Bayesian imperfect repair model

An imperfect repair model proposed by Brown and Proschan(J. Appl. Prob. 20. 1983) is extended in this paper. We propose a new Bayesian imperfect repair model where the probability of perfect repair, P, is considered to be a random variable. Assuming that P has a prior distribution Π(p), we obtain the distribution of waiting times between two successive perfect repairs and its corresponding failure rate. The posterior distribution of P and its estimators are discussed. We also study some preservation properties for certain nonparametric classes of life distributions and the monotonicity properties for several parameters. Examples are presented to illustrate our results.