Optimal non‐periodic inspection scheme for a multi‐component repairable system using A* search algorithm

This paper proposes an approach for finding an optimal non‐periodic inspection scheme on a finite time horizon for a multi‐component repairable system. The system consists of several components, each of which is subjected to soft failure. Soft failures of each component do not cause the system to stop functioning, but increase the system operating costs and are detected only if inspection is performed. Thus, the system is inspected at the scheduled inspection instances and if any of its components is found to have failed, the failed component is minimally repaired. The system’s expected total cost associated with a given inspection scheme includes inspection costs, repair costs, and the penalty costs that are incurred due to the time delay between the actual occurrence of a soft failure of the components and its detection at an inspection. The objective is to determine the optimal inspection scheme which minimizes system’s expected total cost. In the proposed approach, the system’s expected total cost is first formulated in terms of inspection scheme. Then, A^* search algorithm, with a proposed heuristic cost function for calculating lower bounds, is employed to search through alternative inspection schemes to determine the optimal one. The proposed approach is illustrated through a numerical example.