Bayesian Methods in Reliability

1. Introduction to Bayesian Methods in Reliability.- 1. Why Bayesian Methods?.- 1.1 Sparse data.- 1.2 Decision problems.- 2. Bayes' Theorem.- 3. Examples from a Safety Study on Gas transmission Pipelines.- 3.1 Estimating the probability of the development of a big hole.- 3.2 Estimating the leak rate of a gas transmission pipeline.- 4. Conclusions.- References.- 2. An Overview of the Bayesian Approach.- 1. Background.- 2. Probability Concepts.- 3. Notation.- 4. Reliability Concepts and Models.- 5. Forms of Data.- 6. Statistical Problems.- 7. Review of Non-Bayesian Statistical Methods.- 8. Desiderata for Decision-Oriented Statistical Methodology.- 9. Decision-Making.- 10. Degrees of Belief as Probabilities.- 11. Bayesian Statistical Philosophy.- 12. A Simple Illustration of Bayesian Learning.- 13. Bayesian Approaches to Typical Statistical Questions.- 14. Assessment of Prior Densities.- 15. Bayesian Inference for some Univariate Probability Models.- 16. Approximate Analysis under Great Prior Uncertainty.- 17. Problems Involving many Parameters: Empirical Bayes.- 18. Numerical Methods for Practical Bayesian Statistics.- References.- 3. Reliability Modelling and Estimation.- 1. Non-Repairable Systems.- 1.1 Introduction.- 1.2 Describing reliability.- 1.3 Failure time distributions.- 2. Estimation.- 2.1 Introduction.- 2.2 Classical methods.- 2.3 Bayesian methods.- 3. Reliability estimation.- 3.1 Introduction.- 3.2 Binomial sampling.- 3.3 Pascal sampling.- 3.4 Poisson sampling.- 3.5 Hazard rate estimation.- References.- 4. Repairable Systems and Growth Models.- 1. Introduction.- 2. Good as New: the Renewal Process.- 3. Estimation.- 4. The Poisson Process.- 5. Bad as old: the Non-Homogeneous Poisson Process.- 6. Classical Estimation.- 7. Exploratory Analysis.- 8. The Duane Model.- 9. Bayesian Analysis.- References.- 5. The Use of Expert Judgement in Risk Assessment.- 1. Introduction.- 2. Independence Preservation.- 3. The Quality of Experts' Judgement.- 4. Calibration Sets and Seed Variables.- 5. A Classical Model.- 6. Bayesian Models.- 7. Some Experimental Results.- References.- 6. Forecasting Software Reliability.- 1. Introduction.- 2. The Software Reliability Growth Problem.- 3. Some Software Reliability Growth Models.- 3.1 Jelinski and Moranda (JM).- 3.2 Bayesian Jelinski-Moranda (BJM).- 3.3 Littlewood (L).- 3.4 Littlewood and Verrall (LV).- 3.5 Keiller and Littlewood (KL).- 3.6 Weibull order statistics (W).- 3.7 Duane (D).- 3.8 Goel-Okumoto (GO).- 3.9 Littlewood NHPP (LNHPP).- 4. Examples of Use.- 5. Analysis of Predictive Quality.- 5.1 The u-plot.- 5.2 The y-plot, and scatter plot of u's.- 5.3 Measures of 'noise'.- 5.3.1 Braun statistic.- 5.3.2 Median variability.- 5.3.3 Rate variability.- 5.4 Prequential likelihood.- 6. Examples of Predictive Analysis.- 7. Adapting and Combining Predictions; Future Directions.- 8 Summary and Conclusions.- Acknowledgements.- References.- References.- Author index.