Contents. Preface to Second Edition Preface to First Edition Abbreviations PART I PRINCIPLES OF STATISTICAL THINKING AND ANALYSIS 1

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1 Contents Preface to Second Edition Preface to First Edition Abbreviations xv xvii xix PART I PRINCIPLES OF STATISTICAL THINKING AND ANALYSIS 1 1 The Role of Statistical Methods in Modern Industry and Services The different functional areas in industry and services The quality-productivity dilemma Fire-fighting Inspection of products Process control Quality by design Information quality and practical statistical efficiency Chapter highlights Exercises 12 2 Analyzing Variability: Descriptive Statistics Random phenomena and the structure of observations Accuracy and precision of measurements The population and the sample Descriptive analysis of sample values Frequency distributions of discrete random variables Frequency distributions of continuous random variables Statistics of the ordered sample Statistics of location and dispersion Prediction intervals Additional techniques of exploratory data analysis Box and whiskers plot Quantile plots Stem-and-leaf diagrams Robust statistics for location and dispersion Chapter highlights Exercises 38 3 Probability Models and Distribution Functions Basic probability Events and sample spaces: Formal presentation of random measurements Basic rules of operations with events: Unions, intersections Probabilities of events 44

2 W/7 Contents Probability functions for random sampling Conditional probabilities and independence of events Bayes formula and its application Random variables and their distributions Discrete and continuous distributions Expected values and moments of distributions The standard deviation, quantiles, measures of skewness and kurtosis Moment generating functions Families of discrete distribution The binomial distribution The hypergeometric distribution The Poisson distribution The geometric and negative binomial distributions Continuous distributions The uniform distribution on the interval (a, b), a < b The normal and log-normal distributions The exponential distribution The gamma and Weibull distributions The Beta distributions Joint, marginal and conditional distributions Joint and marginal distributions Covariance and correlation Conditional distributions Some multivariate distributions The multinomial distribution The multi-hypergeometric distribution The bivariate normal distribution Distribution of order statistics Linear combinations of random variables Large sample approximations The law of large numbers The Central Limit Theorem Some normal approximations Additional distributions of statistics of normal samples Distribution of the sample variance The "Student" i-statistic Distribution of the variance ratio Chapter highlights Exercises Statistical Inference and Bootstrapping Sampling characteristics of estimators Some methods of point estimation Moment equation estimators The method of least squares Maximum likelihood estimators Comparison of sample estimates Basic concepts Some common one-sample tests of hypotheses Confidence intervals 128

3 Contents ix Confidence intervals for //; a known Confidence intervals for / ; a unknown Confidence intervals for a Confidence intervals for p 4.5 Tolerance intervals Tolerance intervals for the normal distributions 4.6 Testing for normality with probability plots 4.7 Tests of goodness of fit The chi-square test (large samples) The Kolmogorov-Smirnov test 4.8 Bayesian decision procedures Prior and posterior distributions Bayesian testing and estimation Credibility intervals for real parameters 4.9 Random sampling from reference distributions 4.10 Bootstrap sampling The bootstrap method Examining the bootstrap method Harnessing the bootstrap method 4.11 Bootstrap testing of hypotheses Bootstrap testing and confidence intervals for the mean Studentized test for the mean Studentized test for the difference of two means Bootstrap tests and confidence intervals for the variance Comparing statistics of several samples 4.12 Bootstrap tolerance intervals Bootstrap tolerance intervals for Bernoulli samples Tolerance interval for continuous variables Distribution-free tolerance intervals 4.13 Non-parametric tests The sign test The randomization test The Wilcoxon Signed Rank test 4.14 Description of MINITAB macros (available for download from Appendix VI of the book website) 4.15 Chapter highlights 4.16 Exercises 5 Variability in Several Dimensions and Regression Models 5.1 Graphical display and analysis Scatterplots Multiple boxplots 5.2 Frequency distributions in several dimensions Bivariate joint frequency distributions Conditional distributions 5.3 Correlation and regression analysis Covariances and correlations Fitting simple regression lines to data 5.4 Multiple regression Regression on two variables 5.5 Partial regression and correlation

