signs
202 4.2.2.2 A CUSUM Sign Control Chart with Runs-type Signaling Rules 203
4.2.2.3 Methods of Calculating the Run-length Distribution 203 4.2.2.4
CUSUM Control Charts Based on Signed-ranks 205 4.2.3 EWMA Control Charts
208 4.2.3.1 EWMA Control Charts Based on Signs 208 4.2.3.2 EWMA Control
Charts Based on Signs with Runs-type Signaling Rules 210 4.2.3.3 Methods of
Calculating the Run-length Distribution 210 4.2.3.4 EWMA Control Charts
Based on Signed-ranks 214 4.2.3.5 An EWMA-SR control chart with runs-type
signaling rules 216 4.2.3.6 Methods of Calculating the Run-length
Distribution 216 4.3 Distribution-free Control Charts in Case K:
Illustrative Examples 219 4.3.1 Shewhart Control Charts 219 4.3.2 CUSUM
Control Charts 229 4.3.3 EWMA Control Charts 243 4.4 Distribution-free
Variables Control Charts in Case U 253 4.4.1 Shewhart Control Charts 254
4.4.1.1 Shewhart Control Charts Based on the Precedence Statistic 254
4.4.1.2 Shewhart Control Charts Based on the Mann-Whitney Test Statistic
275 4.4.2 CUSUM Control Charts 281 4.4.2.1 CUSUM Control Charts Based on
the Exceedance Statistic 281 4.4.2.2 CUSUM Control Charts Based on the
Wilcoxon Rank-sum Statistic 285 4.4.3 EWMA Control Charts 287 4.4.3.1 EWMA
Control Charts Based on the Exceedance Statistic 287 4.4.3.2 EWMA Control
Charts Based on the Wilcoxon Rank-sum Statistic 290 4.5 Distribution-free
Control Charts in Case U: Illustrative Examples 293 4.5.1 Shewhart Control
Charts 293 4.5.2 CUSUM Control Charts 295 4.5.3 EWMA Control Charts 302 4.6
Effects of Parameter Estimation 307 4.7 Size of Phase I Data 307 4.8
Control Chart Enhancements 308 4.8.1 Sensitivity and Runs-type Signaling
Rules 308 Appendix 4.1 Shewhart Control Charts 311 Appendix 4.1.1 The
Shewhart-Prec Control Chart 311 Appendix 4.2 CUSUM Control Charts 312
Appendix 4.2.1 The CUSUM-EX Control Chart 312 Appendix 4.2.2 The CUSUM-rank
Control Chart 314 Appendix 4.3 EWMA Control Charts 317 Appendix 4.3.1 The
EWMA-SN Control Chart 317 Appendix 4.3.2 The EWMA-SR Control Chart 318
Appendix 4.3.3 The EWMA-EX Control Chart 319 Appendix 4.3.4 The EWMA-rank
Control Chart 323 5 Miscellaneous Univariate Distribution-free
(Nonparametric) Variables Control Charts 325 Chapter Overview 325 5.1
Introduction 325 5.2 Other Univariate Distribution-free (Nonparametric)
Variables Control Charts 326 5.2.1 Phase I Control Charts 326 5.2.1.1
Introduction 326 5.2.1.2 Phase I Control Charts for Location 331 5.2.2
Special Cases of Precedence Charts 343 5.2.2.1 The Min Chart 343 5.2.2.2
The CUMIN Chart 346 5.2.3 Control Charts Based on Bootstrapping 348 5.2.3.1
Methodology 351 5.2.4 Change-point Models 353 5.2.5 Some Adaptive Charts
357 5.2.5.1 Introduction 357 5.2.5.2 Variable Sampling Interval (VSI) and
Variable Sample Size (VSS) Charts 358 5.2.5.3 Other Adaptive Schemes 359
5.2.5.4 Properties and Performance Measures of Adaptive Charts 360 5.2.5.5
Adaptive Nonparametric Control Charts 362 Appendix A Tables 369 Appendix B
Programmes 381 References 413 Index 425
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
Sensitivity Rules 91 3.5.2 Runs-type Signaling Rules 95 3.5.2.1 Signaling
Indicators 97 3.6 Run-length Distribution in the Specified Parameter Case
(Case K) 110 3.6.1 Methods of Calculating the Run-length Distribution 110
3.6.1.1 The Exact Approach (for Shewhart and some Shewhart-type Charts) 110
3.6.1.2 The Markov Chain Approach 111 3.6.1.3 The Integral Equation
