Fully revised and updated, this book combines a theoretical background with examples and references to R, MINITAB and JMP, enabling practitioners to find state-of-the-art material on both foundation and implementation tools to support their work. Topics addressed include computer-intensive data analysis, acceptance sampling, univariate and multivariate statistical process control, design of experiments, quality by design, and reliability using classical and Bayesian methods. The book can be used for workshops or courses on acceptance sampling, statistical process control, design of experiments, and reliability.

Graduate and post-graduate students in the areas of statistical quality and engineering, as well as industrial statisticians, researchers and practitioners in these fields will all benefit from the comprehensive combination of theoretical and practical information provided in this single volume.

Modern Industrial Statistics: With applications in R, MINITAB and JMP:

• Combines a practical approach with theoretical foundations and computational support.
• Provides examples in R using a dedicated package called MISTAT, and also refers to MINITAB and JMP.
• Includes exercises at the end of each chapter to aid learning and test knowledge.
• Provides over 40 data sets representing real-life case studies.
• Is complemented by a comprehensive website providing an introduction to R, and installations of JMP scripts and MINITAB macros, including effective tutorials with introductory material: www.wiley.com/go/modern_industrial_statistics.

Preface to Second Edition xv

Preface to First Edition xvii

Abbreviations xix

PART I PRINCIPLES OF STATISTICAL THINKING AND ANALYSIS 1

1 The Role of Statistical Methods in Modern Industry and Services 3

1.1 The different functional areas in industry and services 3

1.2 The quality-productivity dilemma 5

1.3 Fire-fighting 6

1.4 Inspection of products 7

1.5 Process control 7

1.6 Quality by design 8

1.7 Information quality and practical statistical efficiency 9

1.8 Chapter highlights 11

1.9 Exercises 12

2 Analyzing Variability: Descriptive Statistics 13

2.1 Random phenomena and the structure of observations 13

2.2 Accuracy and precision of measurements 17

2.3 The population and the sample 18

2.4 Descriptive analysis of sample values 19

2.4.1 Frequency distributions of discrete random variables 19

2.4.2 Frequency distributions of continuous random variables 23

2.4.3 Statistics of the ordered sample 26

2.4.4 Statistics of location and dispersion 28

2.5 Prediction intervals 32

2.6 Additional techniques of exploratory data analysis 32

2.6.1 Box and whiskers plot 33

2.6.2 Quantile plots 34

2.6.3 Stem-and-leaf diagrams 34

2.6.4 Robust statistics for location and dispersion 36

2.7 Chapter highlights 38

2.8 Exercises 38

3 Probability Models and Distribution Functions 41

3.1 Basic probability 41

3.1.1 Events and sample spaces: Formal presentation of random measurements 41

3.1.2 Basic rules of operations with events: Unions, intersections 42

3.1.3 Probabilities of events 44

3.1.4 Probability functions for random sampling 46

3.1.5 Conditional probabilities and independence of events 47

3.1.6 Bayes formula and its application 49

3.2 Random variables and their distributions 51

3.2.1 Discrete and continuous distributions 51

3.2.2 Expected values and moments of distributions 55

3.2.3 The standard deviation, quantiles, measures of skewness and kurtosis 57

3.2.4 Moment generating functions 59

3.3 Families of discrete distribution 60

3.3.1 The binomial distribution 60

3.3.2 The hypergeometric distribution 62

3.3.3 The Poisson distribution 65

3.3.4 The geometric and negative binomial distributions 67

3.4 Continuous distributions 69

3.4.1 The uniform distribution on the interval (a, b), a < b 69

3.4.2 The normal and log-normal distributions 70

3.4.3 The exponential distribution 75

3.4.4 The gamma and Weibull distributions 77

3.4.5 The Beta distributions 80

