Contents ------------ Chapter 1 Introduction 1 (*This integer is the page number) ------------- 1.1 Quality and the Early History of Quality Improvement 1 1.2 Quality Management 3 1.3 Statistical Process Control 6 1.4 Organization of the Book 8 1.5 Exercises 9 Chapter 2 Basic Statistical Concepts and Methods 11 ------------- 2.1 Introduction 11 2.2 Population and Population Distribution 11 2.3 Important Continuous Distributions 14 2.3.1 Normal distribution 15 2.3.2 Chi-square distribution 15 2.3.3 t distribution 16 2.3.4 F distribution 18 2.3.5 Weibull distribution and exponential distribution 18 2.4 Important Discrete Distributions 19 2.4.1 Binary variable and Bernoulli distribution 19 2.4.2 Binomial and multinomial distributions 19 2.4.3 Geometric distribution 20 2.4.4 Hypergeometric distribution 20 2.4.5 Poisson distribution 21 2.5 Data and Data Description 21 2.6 Tabular and Graphical Methods for Describing Data 25 2.6.1 Frequency table, pie chart, and bar chart 25 2.6.2 Dot plot, stem-and-leaf plot, and box plot 26 2.6.3 Frequency histogram and density histogram 28 2.7 Parametric Statistical Inferences 33 2.7.1 Point estimation and sampling distribution 33 2.7.2 Maximum likelihood estimation and least squares estimation 38 2.7.3 Confidence intervals and hypothesis testing 41 2.7.4 The delta method and the bootstrap method 49 2.8 Nonparametric Statistical Inferences 50 2.8.1 Order statistics and their properties 51  2.8.2 Goodness-of-fit tests 54 2.8.3 Rank tests 56 2.8.4 Nonparametric density estimation 61 2.8.5 Nonparametric regression 62 2.9 Exercises 67 Chapter 3 Univariate Shewhart Charts and Process Capability 73 ------------- 3.1 Introduction 73 3.2 Shewhart Charts for Numerical Variables 74 3.2.1 The X and R charts 74 3.2.2 The X and s charts 84 3.2.3 The X and R charts for monitoring individual observations 88 3.3 Shewhart Charts for Categorical Variables 91 3.3.1 The p chart and m p chart 91 3.3.2 The c chart, u chart, and D chart 97 3.4 Process Capability Analysis 102 3.4.1 Process capability and its measurement 102 3.4.2 Process capability ratios 103 3.5 Some Discussions 110 3.6 Exercises 112 Chapter 4 Univariate CUSUM Charts 119 ------------- 4.1 Introduction 119 4.2 Monitoring the Mean of a Normal Process 121 4.2.1 The V-mask and decision interval forms of the CUSUM chart 121 4.2.2 Design and implementation of the CUSUM chart 126 4.2.3 Cases with correlated observations 135 4.2.4 Optimality of the CUSUM chart 141 4.3 Monitoring the Variance of a Normal Process 144 4.3.1 Process variability and quality of products 144 4.3.2 CUSUM charts for monitoring process variance 146 4.3.3 Joint monitoring of process mean and variance 151 4.4 CUSUM Charts for Distributions in Exponential Family 154 4.4.1 Cases with some continuous distributions in the exponential family 155 4.4.2 Cases with discrete distributions in the exponential family 158 4.5 Self-Starting and Adaptive CUSUM Charts 162 4.5.1 Self-Starting CUSUM charts 162 4.5.2 Adaptive CUSUM charts 168 4.6 Some Theory for Computing ARL Values 169 4.6.1 The Markov chain approach 170 4.6.2 The integral equations approach 172 4.7 Some Discussions 173 4.8 Exercises 174 Chapter 5 Univariate EWMA Charts 181 ------------- 5.1 Introduction 181 5.2 Monitoring the Mean of a Normal Process 182 5.2.1 Design and implementation of the EWMA chart 182 5.2.2 Cases with correlated observations 191 5.2.3 Comparison with CUSUM charts 193 5.3 Monitoring the Variance of a Normal Process 197 5.3.1 Monitoring the process variance 199 5.3.2 Joint monitoring of the process mean and variance 205 5.4 Self-Starting and Adaptive EWMA Charts 211 5.4.1 Self-starting EWMA charts 211 5.4.2 Adaptive EWMA charts 214 5.5 Some Discussions 219 5.6 Exercises 221 Chapter 6 Univariate Control Charts by Change-Point Detection 225 ------------- 6.1 Introduction 225 6.2 Univariate Change-Point Detection 226 6.2.1 Detection of a single change-point 226 6.2.2 Detection of multiple change-points 230 6.3 Control Charts by Change-Point Detection 233 6.3.1 Monitoring of the process mean 233 6.3.2 Monitoring of the process variance 241 6.3.3 Monitoring of both the process mean and variance 247 6.4 Some Discussions 252 6.5 Exercises 254 Chapter 7 Multivariate Statistical Process Control 257 ------------- 7.1 Introduction 257 7.2 Multivariate Shewhart Charts 258 7.2.1 Multivariate normal distributions and some basic properties 258 7.2.2 Some multivariate Shewhart charts 264 7.3 Multivariate CUSUM Charts 271 7.3.1 MCUSUM charts for monitoring the process mean 271 7.3.2 MCUSUM charts for monitoring the process covariance matrix 281 7.4 Multivariate EWMA Charts 284 7.4.1 MEWMA charts for monitoring the process mean 284 7.4.2 MEWMA charts for monitoring the process covariance matrix 289 7.5 Multivariate Control Charts by Change-Point Detection 294 7.6 Multivariate Control Charts by LASSO 299 7.6.1 LASSO for regression variable selection 300 7.6.2 A LASSO-based MEWMA chart 300 7.7 Some Discussions 306 7.8 Exercises 308 Chapter 8 Univariate Nonparametric Process Control 315 ------------- 8.1 Introduction 315 8.2 Rank-Based Nonparametric Control Charts 317 8.2.1 Nonparametric Shewhart charts 317 8.2.2 Nonparametric CUSUM charts 324 8.2.3 Nonparametric EWMA charts 330 8.2.4 Nonparametric CPD charts 338 8.3 Nonparametric SPC by Categorical Data Analysis 341 8.3.1 Process monitoring by categorizing process observations 342 8.3.2 Alternative control charts and some comparisons 348 8.4 Some Discussions 356 8.5 Exercises 358 Chapter 9 Multivariate Nonparametric Process Control 363 ------------- 9.1 Introduction 363 9.2 Rank-Based Multivariate Nonparametric Control Charts 366 9.2.1 Control charts based on longitudinal ranking 366 9.2.2 Control charts based on cross-component ranking 376 9.3 Multivariate Nonparametric SPC by Log-Linear Modeling 387 9.3.1 Analyzing categorical data by log-linear modeling 389 9.3.2 Nonparametric SPC by log-linear modeling 392 9.4 Some Discussions 401 9.5 Exercises 402 Chapter 10 Profile Monitoring 407 --------------- 10.1 Introduction 407 10.2 Parametric Profile Monitoring 408 10.2.1 Linear profile monitoring 408 10.2.2 Nonlinear profile monitoring 418 10.3 Nonparametric Profile Monitoring 423 10.3.1 Nonparametric mixed-effects modeling 424 10.3.2 Phase II nonparametric profile monitoring 428 10.4 Some Discussions 433 10.5 Exercises 434 Appendix A R Functions for SPC 437 --------------- A.1 Basic R Functions 437 A.2 R Packages for SPC 440 A.3 List of R Functions Used in the Book 440 Appendix B Datasets Used in the Book 447 --------------- Bibliography 451 Index 479