Approach 128 3.6.1.4 The Computer Simulations (the Monte Carlo) Approach
128 3.7 Parameter Estimation Problem and Its Effects on the Control Chart
Performance 131 3.8 Parametric Variables Control Charts in Case U 133 3.8.1
Shewhart Control Charts in Case U 133 3.8.1.1 Shewhart Control Charts for
the Mean in Case U 133 3.8.1.2 Shewhart Control Charts for the Standard
Deviation in Case U 134 3.8.2 CUSUM Chart for the Mean in Case U 137 3.8.3
EWMA Chart for the Mean in Case U 137 3.9 Types of Parametric Control
Charts in Case U: Illustrative Examples 138 3.9.1 Charts for the Mean 138
3.9.2 Charts for the Standard Deviation 141 3.9.2.1 Using the Estimator Sp
144 3.10 Run-length Distribution in the unknown Parameter Case (Case U) 153
3.10.1 Methods of Calculating the Run-length Distribution and Its
Properties: The Conditioning/Unconditioning Method 153 3.10.1.1 The
Shewhart Chart for the Mean in Case U 153 3.10.1.2 The Shewhart Chart for
the Variance in Case U 169 3.10.1.3 The CUSUM Chart for the Mean in Case U
170 3.10.1.4 The EWMA Chart for the Mean in Case U 171 3.11 Control Chart
Enhancements 172 3.11.1 Run-length Calculation for Runs-type Signaling
Rules in Case U 172 3.12 Phase I Control Charts 174 3.12.1 Phase I X-chart
174 3.13 Size of Phase I Data 176 3.14 Robustness of Parametric Control
Charts 177 Appendix 3.1 Some Derivations for the EWMA Control Chart 178
Appendix 3.2 Markov Chains 180 Appendix 3.3 Some Derivations for the
Shewhart Dispersion Charts 184 4 Nonparametric (Distribution-free)
Univariate Variables Control Charts 187 Chapter Overview 187 4.1
Introduction 187 4.2 Distribution-free Variables Control Charts in Case K
189 4.2.1 Shewhart Control Charts 189 4.2.1.1 Shewhart Control Charts Based
on Signs 189 4.2.1.2 Shewhart Control Charts Based on Signed-ranks 196
4.2.2 CUSUM Control Charts 202 4.2.2.1 CUSUM Control Charts Based on Signs
202 4.2.2.2 A CUSUM Sign Control Chart with Runs-type Signaling Rules 203
4.2.2.3 Methods of Calculating the Run-length Distribution 203 4.2.2.4
CUSUM Control Charts Based on Signed-ranks 205 4.2.3 EWMA Control Charts
208 4.2.3.1 EWMA Control Charts Based on Signs 208 4.2.3.2 EWMA Control
Charts Based on Signs with Runs-type Signaling Rules 210 4.2.3.3 Methods of
Calculating the Run-length Distribution 210 4.2.3.4 EWMA Control Charts
Based on Signed-ranks 214 4.2.3.5 An EWMA-SR control chart with runs-type
signaling rules 216 4.2.3.6 Methods of Calculating the Run-length
Distribution 216 4.3 Distribution-free Control Charts in Case K:
Illustrative Examples 219 4.3.1 Shewhart Control Charts 219 4.3.2 CUSUM
Control Charts 229 4.3.3 EWMA Control Charts 243 4.4 Distribution-free
Variables Control Charts in Case U 253 4.4.1 Shewhart Control Charts 254
4.4.1.1 Shewhart Control Charts Based on the Precedence Statistic 254
4.4.1.2 Shewhart Control Charts Based on the Mann-Whitney Test Statistic
275 4.4.2 CUSUM Control Charts 281 4.4.2.1 CUSUM Control Charts Based on
the Exceedance Statistic 281 4.4.2.2 CUSUM Control Charts Based on the
Wilcoxon Rank-sum Statistic 285 4.4.3 EWMA Control Charts 287 4.4.3.1 EWMA
Control Charts Based on the Exceedance Statistic 287 4.4.3.2 EWMA Control
Charts Based on the Wilcoxon Rank-sum Statistic 290 4.5 Distribution-free
Control Charts in Case U: Illustrative Examples 293 4.5.1 Shewhart Control
Charts 293 4.5.2 CUSUM Control Charts 295 4.5.3 EWMA Control Charts 302 4.6
