A discrete replacement model for a two-unit parallel system subject to failure rate interaction

In this paper, a repairable two-unit parallel system with failure rate interaction between units is studied. Failure rate interaction between units is described as follows. Unit-1 failure whenever occurs can increase the failure rate of unit-2 of some amount, while unit-2 failure can induce unit-1 into simultaneous failure. We consider a discrete replacement policy N based on the number of unit-1 failure. The system is replaced at the instant of the N-th failure of unit-1 or on simultaneous failure of the system. Our problem is to determine an optimal replacement policy N (*) such that the expected cost rate per unit time is minimized. The explicit expression of the expected cost rate per unit time is derived by introducing relative costs and the corresponding optimal number N* is also verified finite and unique under some specific conditions.