Optimal replacement policies with minimal repair and random cost

Abstract

When a system fails usually two actions take place; either replacement of system with a brand new one or repairing it if possible. In this study, it is assumed that system under consideration is repairable and is minimally repaired at failures with a random repair cost. Two replacement models are provided under this set-up. First model assumes that the system is replaced when the total cost of minimal repairs exceeds a total cost limit. Second model incorporates the number of failures into replacement decision. Here the concept of critical failure is introduced and used by means of two sub-models. In the first sub-model it is assumed that the system is replaced at the kth critical failure or at cige T. And the second sub-model assumes that the system is replaced at the first critical failure occurs after age T. The first model is just constructed but cannot be solved due to complexity of the resultant function. But, solution methods of the sub-models of second model are provided.