(The)stress-strength model and its generalizations : theory and applications

목차 (Table of Contents)

• CONTENTS
• Preface = ⅶ
• Chapter 1 The Stress-Strength Models. Mathematics, History, and Applications = 1
• 1.1 What are the Stress-Strength Models? = 1
• 1.2 Motivation and Mathematical Formulations = 3
• 1.2.1 Motivations = 3
• 1.2.2 Mathematical Formulations = 5
• 1.3 Stress-Strength Models : History and Geography = 6
• 1.3.1 History = 6
• 1.3.2 Geography = 8
• 1.4 Applications = 9
• Chapter 2 The Theory and Some Useful Approaches = 11
• 2.1 The Maximum Likelihood Estimators = 11
• 2.1.1 The Theory = 11
• 2.1.2 Construction of the MLE = 12
• 2.1.3 One-parameter Exponential Distribution = 14
• 2.1.4 Multivariate Case = 15
• 2.2 Unbiased Estimation = 16
• 2.2.1 The Theory = 16
• 2.2.2 Construction of UMVUEs = 18
• 2.2.3 One-parameter Exponential Distribution = 20
• 2.2.4 A Multivariate Case = 23
• 2.3 Bayes and Empirical Bayes Estimation of R = 23
• 2.3.1 The Theory = 23
• 2.3.2 The Choice of a Prior = 25
• 2.3.3 One-parameter Exponential Distribution = 27
• 2.3.4 Bayes Predictive and Empirical Bayes Estimation = 29
• 2.4 Interval Estimation = 30
• 2.4.1 The Theory = 30
• 2.4.2 Exact Methods of Interval Estimation = 31
• 2.4.3 Asymptotic Methods of Interval Estimation = 31
• 2.4.4 Bayesian Credible Sets = 33
• 2.4.5 Hypothesis Testing : Theory and Methods = 33
• 2.4.6 One-parameter Exponential Distribution = 36
• 2.5 Transformation Methods = 39
• 2.5.1 The Theory = 39
• 2.5.2 Examples of Transformations = 42
• 2.5.3 The Rayleigh Distribution = 42
• 2.6 Exercises = 46
• Chapter 3 Parametric Point Estimation = 47
• 3.1 The Maximum Likelihood Estimation(Univariate Case) = 47
• 3.1.1 The Normal Distribution = 47
• 3.1.2 The Two-parameter Exponential Distribution = 48
• 3.1.3 The Gamma Distribution = 49
• 3.1.4 The Truncation Parameter Families = 51
• 3.1.5 The Pareto Distribution = 52
• 3.1.6 The Weibull Distribution = 53
• 3.1.7 Burr Type Ⅹ and Type XII Distributions = 54
• 3.1.8 The Generalized Gamma Distribution = 55
• 3.1.9 Other Distributions = 58
• 3.2 Unbiased Estimation(Univariate Case) = 59
• 3.2.1 The Normal Distribution = 59
• 3.2.2 The Two-parameter Exponential Distribution = 61
• 3.2.3 The Gamma Distribution = 63
• 3.2.4 The Truncation Parameter Families = 64
• 3.2.5 The Generalized Gamma Distribution = 69
• 3.2.6 Other Distributions = 70
• 3.3 Bayes and Empirical Bayes Estimation(Univariate Case) = 71
• 3.3.1 The Normal Distribution = 72
• 3.3.2 The One-Parameter Exponential Distribution = 74
• 3.3.3 The Weibull Distribution = 75
• 3.3.4 The Burr-Type Ⅹ Distribution = 77
• 3.4 Elliptical Distributions = 78
• 3.4.1 Maximum Likelihood Estimation = 79
• 3.4.2 Bayes Estimation = 82
• 3.4.3 The Pearson Type Ⅱ Distribution = 84
• 3.4.4 The Multivariate T and Cauchy Distributions = 86
• 3.5 The Multivariate Normal Distribution = 88
• 3.5.1 Maximum Likelihood Estimation = 88
• 3.5.2 Unbiased Estimation = 90
• 3.5.3 Bayes Estimation = 92
• 3.6 Bivariate Exponential Distributions(BVED) = 95
• 3.6.1 Various Types of Exponential Distributions = 96
• 3.6.2 Stress-Strength Estimators for the Marshall-Olkin BVED = 97
• 3.6.3 Stress-Strength Probabilities and Their Estimators for Other BVEDs = 100
• 3.7 Discrete Distributions = 101
• 3.7.1 Multivariate Discrete Distributions = 101
• 3.7.2 Univariate Discrete Distributions = 103
• 3.8 Exercises = 105
• Chapter 4 Parametric Statistical Inference = 109
• 4.1 Confidence Intervals Based on Exact Distributions = 109
• 4.1.1 The Normal Distribution : Dependent Variables = 110
• 4.1.2 The Normal Distribution : Independent Variables = 112
• 4.1.3 The Gamma Distribution = 114
