Optimal replacement scheduling for a multi-component system with failure interaction

In this study, we consider a system consisting of n different components with failure interaction. Each component suffers from either minor or major failure: the former is removed via minimal repair, while the latter induces complete failure of the system and requires corrective replacement of the system. This study investigates two scheduling problems of preventive replacement policies for a multi-component system that incorporates minimal repair, shortage, and excess costs. First, we consider the scheduling problem of an age replacement policy, in which the system is replaced at a planned time T or upon the occurrence of any major failure. Next, we consider that the system operates N successive random jobs without interruptions. In this scheduling problem, the system is replaced upon the accomplishment of N jobs or upon the occurrence of any major failure. For each scheduling problem, we derive the optimal scheduling parameter (T* or N*) analytically and numerically, according to their existence and uniqueness based on minimizing the mean cost rate function. Finally, a numerical example is designed to validate the theoretical results in this article.