Non‐periodic inspection and replacement policy of system subject to non‐homogeneous gamma degradation process

Abstract

The non‐homogeneous gamma process can exhibit a convex average trend with a non‐linear shape parameter, providing significant flexibility in fitting an accelerated degradation process. However, few studies have been conducted on the maintenance modeling of systems undergoing a non‐homogeneous gamma degradation process despite its versatility. Meanwhile, most maintenance studies adopt a periodic inspection policy to reveal the degradation level. However, it is reasonable to inspect less frequently when the degradation level of the system is low and to perform inspections more frequently when the degradation level increases. Therefore, we conduct a study on the inspection/replacement policy of systems undergoing a non‐homogeneous gamma degradation process, where three non‐periodic inspection policies are investigated. We formulate the problem as a SMDP framework and present a value iteration algorithm to obtain the optimal action at each decision epoch that minimizes the long‐term average cost. A comprehensive numerical study is provided to illustrate the effectiveness of our proposed model.