A Finite‐Horizon Condition‐Based Maintenance and Spare Parts Ordering Policy for a Two‐Unit System Subject to Stochastic Dependence

ABSTRACT Efficient joint coordination of condition‐based maintenance (CBM) and spare parts control for critical components can reduce overall operational costs and mitigate failure risks. This paper investigates a joint CBM and spare parts ordering policy for a system with two heterogeneous and dependent components, whose degradation follows a bivariate inverse Gaussian process. The system is periodically inspected, with preventive or corrective replacements and ordering decisions made based on observed system degradation and inventory states at each inspection. We formulate this joint optimization problem as a Markov decision process (MDP) model to minimize the expected total discounted cost evaluated over a finite planning horizon. A backward dynamic programming algorithm is applied to derive the optimal joint maintenance and ordering policy, and its structural properties are analyzed. A numerical study is conducted to validate the structural insights and the effectiveness of the proposed optimization model. Sensitivity analyses are performed to examine the effects of the stochastic dependence coefficient, maintenance setup cost, discount rate, system downtime cost, and holding cost on the optimal policies. Results show that stronger positive stochastic dependence between components prompts maintenance clustering and asymmetric spare parts ordering, higher system downtime cost and higher unit holding cost per unit time encourages more proactive replacements and ordering to prevent unexpected failures. In contrast, a higher discount rate results in deferred maintenance and ordering actions. Moreover, under spare parts scarcity, a higher maintenance setup cost leads to increased tolerance for failure risks.