Estimating the probability of perfect preventive maintenance in the Brown–Proschan imperfect PM model

We propose a method for estimating the probability of perfect PM from successive failure times of a repairable system. The system under study is maintained preventively at periodic times, and it undergoes minimal repair at failure. We consider Brown–Proschan imperfect PM model in which the system is restored to a condition as good as new with probability 𝓅, and is otherwise restored to its condition just prior to failure. We discuss the identifiability problem when the PM modes are not recorded. The expectation-maximization principle is employed to handle the incomplete data problem. We assume that the lifetime distribution belongs to a parametric family with increasing failure rate. For the two parameter Weibull lifetime distribution, we propose a specific algorithm for finding the maximum likelihood estimates of the reliability parameters; the probability of perfect PM (𝓅), as well as the distribution parameters. The estimation method will provide useful results for maintaining real systems.