Multi-level maintenance optimization for systems with variable shock-dependent mission execution rates

For mission-oriented systems exposed to external shocks, mission execution efficiency varies with shock severity, and system degradation is closely dependent on shock impacts. Meanwhile, multi-level maintenance strategies with distinct repair effects are widely adopted in engineering practice to mitigate shock-induced deterioration. However, existing models rarely coordinate the dual impacts of shocks with multi-level maintenance decisions in a unified optimization framework, leading to a non-negligible research gap. To fill this gap, this paper proposes a reliability and maintenance optimization model for mission systems subject to internal degradation and external random shocks. Shocks arrive stochastically and bring dual impacts: accelerating the multi-state degradation process and decreasing the mission execution rate. Upon each shock arrival, an inspection is executed, and four maintenance actions are considered: inaction, low-level preventive maintenance, high-level preventive maintenance, and corrective maintenance. Low-level maintenance partially mitigates shock effects probabilistically at a low cost, high-level maintenance eliminates such impacts entirely at a higher cost, and corrective maintenance perfectly renews the failed system once system failure occurs. The operation-maintenance process is formulated as a semi-Markov decision process (SMDP), and the value iteration algorithm is employed to obtain the optimal maintenance policy. Finally, numerical examples, sensitivity analyses, and policy comparisons are provided to demonstrate the effectiveness and superiority of the proposed model and policy.