Predictive Opportunistic Maintenance for k-out-of-n Systems with Heterogeneous Two-Stage Degradation

Predictive opportunistic maintenance can improve maintenance coordination in multi-component systems by jointly exploiting health information and shared maintenance opportunities. However, redundancy and component heterogeneity complicate maintenance timing and component selection. Consequently, this paper proposes a reliability-centered predictive opportunistic maintenance framework for k-out-of-n systems with heterogeneous two-stage degrading components. Firstly, a two-stage Wiener process is used to characterize heterogeneous component degradation, with preventive maintenance restricted to defective-stage components. Secondly, future component reliabilities are aggregated according to the k-out-of-n structure to incorporate system redundancy into maintenance triggering. Thirdly, a hierarchical maintenance mechanism distinguishes necessary reliability-restoration actions from opportunistic replacements: failed components are correctively maintained, a minimum-cost necessary preventive-maintenance set is selected when required, and additional high-risk defective components are opportunistically maintained within the same maintenance event. Finally, the state-assessment interval, system maintenance threshold, and opportunistic-maintenance threshold are jointly optimized under a long-run average cost criterion. Numerical results confirm the economic advantage of the proposed policy over the benchmark strategies.