Periodic inspection optimization model for a two‐component repairable system with failure interaction

This paper proposes a model to find the optimal periodic inspection interval on a finite time horizon for a two‐component repairable system with failure interaction. Failure of the first component is soft, namely, it does not cause the system stop. The second component’s failure is hard, i.e. as soon as it occurs, the system stops operating. Failure of the first component has no effect on the second component’s behavior; however, any failure of the second component increases the first component’s failure rate. Failure of the first component increases the system operating costs and is detected only if inspection is performed. Thus, the first component is periodically inspected and if a failure is observed during the inspection, it is repaired. When the second component fails it is also repaired. Repairs of components restore them to as good as new. The objective is to find the optimal inspection interval for the first component such that, on a finite time horizon, the expected total cost is minimized. The proposed modeling approach can be used in electrical distribution systems, where capacitor bank (first component) and high power transformer (second component) are coupled in a distribution substation. A simplified numerical example is given.