3.5 Joint, marginal and conditional distributions 82

3.5.1 Joint and marginal distributions 82

3.5.2 Covariance and correlation 84

3.5.3 Conditional distributions 86

3.6 Some multivariate distributions 88

3.6.1 The multinomial distribution 88

3.6.2 The multi-hypergeometric distribution 89

3.6.3 The bivariate normal distribution 90

3.7 Distribution of order statistics 92

3.8 Linear combinations of random variables 94

3.9 Large sample approximations 98

3.9.1 The law of large numbers 98

3.9.2 The Central Limit Theorem 99

3.9.3 Some normal approximations 99

3.10 Additional distributions of statistics of normal samples 101

3.10.1 Distribution of the sample variance 101

3.10.2 The “Student” t-statistic 102

3.10.3 Distribution of the variance ratio 102

3.11 Chapter highlights 104

3.12 Exercises 105

4 Statistical Inference and Bootstrapping 113

4.1 Sampling characteristics of estimators 113

4.2 Some methods of point estimation 114

4.2.1 Moment equation estimators 115

4.2.2 The method of least squares 116

4.2.3 Maximum likelihood estimators 118

4.3 Comparison of sample estimates 120

4.3.1 Basic concepts 120

4.3.2 Some common one-sample tests of hypotheses 122

4.4 Confidence intervals 128

4.4.1 Confidence intervals for ��; �� known 129

4.4.2 Confidence intervals for ��; �� unknown 130

4.4.3 Confidence intervals for �� 2 130

4.4.4 Confidence intervals for p 130

4.5 Tolerance intervals 132

4.5.1 Tolerance intervals for the normal distributions 132

4.6 Testing for normality with probability plots 134

4.7 Tests of goodness of fit 137

4.7.1 The chi-square test (large samples) 137

4.7.2 The Kolmogorov-Smirnov test 139

4.8 Bayesian decision procedures 140

4.8.1 Prior and posterior distributions 141

4.8.2 Bayesian testing and estimation 144

4.8.3 Credibility intervals for real parameters 147

4.9 Random sampling from reference distributions 148

4.10 Bootstrap sampling 150

4.10.1 The bootstrap method 150

4.10.2 Examining the bootstrap method 151

4.10.3 Harnessing the bootstrap method 152

4.11 Bootstrap testing of hypotheses 152

4.11.1 Bootstrap testing and confidence intervals for the mean 153

4.11.2 Studentized test for the mean 153

4.11.3 Studentized test for the difference of two means 155

4.11.4 Bootstrap tests and confidence intervals for the variance 157

4.11.5 Comparing statistics of several samples 158

4.12 Bootstrap tolerance intervals 161

4.12.1 Bootstrap tolerance intervals for Bernoulli samples 161

4.12.2 Tolerance interval for continuous variables 163

4.12.3 Distribution-free tolerance intervals 164

4.13 Non-parametric tests 165

4.13.1 The sign test 165

4.13.2 The randomization test 166

4.13.3 The Wilcoxon Signed Rank test 168

4.14 Description of MINITAB macros (available for download from Appendix VI of the book website) 170

4.15 Chapter highlights 170

4.16 Exercises 171

5 Variability in Several Dimensions and Regression Models 177

5.1 Graphical display and analysis 177

5.1.1 Scatterplots 177

5.1.2 Multiple boxplots 179

5.2 Frequency distributions in several dimensions 181

5.2.1 Bivariate joint frequency distributions 182

5.2.2 Conditional distributions 185

5.3 Correlation and regression analysis 185

5.3.1 Covariances and correlations 185

5.3.2 Fitting simple regression lines to data 187

5.4 Multiple regression 192

5.4.1 Regression on two variables 194

5.5 Partial regression and correlation 198

5.6 Multiple linear regression 200

5.7 Partial F-tests and the sequential SS 204

5.8 Model construction: Step-wise regression 206

5.9 Regression diagnostics 209

5.10 Quantal response analysis: Logistic regression 211

5.11 The analysis of variance: The comparison of means 213

5.11.1 The statistical model 213

5.11.2 The one-way analysis of variance (ANOVA) 214

5.12 Simultaneous confidence intervals: Multiple comparisons 216

5.13 Contingency tables 220

5.13.1 The structure of contingency tables 220

5.13.2 Indices of association for contingency tables 223

5.14 Categorical data analysis 227

