Bayesian Reliability

"Bayesian Reliability presents modern methods and techniques for analyzing reliability data from a Bayesian perspective. The adoption and application of Bayesian methods in virtually all branches of science and engineering have significantly increased over the past few decades. This increase is largely due to advances in simulation-based computational tools for implementing Bayesian methods."--BOOK JACKET.

Harry Martz is retired from the Statistical Sciences Group at Los Alamos National Laboratory and is a Fellow of the American Statistical Association. Shane Reese is an Associate Professor in the Department of Statistics at Brigham Young University. Alyson Wilson is a Technical Staff Member in the Statistical Sciences Group at Los Alamos National Laboratory. Michael Hamada is a Technical Staff Member in the Statistical Sciences Group at Los Alamos National Laboratory and is a Fellow of the American Statistical Association.

Preface	p. VII
Reliability Concepts	p. 1
Defining Reliability	p. 1
Measures of Random Variation	p. 2
Examples of Reliability Data	p. 10
Bernoulli Success/Failure Data	p. 10
Failure Count Data	p. 10
Lifetime/Failure Time Data	p. 11
Degradation Data	p. 12
Censoring	p. 13
Bayesian Reliability Analysis	p. 15
Related Reading	p. 18
Exercises for Chapter 1	p. 19
Bayesian Inference	p. 21
Introductory Concepts	p. 21
Maximum Likelihood Estimation	p. 24
Classical Point and Interval Estimation for a Proportion	p. 26
Fundamentals of Bayesian Inference	p. 27
The Prior Distribution	p. 28
Combining Data with Prior Information	p. 30
Prediction	p. 35
The Marginal Distribution of the Data and Bayes' Factors	p. 36
A Lognormal Example	p. 39
More on Prior Distributions	p. 46
Noninformative and Diffuse Prior Distributions	p. 46
Conjugate Prior Distributions	p. 47
Informative Prior Distributions	p. 47
Related Reading	p. 49
Exercises for Chapter 2	p. 49
Advanced Bayesian Modeling and Computational Methods	p. 51
Introduction to Markov Chain Monte Carlo (MCMC)	p. 51
Metropolis-Hastings Algorithms	p. 52
Gibbs Sampler	p. 60
Output Analysis	p. 64
Hierarchical Models	p. 68
MCMC Estimation of Hierarchical Model Parameters	p. 71
Inference for Launch Vehicle Probabilities	p. 71
Empirical Bayes	p. 73
Goodness of Pit X	p. 76
Related Reading .I	p. 82
Exercises for Chapter 3	p. 82
Component Reliability	p. 85
Introduction	p. 85
Discrete Data Models for Reliability	p. 86
Success/Failure Data	p. 86
Failure Count Data	p. 87
Failure Time Data Models for Reliability	p. 90
Exponential Failure Times	p. 91
Weibull Failure Times	p. 97
Lognormal Failure Times	p. 102
Gamma Failure Times	p. 104
Inverse Gaussian Failure Times	p. 105
Normal Failure Times	p. 106
Censored Data	p. 107
Multiple Units and Hierarchical Modeling	p. 111
Model Selection	p. 116
Bayesian Information Criterion	p. 116
Deviance Information Criterion	p. 117
Akaike Information Criterion	p. 120
Related Reading	p. 120
Exercises for Chapter 4	p. 120
System Reliability	p. 125
System Structure	p. 125
Reliability Block Diagrams	p. 126
Structure Functions	p. 126
Minimal Path and Cut Sets	p. 129
Fault Trees	p. 131
System Analysis	p. 135
Calculating System Reliability	p. 135
Prior Distributions for Systems	p. 138
Fault Trees with Bernoulli Data	p. 141
Fault Trees with Lifetime Data	p. 145
Bayesian Network Models	p. 147
Models for Dependence	p. 155
Related Reading	p. 158
Exercises for Chapter 5	p. 159
Repairable System Reliability	p. 161
Introduction	p. 161
Types of Data	p. 162
Characteristics of System Repairs	p. 162
Renewal Processes	p. 163
Poisson Processes	p. 165
Homogeneous Poisson Processes (HPPs	p. 167
Nonhomogeneous Poisson Processes (NHPPs)	p. 170