• 4.1.4 The Generalized Gamma Distribution = 115
• 4.1.5 The Burr Type X Distribution = 117
• 4.2 Asymptotic Confidence Intervals = 118
• 4.2.1 The Normal Distribution = 118
• 4.2.2 The Left-Truncated Exponential Distribution = 119
• 4.2.3 The Two-parameter Exponential Distribution = 119
• 4.3 Bayesian Credible Sets = 123
• 4.3.1 The Normal Distribution : Independent Variables = 123
• 4.3.2 The Weibull Distribution = 125
• 4.4 Hypothesis Testing = 126
• 4.4.1 Tests Based on Exact Confidence Intervals = 127
• 4.4.2 Tests Based on Generalized p-values = 129
• 4.4.3 Bayesian Tests = 131
• 4.5 Bootstrap = 132
• 4.5.1 The Concept of the Bootstrap = 132
• 4.5.2 Bootstrap-Based Asymptotic Confidence Intervals = 133
• 4.5.3 The Percentile Method = 135
• 4.6 Exercises = 137
• Chapter 5 Nonparametric Models = 139
• 5.1 Point Estimation of R ＝ P(X〈 Y) = 140
• 5.1.1 Initial Results. The WMW Statistic = 140
• 5.1.2 Nonparametric UMVUE of R = 141
• 5.2 Estimation of the Variance of $$\hat R$$ = 144
• 5.2.1 Estimators Based on Rank Statistics = 144
• 5.2.2 Estimators Based on Empirical Distribution Functions = 147
• 5.2.3 Jackknife Estimators = 148
• 5.3 Interval Estimation of R = 149
• 5.3.1 Confidence Intervals Based on Classical Inequalities = 150
• 5.3.2 Confidence Intervals Based on the Kolmogorov-Smirnov Statistics = 151
• 5.3.3 Confidence Intervals Based on the Asymptotic Normality = 154
• 5.3.4 Confidence Intervals Based on Pivotal Quantities = 155
• 5.3.5 Confidence Intervals Constructed by Bootstrap Method = 157
• 5.4 Nonparametric Bayes and Empirical Bayes Estimation = 158
• 5.4.1 Dirichlet Process Preliminaries = 158
• 5.4.2 Nonparametric Bayes Estimation of R = 160
• 5.4.3 Nonparametric Empirical Bayes Estimation of R = 161
• 5.5 Probability Design Approach to Estimation of R = 164
• 5.6 Exercises = 167
• Chapter 6 Some Selected Special Cases = 169
• 6.1 Stress-Strength Models for System Reliability = 170
• 6.1.1 Various Models for System Reliability = 170
• 6.1.2 Estimation of System Reliability Based on Numerical Data = 172
• 6.1.3 Estimation of System Reliability Based on Count Data = 174
• 6.2 Estimation of P(X₁〈 X₂〈 … 〈 $$X_k$$) = 177
• 6.2.1 General Case = 177
• 6.2.2 Estimation of P(X 〈 Y 〈 Z) = 180
• 6.3 Linear Models Formulations for Stress-Strength Systems = 182
• 6.3.1 Stress-Strength Models with Explanatory Variables = 182
• 6.3.2 ANOVA Formulations of Stress-Strength Models = 187
• 6.4 Stress-Strength Models with Grouped and Categorical Data = 189
• 6.4.1 Point Estimation = 189
• 6.4.2 Confidence Intervals = 192
• 6.5 Stochastic Processes Formulations of Stress-Strength Systems = 195
• 6.5.1 General Stochastic Systems = 195
• 6.5.2 Markov Models for System Reliability = 197
• 6.5.3 Stochastic Time Series Models = 197
• 6.6 Exercises = 199
• Chapter 7 Applications and Examples = 201
• 7.1 Applicability of the Stress-Strength Model = 201
• 7.2 Engineering and Military Applications of the Stress-Strength Model = 205
• 7.2.1 The Rocket Motor Case Example = 205
• 7.2.2 Comparison of Two Treatments in Engineering Setting = 207
• 7.2.3 Military Applications = 211
• 7.3 Applications in Medicine and Psychology = 214
• 7.3.1 Applications Based on Numerical Data = 214
• 7.3.2 Applications Based on Categorized Data = 216
• 7.4 ROC Curves Analysis = 223
• 7.4.1 ROC Curves and Their Relation to P(X〈 Y) = 223
• 7.4.2 Applications of ROC Curves = 226
• 7.5 Some Other Applications = 227
• 7.5.1 Estimation of Strength Characteristics from the Distribution of Stress = 227
• 7.5.2 A Relation Between the Stress-Strength Model and the Process Capability Index = 230
• Bibliography = 233
• Index = 251