Optimal periodic maintenance policies for a parallel redundant system with component dependencies

In this paper, we investigate modified periodic maintenance policies for a parallel redundant system with three types of dependencies including stochastic dependence, structural dependence, and economic dependence, where they are seldom taken into account simultaneously in previous researches. More specifically, the stochastic dependence is modelled when multiple external shocks selectively affect the distinct components according to their sizes, attributes, and functions, leading to the existence of common cause failure. In addition, the structural dependence is considered as the parallel system is packaged and just systematic preventive maintenance is available. Finally, the economic dependence is introduced when developing preventive maintenance models, where the replacement costs among all items are associated. System reliability function is derived analytically in terms of cumulative shock damage theory and Laplace transform, and then four modified periodic maintenance policies are developed, in which the expected maintenance cost rate is minimized to seek the optimal replacement interval. An illustrative example of a silicon micro-electro-mechanical system (MEMS), which is composed of multiple non-identical resonators in parallel, is arranged to validate the theoretical results and to show the significance of considering component dependencies when scheduling preventive maintenance policies.