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Bayesian reliability methods permit the formal incorporation of pertinent supplementary information about the parameters of interest in a statistical analysis beyond that contained in the sample data. This additional information is contained in the prior distribution of the parameters. Bayes' theorem is used to combine the prior and sampling distributions to form the posterior distribution of the parameters. Then all the desired inferences are obtained from this joint posterior. In most practical applications, Markov chain Monte Carlo sampling techniques are used to numerically perform the required calculations. A real-world reliability example that illustrates the Bayesian approach is presented. Keywords: Bayes' theorem; prior; posterior; predictive; degree of belief; censoring; credible interval; Markov chain Monte Carlo; Win BUGS ; hierarchical Bayesian
Hill et al. (Fri,) studied this question.