Optimal replacement policies for two-component parallel system with stochastic dependence

In this paper, age replacement policies for two-component parallel system with stochastic dependence are investigated. The stochastic dependence considered, is modeled by a one-sided domino effect. The failure of component 1 at instant t may induce the failure of component 2 at instant t + τ with a given probability. The time delay is a random variable with known probability density function. The system is considered in a failed state when both components are failed. The proposed replacement policies suggest to replace the system upon failure or at age T whichever occurs first. In the first policy, costs and durations associated with maintenance activities are supposed to be constant. In the second replacement policy, the preventive replacement cost depends on the system´s state and age. The expected cost per unit of time over an infinite span is derived and numerical examples are presented. The mathematical model can be used to analyze the stochastic dependence on the performance of the system.