Effects of Parameter Estimation 307 4.7 Size of Phase I Data 307 4.8
Control Chart Enhancements 308 4.8.1 Sensitivity and Runs-type Signaling
Rules 308 Appendix 4.1 Shewhart Control Charts 311 Appendix 4.1.1 The
Shewhart-Prec Control Chart 311 Appendix 4.2 CUSUM Control Charts 312
Appendix 4.2.1 The CUSUM-EX Control Chart 312 Appendix 4.2.2 The CUSUM-rank
Control Chart 314 Appendix 4.3 EWMA Control Charts 317 Appendix 4.3.1 The
EWMA-SN Control Chart 317 Appendix 4.3.2 The EWMA-SR Control Chart 318
Appendix 4.3.3 The EWMA-EX Control Chart 319 Appendix 4.3.4 The EWMA-rank
Control Chart 323 5 Miscellaneous Univariate Distribution-free
(Nonparametric) Variables Control Charts 325 Chapter Overview 325 5.1
Introduction 325 5.2 Other Univariate Distribution-free (Nonparametric)
Variables Control Charts 326 5.2.1 Phase I Control Charts 326 5.2.1.1
Introduction 326 5.2.1.2 Phase I Control Charts for Location 331 5.2.2
Special Cases of Precedence Charts 343 5.2.2.1 The Min Chart 343 5.2.2.2
The CUMIN Chart 346 5.2.3 Control Charts Based on Bootstrapping 348 5.2.3.1
Methodology 351 5.2.4 Change-point Models 353 5.2.5 Some Adaptive Charts
357 5.2.5.1 Introduction 357 5.2.5.2 Variable Sampling Interval (VSI) and
Variable Sample Size (VSS) Charts 358 5.2.5.3 Other Adaptive Schemes 359
5.2.5.4 Properties and Performance Measures of Adaptive Charts 360 5.2.5.5
Adaptive Nonparametric Control Charts 362 Appendix A Tables 369 Appendix B
Programmes 381 References 413 Index 425
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
Sensitivity Rules 91 3.5.2 Runs-type Signaling Rules 95 3.5.2.1 Signaling
Indicators 97 3.6 Run-length Distribution in the Specified Parameter Case
(Case K) 110 3.6.1 Methods of Calculating the Run-length Distribution 110
3.6.1.1 The Exact Approach (for Shewhart and some Shewhart-type Charts) 110
3.6.1.2 The Markov Chain Approach 111 3.6.1.3 The Integral Equation
Approach 128 3.6.1.4 The Computer Simulations (the Monte Carlo) Approach
128 3.7 Parameter Estimation Problem and Its Effects on the Control Chart
Performance 131 3.8 Parametric Variables Control Charts in Case U 133 3.8.1
Shewhart Control Charts in Case U 133 3.8.1.1 Shewhart Control Charts for
the Mean in Case U 133 3.8.1.2 Shewhart Control Charts for the Standard
Deviation in Case U 134 3.8.2 CUSUM Chart for the Mean in Case U 137 3.8.3
EWMA Chart for the Mean in Case U 137 3.9 Types of Parametric Control
Charts in Case U: Illustrative Examples 138 3.9.1 Charts for the Mean 138
3.9.2 Charts for the Standard Deviation 141 3.9.2.1 Using the Estimator Sp
144 3.10 Run-length Distribution in the unknown Parameter Case (Case U) 153
3.10.1 Methods of Calculating the Run-length Distribution and Its
Properties: The Conditioning/Unconditioning Method 153 3.10.1.1 The
Shewhart Chart for the Mean in Case U 153 3.10.1.2 The Shewhart Chart for
the Variance in Case U 169 3.10.1.3 The CUSUM Chart for the Mean in Case U
170 3.10.1.4 The EWMA Chart for the Mean in Case U 171 3.11 Control Chart
Enhancements 172 3.11.1 Run-length Calculation for Runs-type Signaling
Rules in Case U 172 3.12 Phase I Control Charts 174 3.12.1 Phase I X-chart
174 3.13 Size of Phase I Data 176 3.14 Robustness of Parametric Control
Charts 177 Appendix 3.1 Some Derivations for the EWMA Control Chart 178
Appendix 3.2 Markov Chains 180 Appendix 3.3 Some Derivations for the