Power Law Processes (PLPs)	p. 170
Log-Linear Processes	p. 176
Alternatives to NHPPs	p. 176
Modulated Power Law Processes (MPLPs)	p. 176
Piecewise Exponential Model (PEXP)	p. 179
Goodness of Fit and Model Selection	p. 180
Current Reliability and Other Performance Criteria	p. 181
Current Reliability	p. 181
Other Performance Criteria	p. 182
Multiple-Unit Systems and Hierarchical Modeling	p. 183
Availability	p. 192
Other Data Types for Availability	p. 194
Complex System Availability	p. 196
Related Reading	p. 198
Exercises for Chapter 6	p. 199
Regression Models in Reliability	p. 203
Introduction	p. 203
Covariate Types	p. 204
Covariate Relationships	p. 205
Logistic Regression Models for Binomial Data	p. 205
Poisson Regression Models for Count Data	p. 215
Regression Models for Lifetime Data	p. 221
Model Selection	p. 228
Residual Analysis	p. 229
Accelerated Life Testing	p. 235
Common Accelerating Variables and Relationships	p. 237
Reliability Improvement Experiments	p. 243
Other Regression Situations	p. 258
Related Reading	p. 259
Exercises for Chapter 7	p. 259
Using Degradation Data to Assess Reliability	p. 271
Introduction	p. 271
Comparison with Lifetime Data	p. 278
More Complex Degradation Data Models	p. 279
Reliability Function	p. 281
Diagnostics for Degradation Data Models	p. 283
Incorporating Covariates	p. 287
Accelerated Degradation Testing	p. 288
Improving Reliability Using Designed Experiments	p. 295
Destructive Degradation Data	p. 298
An Alternative Degradation Data Model Using Stochastic Processes	p. 306
Related Reading	p. 309
Exercises for Chapter 8	p. 310
Planning for Reliability Data Collection	p. 319
Introduction	p. 319
Planning Criteria, Optimization, and Implementation	p. 320
Optimization in Planning	p. 321
Implementing the Simulation-Based Framework	p. 323
Planning for Binomial Data	p. 324
Planning for Lifetime Data	p. 327
Planning Accelerated Life Tests	p. 328
Planning for Degradation Data	p. 330
Planning for System Reliability Data	p. 331
Related Reading	p. 339
Exercises for Chapter 9	p. 339
Assurance Testing	p. 343
Introduction	p. 343
Classical Risk Criteria	p. 345
Average Risk Criteria	p. 345
Posterior Risk Criteria	p. 346
Binomial Testing	p. 348
Binomial Posterior Consumer's and Producer's Risks	p. 349
Hybrid Risk Criterion	p. 353
Poisson Testing	p. 354
Weibull Testing	p. 358
Single Weibull Population Testing	p. 360
Combined Weibull Accelerated/Assurance Testing	p. 364
Related Reading	p. 368
Exercises for Chapter 10	p. 369
Acronyms and Abbreviations	p. 375
Special Functions and Probability Distributions	p. 377
Greek Alphabet	p. 377
Special Functions	p. 377
Beta Function	p. 377
Binomial Coefficient	p. 378
Determinant	p. 378
Factorial	p. 378
Gamma Function	p. 378
Incomplete Beta Function	p. 378
Incomplete Beta Function Ratio	p. 378
Indicator Function	p. 379
Logarithm	p. 379
Lower Incomplete Gamma Function	p. 379
Standard Normal Cumulative Density Function	p. 379
Standard Normal Probability Density Function	p. 379
Trace	p. 379
Upper Incomplete Gamma Function	p. 379
Probability Distributions	p. 380
Bernoulli	p. 380
Beta	p. 380
Binomial	p. 382
Bivariate Exponential	p. 382
Chi-squared	p. 383
Dirichlet	p. 383
Exponential	p. 386
Extreme Value	p. 386
Gamma	p. 389
Inverse Chi-squared	p. 389
Inverse Gamma	p. 392
Inverse Gaussian	p. 392
Inverse Wishart	p. 392
Logistic	p. 396
Lognormal	p. 396
Multinomial	p. 399
Multivariate Normal	p. 399
Negative Binomial	p. 399
Negative Log-Gamma	p. 401
Normal	p. 403
Pareto	p. 403
Poisson	p. 403
Poly-Weibull	p. 403
Student's t	p. 406
Uniform	p. 408
Weibull	p. 408
Wishart	p. 411
Reference	p. 413
Author Index	p. 427
Subject Index [431
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