5.14.1 Comparison of binomial experiments 227

5.15 Chapter highlights 229

5.16 Exercises 230

PART II ACCEPTANCE SAMPLING 235

6 Sampling for Estimation of Finite Population Quantities 237

6.1 Sampling and the estimation problem 237

6.1.1 Basic definitions 237

6.1.2 Drawing a random sample from a finite population 238

6.1.3 Sample estimates of population quantities and their sampling distribution 239

6.2 Estimation with simple random samples 241

6.2.1 Properties of Xn and S2 n under RSWR 242

6.2.2 Properties of Xn and S2 n under RSWOR 244

6.3 Estimating the mean with stratified RSWOR 248

6.4 Proportional and optimal allocation 249

6.5 Prediction models with known covariates 252

6.6 Chapter highlights 255

6.7 Exercises 256

7 Sampling Plans for Product Inspection 258

7.1 General discussion 258

7.2 Single-stage sampling plans for attributes 259

7.3 Approximate determination of the sampling plan 262

7.4 Double-sampling plans for attributes 264

7.5 Sequential sampling 267

7.6 Acceptance sampling plans for variables 270

7.7 Rectifying inspection of lots 272

7.8 National and international standards 274

7.9 Skip-lot sampling plans for attributes 276

7.9.1 The ISO 2859 skip-lot sampling procedures 276

7.10 The Deming inspection criterion 278

7.11 Published tables for acceptance sampling 279

7.12 Chapter highlights 280

7.13 Exercises 281

PART III STATISTICAL PROCESS CONTROL 283

8 Basic Tools and Principles of Process Control 285

8.1 Basic concepts of statistical process control 285

8.2 Driving a process with control charts 294

8.3 Setting up a control chart: Process capability studies 298

8.4 Process capability indices 300

8.5 Seven tools for process control and process improvement 302

8.6 Statistical analysis of Pareto charts 305

8.7 The Shewhart control charts 308

8.7.1 Control charts for attributes 309

8.7.2 Control charts for variables 311

8.8 Chapter highlights 316

8.9 Exercises 316

9 Advanced Methods of Statistical Process Control 319

9.1 Tests of randomness 319

9.1.1 Testing the number of runs 319

9.1.2 Runs above and below a specified level 321

9.1.3 Runs up and down 323

9.1.4 Testing the length of runs up and down 324

9.2 Modified Shewhart control charts for X 325

9.3 The size and frequency of sampling for Shewhart control charts 328

9.3.1 The economic design for X-charts 328

9.3.2 Increasing the sensitivity of p-charts 328

9.4 Cumulative sum control charts 330

9.4.1 Upper Page’s scheme 330

9.4.2 Some theoretical background 333

9.4.3 Lower and two-sided Page’s scheme 335

9.4.4 Average run length, probability of false alarm and conditional expected delay 339

9.5 Bayesian detection 342

9.6 Process tracking 346

9.6.1 The EWMA procedure 347

9.6.2 The BECM procedure 348

9.6.3 The Kalman filter 350

9.6.4 Hoadley’s QMP 351

9.7 Automatic process control 354

9.8 Chapter highlights 356

9.9 Exercises 357

10 Multivariate Statistical Process Control 361

10.1 Introduction 361

10.2 A review of multivariate data analysis 365

10.3 Multivariate process capability indices 367

10.4 Advanced applications of multivariate control charts 370

10.4.1 Multivariate control charts scenarios 370

10.4.2 Internally derived targets 370

10.4.3 Using an external reference sample 371

10.4.4 Externally assigned targets 372

10.4.5 Measurement units considered as batches 373

10.4.6 Variable decomposition and monitoring indices 373

10.5 Multivariate tolerance specifications 374

10.6 Chapter highlights 376

10.7 Exercises 377

PART IV DESIGN AND ANALYSIS OF EXPERIMENTS 379

11 Classical Design and Analysis of Experiments 381

11.1 Basic steps and guiding principles 381

11.2 Blocking and randomization 385

11.3 Additive and non-additive linear models 385

11.4 The analysis of randomized complete block designs 387

11.4.1 Several blocks, two treatments per block: Paired comparison 387

11.4.2 Several blocks, t treatments per block 391

11.5 Balanced incomplete block designs 394

11.6 Latin square design 397

