Optimal Inspection Interval for a Two-Component System with Failure Dependency

In this paper, optimization of periodic inspection interval for a two-component system with failure dependency is presented. Failure of the first component is soft, namely, it does not cause the system stop, but it increases the system operating costs. The second component’s failure is hard, i.e. as soon as it occurs, the system stops operating. Any failure of the second component increases the first component’s failure rate. Failure of the first component is only detected if inspection is performed. Thus, the first component is periodically inspected and if found failed, it is perfectly repaired and it is restored to as good as new. Failure of the second component is detected as soon as it occurs. Since this failure causes the system stop, it is immediately replaced. It is assumed that the time for replacement or repaired is negligible. We model the first component’s failure as a non-homogeneous Poisson process (NHPP) with increasing failure rate and the second component’s failure as a homogeneous Poisson process (HPP) with constant failure rate. The objective is to find the optimal inspection interval for the first component such that the expected total cost per unit time is minimized. A simplified numerical example along with sensitivity analysis on cost parameters is given.