ESTIMATING SYSTEM RELIABILITY WITH FULLY MASKED DATA UNDER BROWN-PROSCHAN IMPERFECT REPAIR MODEL

This article presents a statistical procedure for estimating the lifet ime distribution of a repairable system based on consecutive inter-fai lure times of the system. The system under consideration is subject to the Brown-Proschan imperfect repair model. The model postulates that at Failure the system is repaired to a condition as good as new with p robability p, and is otherwise repaired to its condition just prior to failure. The estimation procedure is developed in a parametric framew ork for incomplete set of data where the repair modes are not recorded . The expectation-maximization principle is employed to handle the inc omplete data problem. Under the assumption that the lifetime distribut ion belongs to the two-parameter Weibull family, we develop a specific algorithm for finding the maximum likelihood estimates of the reliabi lity parameters; the probability of perfect repair (p), as well as the Weibull shape and scale parameters (alpha,beta). The proposed algorit hm is applicable to other parametric lifetime distributions with aging property and explicit form of the survival function, by just modifyin g the maximization step. We derive some lemmas which are essential to the estimation procedure. The lemmas characterize the dependency among consecutive lifetimes. A Monte Carlo study is also performed to show the consistency and good properties of the estimates. Since useful res earch is available regarding optimal maintenance policies based on the Brown-Proschan model, the estimation results will provide realistic s olutions for maintaining real systems. (C) 1998 Elsevier Science Limit ed.