optimal number of imperfect repairs for deteriorating systems

A periodic maintenance policy through either an imperfect repair or replacement is proposed for a repairable system. it is assumed that the system is subject to an inverse gaussian degradation process. the effect of imperfect repair is modelled through both arithmetic reduction of degradation and arithmetic reduction of age approaches. the degradation level of the system is measured after each imperfect repair in periodic time intervals. the system is replaced if its deterioration level exceeds a pre-determined technical threshold or at the nth inspection time, whichever occurs first. the main goal of the paper is to find the optimal value of n based on expected cost rate function. some theoretical results are derived and then the optimal policy is obtained numerically. the effect of imperfect repair, the inspection time interval, the value of technical degradation threshold, and the costs of interest are all studied on the optimal policy.