4 X Contents 5.6 Multiple linear regression Partial /-'-tests and the sequential SS Model construction: Step-wise regression Regression diagnostics Quantal response analysis: Logistic regression The analysis of variance: The comparison of means The statistical model The one-way analysis of variance (ANOVA) Simultaneous confidence intervals: Multiple comparisons Contingency tables The structure of contingency tables Indices of association for contingency tables Categorical data analysis Comparison of binomial experiments Chapter highlights Exercises 230 PART II ACCEPTANCE SAMPLING Sampling for Estimation of Finite Population Quantities Sampling and the estimation problem Basic definitions Drawing a random sample from a finite population Sample estimates of population quantities and their sampling distribution Estimation with simple random samples Properties of X n and S 1 - under RSWR Properties of X n and Sj under RSWOR Estimating the mean with stratified RSWOR Proportional and optimal allocation Prediction models with known covariates Chapter highlights Exercises Sampling Plans for Product Inspection General discussion Single-stage sampling plans for attributes Approximate determination of the sampling plan Double-sampling plans for attributes Sequential sampling Acceptance sampling plans for variables Rectifying inspection of lots National and international standards Skip-lot sampling plans for attributes The ISO 2859 skip-lot sampling procedures The Deming inspection criterion Published tables for acceptance sampling Chapter highlights Exercises 281

5 Contents xi PART III STATISTICAL PROCESS CONTROL Basic Tools and Principles of Process Control Basic concepts of statistical process control Driving a process with control charts Setting up a control chart: Process capability studies Process capability indices Seven tools for process control and process improvement Statistical analysis of Pareto charts The Shewhart control charts Control charts for attributes Control charts for variables Chapter highlights Exercises Advanced Methods of Statistical Process Control Tests of randomness Testing the number of runs Runs above and below a specified level Runs up and down Testing the length of runs up and down Modified Shewhart control charts for X The size and frequency of sampling for Shewhart control charts The economic design for X-charts Increasing the sensitivity of p-charts Cumulative sum control charts Upper Page's scheme Some theoretical background Lower and two-sided Page's scheme Average run length, probability of false alarm and conditional expected delay Bayesian detection Process tracking The EWMA procedure The BECM procedure The Kalman filter Hoadley's QMP Automatic process control Chapter highlights Exercises Multivariate Statistical Process Control Introduction A review of multivariate data analysis Multivariate process capability indices Advanced applications of multivariate control charts Multivariate control charts scenarios Internally derived targets Using an external reference sample Externally assigned targets 372

6 xi i Contents Measurement units considered as batches Variable decomposition and monitoring indices Multivariate tolerance specifications Chapter highlights Exercises 377 PART IV DESIGN AND ANALYSIS OF EXPERIMENTS Classical Design and Analysis of Experiments Basic steps and guiding principles Blocking and randomization Additive and non-additive linear models The analysis of randomized complete block designs Several blocks, two treatments per block: Paired comparison Several blocks, t treatments per block Balanced incomplete block designs Latin square design Full factorial experiments The structure of factorial experiments The ANOVA for full factorial designs Estimating main effects and interactions '" factorial designs "'factorial designs Blocking and fractional replications of 2 m factorial designs Exploration of response surfaces Second order designs Some specific second order designs Approaching the region of the optimal yield Canonical representation Chapter highlights Exercises Quality by Design Off-line quality control, parameter design and the Taguchi method Product and process optimization using loss functions Major stages in product and process design Design parameters and noise factors Parameter design experiments Performance statistics The effects of non-linearity Taguchi's designs Quality by design in the pharmaceutical industry Introduction to quality by design A quality by design case study - the full factorial design A quality by design case study - the profiler and desirability function A quality by design case study - the design space Tolerance designs More case studies The Quinlan experiment at Flex Products, Inc Computer response time optimization 469

7 Contents xiii 12.7 Chapter highlights Exercises Computer Experiments Introduction to computer experiments Designing computer experiments Analyzing computer experiments Stochastic emulators Integrating physical and computer experiments Chapter highlights Exercises 492 PART V RELIABILITY AND SURVIVAL ANALYSIS Reliability Analysis Basic notions Time categories Reliability and related functions System reliability Availability of repairable systems Types of observations on TTF Graphical analysis of life data Non-parametric estimation of reliability Estimation of life characteristics Maximum likelihood estimators for exponential TTF distribution Maximum likelihood estimation of the Weibull parameters Reliability demonstration Binomial testing Exponential distributions Accelerated life testing The Arrhenius temperature model Other models Burn-in procedures Chapter highlights Exercises Bayesian Reliability Estimation and Prediction Prior and posterior distributions Loss functions and Bayes estimators Distribution-free Bayes estimator of reliability Bayes estimator of reliability for exponential life distributions Bayesian credibility and prediction intervals Distribution-free reliability estimation Exponential reliability estimation Prediction intervals Credibility intervals for the asymptotic availability of repairable systems: The exponential case Empirical Bayes method Chapter highlights Exercises 545

8 xiv Contents List of R Packages References and Further Reading Author Index Subject Index Also available on book's website: 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_l.o.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