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.

Optimal scheduling of inspection times in a production process with a finite planning horizon

“…The rules for decommissioning the system (given in Assumptions 4 and 7) are very similar to the replacement rules in the papers by Zuckerman [44] and Sheu et al [31] as well as the conditions for retiring the system in Berrade et al [19]. Rangan's and Grace's [45] 'Replacement Policy T' rules for replacing a system are somewhat similar to the replacement rules used in this paper.…”