Optimal replacement policies for a deteriorating system with imperfect maintenance

Abstract

A system is repaired on failure. With probability p, it is returned to the ‘good as new' state (perfect repair) and with probability 1 – p, it is returned to the functioning state, but is only as good as a system of age equal to its age at failure (imperfect repair). In this article, we develop replacement policies for a deteriorating system with imperfect maintenance. The successive survival times and consecutive repair times form a geometric process which is stochastically non-increasing or non-decreasing respectively. Explicit expressions are obtained for the long-run expected cost under two kinds of replacement policies based on the working age of the system and the number of imperfect repairs before a replacement.