A condition-based maintenance and spare parts ordering policy for a two-component system with dependencies

Efficient integration of Condition-Based Maintenance (CBM) scheduling with spare parts provisioning can significantly reduce operational costs in multi-component systems. This study investigates a joint CBM and spare parts ordering strategy for a system comprising two components that exhibit both stochastic and economic dependencies. Component-level degradation is described using a gamma process with random effects, and the stochastic dependence between components is captured via a copula-based approach. At scheduled inspection intervals, the overall system condition, including component degradation and inventory status, is evaluated to support coordinated maintenance and ordering decisions. The optimization problem is modeled as a Markov decision process (MDP), with the objective of minimizing the expected long-term discounted cost over an infinite time horizon. An exact value iteration algorithm is adopted to derive the optimal policy. A computational example is introduced to validate the efficacy of the developed model, along with a sensitivity analysis performed to evaluate how key parameters affect the optimal solutions.