Component-wise Markov decision process for solving condition-based maintenance of large multi-component systems with economic dependence

Condition-Based Maintenance (CBM) of multi-component systems is a prevalent engineering problem due to its effectiveness in reducing the operational and maintenance costs of a system. However, developing the exact optimal maintenance decisions for a large multi-component system is computationally challenging, even not feasible, due to the exponential growth in system state and action space size with the number of components in the system. To address the scalability issue in CBM of large multi-component systems, we propose a Component-Wise Markov Decision Process(CW-MDP) and an Adjusted Component-Wise Markov Decision Process (ACW-MDP) to obtain an approximation of the optimal system-level CBM decision policy for large systems with heterogeneous components. We propose using an extended single-component action space to model the impact of system-level setup cost on a component-level solution. The theoretical gap between the proposed approach and system-level optima is also derived. Additionally, theoretical convergence and the relationship between ACW-MDP and CW-MDP are derived. The study further shows extensive numerical studies to demonstrate the effectiveness of component-wise solutions for solving large multi-component systems.