Optimal maintenance policy of multiple parts with operating cost dependent on repair level

Abstract

This paper discusses properties of a preventive maintenance policy in multiple part preventive maintenance problems theoretically and numerically. A product such as a machine or an engine consists of multiple important identical parts. Parts are periodically inspected and if a part has a crack then it is either repaired or replaced with new one. If crack of a part is over the critical level then it must be replaced, because it leads to machine’s breakdown and a serious problem. In some kinds of machines, using repaired parts will incur an additional operating cost, because of decrease of its performance. Repair and operation costs are also needed for maintenance. In this paper, an optimal part repair and replacement policy is developed theoretically and numerically. The model is described and formulated as a Markov decision process. For no fixed repair cost it is divided into identical single part maintenance problems, and sufficient conditions under which a threshold type policy is optimal are presented theoretically. Then the cases that optimal policies are not of threshold type are illustrated by numerical experiments.

Keywords

• markov decision process
• maintenance policy
• operating cost
• repair
• replacement
• threshold type policy
• average cost