A dynamic inspection and replacement policy for systems subject to degradation and periodic shocks

Inspection is widely adopted to improve the maintenance efficiency. Most works predetermine a periodic inspection scheme and focus on optimizing the replacement threshold. However, it is reasonable to inspect less frequently when the degradation level of the system is low and to perform inspections more frequently as the degradation level increases. This work investigates a dynamic inspection and replacement policy for systems subject to regular degradation and periodic shocks. The regular degradation of the system is modeled as a Wiener process. Meanwhile, a periodic arrived shock will incur a random amount increment to the degradation, which is assumed to satisfy a gamma distribution. We first consider a single-component system and formulate a Markov decision process to derive the optimal policy that minimizes the long-run discounted maintenance cost. The structural properties of the optimal policy are analyzed, and a value iteration algorithm is presented to obtain the optimal policy. We then extend the model to an N-component system and develop an approximate dynamic programming framework to generate high-quality solutions. A numerical study and a comprehensive sensitivity analysis are provided to illustrate our proposed dynamic inspection and replacement policy.