Bayesian analysis for the power law process based on Markov Chain Monte Carlo

Based on Markov Chain Monte Carlo (MCMC) technique, a simple sampling approach for Bayesian analysis of a power law process was presented under various reasonable noninformative priors. The Bayesian approach provides a unified methodology for both time and failure truncated data. Markov Chain Monte Carlo samples for the power law process are easily obtained from the presented approach. Based on these MCMC samples, not only the posterior distributions of some parameter functions of the power law process are given directly, but also the methodologies for single-sample and two-sample prediction are given easily. The results from an engineering numerical example illustrate the feasibility, rationality and validity of the presented approach. The proposed approach has a certain degree of superiority, thus providing an alternative method for the reliability growth analysis of small-sized samples.