An explainable dynamic programming framework for interpreting optimal condition-based maintenance policies

초록

This study investigates the optimization of condition-based maintenance (CBM) for k-out-of-N systems operating under stochastic degradation and monitored through periodic inspections. The system model accounts for economic dependencies among components within the k-out-of-N system structure, emphasizing group maintenance policies that balance cost efficiency and reliability. To enhance interpretability, we propose an Explainable Dynamic Programming (XDP) framework that decomposes the optimal average cost and associated bias functions into interpretable cost channels: preventive maintenance, corrective maintenance, setup, and system failure costs. The proposed Decomposed Relative Value Evaluation algorithm operationalizes this approach, ensuring that each channel's contribution is computed in a DP-consistent and additive manner. Beyond standard operations-research post-optimality tools, we benchmark XDP against traditional cost breakdowns and sensitivity analysis. While these conventional approaches provide parameter-level shares and response-to-perturbation insights, XDP yields an exact decomposition of the baseline optimal long-run cost into channel-wise contributions and explains state-dependent action choices through cost-channel drivers. The XDP framework enables rigorous comparison between the optimal CBM policy and a widely used heuristic policy, revealing how and why heuristic rules deviate from optimality. Numerical experiments on an aircraft engine system show that the optimal policy achieves a lower total average cost and a more balanced cost distribution across maintenance channels, and that XDP highlights the dominant cost drivers and their trade-offs. Overall, the proposed XDP methodology bridges the gap between dynamic programming–based CBM optimization and practical interpretability, offering a transparent and analytically grounded approach for decision-making in complex reliability systems. © 2026 Elsevier B.V.

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