Reliability-Based Joint Optimization of Self-Healing Resource and Maintenance Policy for Systems in a Multisource Shock Environment

The integration of self-healing resources into systems presents a promising strategy for mitigating operational failure risks. However, the practical application of such systems is critically constrained by the absence of quantifiable management tools for precise performance evaluation and cost effective decision-making. To bridge this gap, we develop a reliability-based management framework tailored for systems with limited self-healing resources that are subject to both natural degradation and multi-source shocks. Unlike prior work, our study explicitly models the stochastic consumption of healing resources and the distinction between self-repairable and irreparable shocks. A closed-form reliability function is derived, with its validity confirmed through a dedicated simulation algorithm to ensure analytical rigor. Building on this foundation, we formulate a joint optimization model to simultaneously determine the optimal quantity of healing resources and the frequency of imperfect maintenance actions, with the objective of minimizing the average long-run cost rate under a availability constraint. A case study on self-healing lithium-ion batteries demonstrates that reliability improvements exhibit diminishing marginal returns as healing resources increase, offering a key managerial insight for resource planning. Extensive sensitivity analyses further confirm the robustness of the proposed methods and furnish engineering managers with actionable strategies to maintain a cost-availability balance amid cost fluctuations.