A maintenance model for a deteriorating system under random environment using partial product process

Abstract

In this paper, deteriorating system maintenance model under random environment using partial product process is studied. Up to time t, assume that the number of random shocks generated by the random environment is a counting process. Whenever a random shock occurs, the operating time of the system is reduced. The successive reductions in the operating time of the system are statistically independent and identically distributed random variables. Assume that the system’s successive operating times after repairs form a decreasing partial product process. Assume that the system’s consecutive repair times after failures constitute an increasing partial product process provided that the system suffers no random shock. A replacement policy N is applied. Afterwards, for minimizing the mean cost per unit time in long-run, an optimal policy N*is determined analytically. A numerical illustration is provided to strengthen the theoretical results.