11.7 Full factorial experiments 402

11.7.1 The structure of factorial experiments 402

11.7.2 The ANOVA for full factorial designs 402

11.7.3 Estimating main effects and interactions 408

11.7.4 2m factorial designs 409

11.7.5 3m factorial designs 417

11.8 Blocking and fractional replications of 2m factorial designs 425

11.9 Exploration of response surfaces 430

11.9.1 Second order designs 431

11.9.2 Some specific second order designs 433

11.9.3 Approaching the region of the optimal yield 438

11.9.4 Canonical representation 440

11.10 Chapter highlights 441

11.11 Exercises 442

12 Quality by Design 446

12.1 Off-line quality control, parameter design and the Taguchi method 447

12.1.1 Product and process optimization using loss functions 447

12.1.2 Major stages in product and process design 448

12.1.3 Design parameters and noise factors 449

12.1.4 Parameter design experiments 450

12.1.5 Performance statistics 452

12.2 The effects of non-linearity 452

12.3 Taguchi’s designs 456

12.4 Quality by design in the pharmaceutical industry 458

12.4.1 Introduction to quality by design 458

12.4.2 A quality by design case study – the full factorial design 459

12.4.3 A quality by design case study – the profiler and desirability function 462

12.4.4 A quality by design case study – the design space 462

12.5 Tolerance designs 462

12.6 More case studies 467

12.6.1 The Quinlan experiment at Flex Products, Inc. 467

12.6.2 Computer response time optimization 469

12.7 Chapter highlights 474

12.8 Exercises 474

13 Computer Experiments 477

13.1 Introduction to computer experiments 477

13.2 Designing computer experiments 481

13.3 Analyzing computer experiments 483

13.4 Stochastic emulators 488

13.5 Integrating physical and computer experiments 491

13.6 Chapter highlights 492

13.7 Exercises 492

PART V RELIABILITY AND SURVIVAL ANALYSIS 495

14 Reliability Analysis 497

14.1 Basic notions 498

14.1.1 Time categories 498

14.1.2 Reliability and related functions 499

14.2 System reliability 500

14.3 Availability of repairable systems 503

14.4 Types of observations on TTF 509

14.5 Graphical analysis of life data 510

14.6 Non-parametric estimation of reliability 513

14.7 Estimation of life characteristics 514

14.7.1 Maximum likelihood estimators for exponential TTF distribution 514

14.7.2 Maximum likelihood estimation of the Weibull parameters 518

14.8 Reliability demonstration 520

14.8.1 Binomial testing 520

14.8.2 Exponential distributions 521

14.9 Accelerated life testing 528

14.9.1 The Arrhenius temperature model 528

14.9.2 Other models 529

14.10 Burn-in procedures 529

14.11 Chapter highlights 530

14.12 Exercises 531

15 Bayesian Reliability Estimation and Prediction 534

15.1 Prior and posterior distributions 534

15.2 Loss functions and Bayes estimators 537

15.2.1 Distribution-free Bayes estimator of reliability 538

15.2.2 Bayes estimator of reliability for exponential life distributions 538

15.3 Bayesian credibility and prediction intervals 539

15.3.1 Distribution-free reliability estimation 539

15.3.2 Exponential reliability estimation 540

15.3.3 Prediction intervals 540

15.4 Credibility intervals for the asymptotic availability of repairable systems: The exponential case 542

15.5 Empirical Bayes method 543

15.6 Chapter highlights 545

15.7 Exercises 545

List of R Packages 547

References and Further Reading 549

Author Index 555

Subject Index 557

Also available on book’s website: www.wiley.com/go/modern_industrial_statistics

Appendix I: An Introduction to R by Stefano Iacus

Appendix II: Basic MINITAB Commands and a Review of Matrix Algebra for Statistics

Appendix III: mistat Manual (mistat.pdf) and List of R Scripts, by Chapter (R_scripts.zip)

Appendix IV: Source Version of mistat Package (mistat_1.0.tar.gz), also available on the

Comprehensive R Archive Network (CRAN) Website.

Appendix V: Data Sets as csv Files

Appendix VI: MINITAB Macros

Appendix VII: JMP Scripts by Ian Cox

Appendix VIII: Solution Manual