An optimal bi-level inspection and maintenance policy for a multi-component system: An enhanced successively approximated point-based value-iteration algorithm

Modern engineered systems are composed of multiple components. These components deteriorate over time, resulting in a decrease in the system’s overall performance. Inspecting the health states of all components provides comprehensive information for making optimal maintenance decisions, which, however, may incur high costs and result in prolonged system downtime. This necessitates combining system-level and component-level inspections into an optimal inspection and maintenance (IM) policy design to maximize overall profit. To date, this topic remains challenging and underexplored, which is investigated in this paper. First, we propose a bi-level IM policy where, at each decision epoch, the operator sequentially determines (i) whether to conduct a component-level inspection and (ii) which components to maintain, based on the system-level performance. Next, we consider that components have different deterioration processes and are subject to non-negligible IM duration, which renders the problem both partially observable and non-equidistant in decision timing. We adopt a Partially Observable Semi-Markov Decision Process (POSMDP) to model the decision-making process and compute the POSMDP quantities. To address the curse of dimensionality posed by the exponential growth of the belief space with respect to the number of components and their discrete states, we develop an enhanced Successively Approximated Point-Based Value-Iteration Algorithm (SARSOP). Two improvements make the algorithm scalable and efficient. First, we introduce macro-actions that enable the operator to defer intervention until system-level performance falls below a predetermined threshold, thereby reducing the depth of the SARSOP search tree by aggregating multiple primitive actions in the original POSMDP. Second, we propose a reward-shaping scheme that encourages SARSOP to prioritize exploration of these macro-actions. A comprehensive case study of photovoltaic (PV) panels demonstrates both the superiorities of the proposed bilevel IM policy and the developed solution algorithm.