Bayesian computation for geometric process in maintenance problems

Geometric process modeling is a useful tool to study repairable deteriorating systems in maintenance problems. This model has been used in a variety of situations such as the determination of the optimal replacement policy and the optimal inspection-repair-replacement policy for standby systems, and the analysis of data with trend. In this article, Bayesian inference for the geometric process with several popular life distributions, for instance, the exponential distribution and the lognormal distribution, are studied. The Gibbs sampler and the Metropolis algorithm are used to compute the Bayes estimators of the parameters in the geometric process. Simulation results are presented to illustrate the use of our procedures.