Semiparametric Bayesian Decision Models for Optimal Replacement

We present a Bayesian decision theoretic approach for developing replacament strategies. In so doing, we consider a semi-parametric model to describe the failure characteristics of systems by specifying a nonparametric form for cumulative intensity function and by tak-ing into account effect of covariates by a parametric form. Use of a gamma process prior for the cumulative intensity function compli-cates the Bayesian analysis when the updating is based on failure count data. We develop a Bayesian analysis of the model using Markov chain Monte Carlo (MCMC) methods and determine replacement strategies. Adoption of MCMC methods involves a data augmentation algorithm. We show the implementation of our approach using actual data.