failure interaction

This paper proposes an approach for nding periodic and non-periodic optimal inspection intervals for a multicomponent repairable system with failure interaction. The failure of one component of the system is hard, i.e., as soon as it occurs, the system stops operating. Failures of other components are soft, namely; they do not cause the system to stop, but increase system operating costs and are detected only if inspection is performed. Thus, the components with soft failure are all inspected at scheduled inspection instances, and are minimally repaired if found to be failed. When the component with hard failure fails, it is also repaired. Each soft failure has no eect on the behavior of the other components; however, any hard failure acts as a shock to other components, without inducing an instantaneous failure, but increasing their failure rate. The system's expected total cost includes inspection costs, repair costs, and penalty costs that are incurred due to time delay between real 168 occurrence of soft failures and their detection at inspections. The objective is to determine both periodic and non-periodic optimal inspection intervals, which yield the minimum expected total cost of the system. In the proposed approach, the system's expected total cost is rst formulated in terms of an inspection scheme. The occurrence of hard failures is modeled by a homogeneous Poisson process (HPP) with constant failure rate, and the occurrence of soft failures is modeled by a nonhomogeneous Poisson process (NHPP) with increasing failure rate. Then, for obtaining the periodic optimal inspection scheme, the expected total cost is evaluated for all alternative periodic inspection schemes to identify the optimal one, which yields minimum cost. For obtaining the non-periodic optimal inspection scheme, 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. A numerical example is given to illustrate the proposed approach.