Shewhart Dispersion Charts 184 4 Nonparametric (Distribution-free)
Univariate Variables Control Charts 187 Chapter Overview 187 4.1
Introduction 187 4.2 Distribution-free Variables Control Charts in Case K
189 4.2.1 Shewhart Control Charts 189 4.2.1.1 Shewhart Control Charts Based
on Signs 189 4.2.1.2 Shewhart Control Charts Based on Signed-ranks 196
4.2.2 CUSUM Control Charts 202 4.2.2.1 CUSUM Control Charts Based on Signs
202 4.2.2.2 A CUSUM Sign Control Chart with Runs-type Signaling Rules 203
4.2.2.3 Methods of Calculating the Run-length Distribution 203 4.2.2.4
CUSUM Control Charts Based on Signed-ranks 205 4.2.3 EWMA Control Charts
208 4.2.3.1 EWMA Control Charts Based on Signs 208 4.2.3.2 EWMA Control
Charts Based on Signs with Runs-type Signaling Rules 210 4.2.3.3 Methods of
Calculating the Run-length Distribution 210 4.2.3.4 EWMA Control Charts
Based on Signed-ranks 214 4.2.3.5 An EWMA-SR control chart with runs-type
signaling rules 216 4.2.3.6 Methods of Calculating the Run-length
Distribution 216 4.3 Distribution-free Control Charts in Case K:
Illustrative Examples 219 4.3.1 Shewhart Control Charts 219 4.3.2 CUSUM
Control Charts 229 4.3.3 EWMA Control Charts 243 4.4 Distribution-free
Variables Control Charts in Case U 253 4.4.1 Shewhart Control Charts 254
4.4.1.1 Shewhart Control Charts Based on the Precedence Statistic 254
4.4.1.2 Shewhart Control Charts Based on the Mann-Whitney Test Statistic
275 4.4.2 CUSUM Control Charts 281 4.4.2.1 CUSUM Control Charts Based on
the Exceedance Statistic 281 4.4.2.2 CUSUM Control Charts Based on the
Wilcoxon Rank-sum Statistic 285 4.4.3 EWMA Control Charts 287 4.4.3.1 EWMA
Control Charts Based on the Exceedance Statistic 287 4.4.3.2 EWMA Control
Charts Based on the Wilcoxon Rank-sum Statistic 290 4.5 Distribution-free
Control Charts in Case U: Illustrative Examples 293 4.5.1 Shewhart Control
Charts 293 4.5.2 CUSUM Control Charts 295 4.5.3 EWMA Control Charts 302 4.6
Effects of Parameter Estimation 307 4.7 Size of Phase I Data 307 4.8
Control Chart Enhancements 308 4.8.1 Sensitivity and Runs-type Signaling
Rules 308 Appendix 4.1 Shewhart Control Charts 311 Appendix 4.1.1 The
Shewhart-Prec Control Chart 311 Appendix 4.2 CUSUM Control Charts 312
Appendix 4.2.1 The CUSUM-EX Control Chart 312 Appendix 4.2.2 The CUSUM-rank
Control Chart 314 Appendix 4.3 EWMA Control Charts 317 Appendix 4.3.1 The
EWMA-SN Control Chart 317 Appendix 4.3.2 The EWMA-SR Control Chart 318
Appendix 4.3.3 The EWMA-EX Control Chart 319 Appendix 4.3.4 The EWMA-rank
Control Chart 323 5 Miscellaneous Univariate Distribution-free
(Nonparametric) Variables Control Charts 325 Chapter Overview 325 5.1
Introduction 325 5.2 Other Univariate Distribution-free (Nonparametric)
Variables Control Charts 326 5.2.1 Phase I Control Charts 326 5.2.1.1
Introduction 326 5.2.1.2 Phase I Control Charts for Location 331 5.2.2
Special Cases of Precedence Charts 343 5.2.2.1 The Min Chart 343 5.2.2.2
The CUMIN Chart 346 5.2.3 Control Charts Based on Bootstrapping 348 5.2.3.1
Methodology 351 5.2.4 Change-point Models 353 5.2.5 Some Adaptive Charts
357 5.2.5.1 Introduction 357 5.2.5.2 Variable Sampling Interval (VSI) and
Variable Sample Size (VSS) Charts 358 5.2.5.3 Other Adaptive Schemes 359
5.2.5.4 Properties and Performance Measures of Adaptive Charts 360 5.2.5.5
Adaptive Nonparametric Control Charts 362 Appendix A Tables 369 Appendix B
Programmes 381 References 413 Index 425