Analysis of time-to-failure data for a repairable system subject to degradation

Abstract

In this paper, a gradually deteriorating system with imperfect repair is considered. The deterioration is modeled by a stationary stochastic process. The system fails once the deterioration level exceeds a given threshold L. At failure, an imperfect repair is performed and the deterioration level is reduced to a fixed value r, say. The system can be repaired n-1 times and will be replaced after the nth failure. The article aims to estimate the parameters of the proposed deterioration process based on the observed failures. To this end we consider the Wiener and Gamma processes which are the most common used stochastic process models. In Wiener process, an explicit expression for the estimators is obtained. Birnbaum–Saunders approximation is extended to estimate the parameters in Gamma process. An optimal replacement policy is also discussed. Finally, a Monte-Carlo simulation is conducted to investigate the performance of estimators.