Dynamic loading and condition-based maintenance policies for multi-state systems with periodic inspection

Many engineering systems suffer gradual deterioration due to both external environmental damage and internal stress caused by working loads. System degradation is directly related to its working load, providing opportunities to control degradation by adjusting the workload. However, most existing research neglects the effect of environmental factors on system failure behavior and maintenance decisions. This paper addresses this research gap by investigating the optimal joint inspection interval, condition-based maintenance, and loading policies for systems operating in a random shock environment. We formulated the problem as a Markov decision process aimed at minimizing the long-run discounted cost, utilizing the value iteration algorithm to find optimal integrated policies while analyzing the corresponding structural properties of the policy. We extended our model by characterizing the shock arrival process with a non-homogeneous Poisson process, conducting comprehensive policy comparison and parameter sensitivity analyses through a numerical example. Our results illustrate that dynamic working load adjustment significantly impacts system degradation and the long-run expected cost. Moreover, the optimal joint policy is highly dependent on the relationship between the working load and system state deterioration. Finally, we derived some managerial implications for the joint development of load regulation and maintenance implementation to support decision-making.