Optimum opportunistic maintenance schedule over variable horizons considering multi-stage degradation and dynamic strategy

•An effective opportunistic model arranges multi-level maintenance for multi-component systems.•A reliability model evaluates complex degradation processes concerning imperfect maintenance.•Embedded dynamic strategy coordinates the maintenance schedules on the system and components.•An adapted renewal theory accommodates the maintenance optimization for variable horizons.•Real case studies are carried out to prove the efficiency and generality of proposed models. A suitable maintenance schedule is crucial for large-scale, complex multi-component systems undertaking a long-term operation to reduce failure risks and improve availability and profitability. Opportunistic maintenance is a popular solution when cost consideration is paramount. However, the extensively adopted single-level preventive maintenance action and single-stage degradation process limit the development and application of opportunistic maintenance. Multi-level preventive maintenance including both perfect and imperfect maintenance actions on multi-stage degradation is considered within an opportunistic model to address this challenge. A reliability evaluation model is first formulated to describe a multi-stage degradation process involving the effect of imperfect maintenance. An opportunistic model is then proposed to arrange reliability proportion thresholds for components in systems. The cost rate is considered as the objective function to accommodate the opportunistic model to variable scheduling horizons. A flexible dynamic strategy is developed within the opportunistic model to coordinate the schedules on the system and components by updating component schedules once a system maintenance action is executed. An improved hybrid genetic algorithm combining differential evolution is adopted to optimize the complex problem. The case studies on a locomotive system provide a better understanding of the proposed models and demonstration of its effectiveness, generality, and robustness.