Bayesian approach to reliability growth based on the Gibbs sampling

For reliability growth modeled by the power law process, a Bayesian inference approach is proposed on the basis of Gibbs sampling. Using samples generated by Gibbs sampling, the proposed approach can conveniently calculate numerical characteristics (NC) of parameters in reliability growth model, and the NC of the function of the parameters with respect to posterior distribution can be easily obtained as well. In traditional Bayesian inference, NC of the parameters and NC of the functions of the parameters are obtained by complicated integral which is difficult to compute in high dimensionality. The proposed approach is applicable not only to single/multiple system, but also to the problem with small size of samples, and its advantages are demonstrated by the given illustrations with accurate solutions.