Imperfect inspection optimization for a two-component system subject to hidden and two-stage revealed failures over a finite time horizon

In this paper, a two-component system is considered. The first component's failure is hidden; i.e., it does not make the system stop. The second component has three possible states, healthy, defective, and failed. The failed state is revealed; i.e., it causes the system stop. Thus, each revealed failure causes a shock on the first component and increases its failure rate. The system is periodically inspected to identify defects and hidden failures. The first component is also opportunistically inspected whenever the second component reveals its failure. Inspections may be imperfect. The goal is to find the optimal periodic inspection interval which minimizes total cost on a finite time horizon. The inspection model is first formulated mathematically. Then, due to the complexity of numerical computing, a simulation algorithm is developed to calculate the expected total cost. The proposed approach is demonstrated through a numerical example for an electrical distribution system.