Optimal number of minimal repairs before replacement based on a cumulative repair-cost limit policy

In this paper, we consider a replacement model with minimal repair based on a cumulative repair-cost limit policy, where the information of all repair costs is used to decide whether the system is repaired or replaced. As a failure occurs, the system experiences one of the two types of failures: a type-I failure (repairable) with probability q, rectified by a minimal repair; or a type-II failure (non-repairable) with probability p (=1 q) that calls for a replacement. Under such a policy, the system is replaced anticipatively at the nth type-I failure, or at the kth type-I failure (k < n) at which the accumulated repair cost exceeds the pre-determined threshold, or any type-II failure, whichever occurs first. The object of this paper is to find the optimal number of minimal repairs before replacement that minimizes the longrun expected cost per unit time of this polish. Our model is a generalization of several classical models in maintenance literature, and a numerical example is presented for illustration.