Optimal periodic replacement policy for a two-unit system with failure rate interaction

In this paper, an economic periodic replacement model for a two-unit system with failure rate interaction between units is presented. In this model, whenever unit 1 fails, it causes a certain amount of damage to unit 2 by increasing the failure rate of unit 2 by a certain degree, while each unit 2 failure induces unit 1 into instantaneous failure. Without failure interaction between units, the failure rates of two units also increase with through an ageing process. The two-unit system is all replaced at age T, or on failure, whichever occurs first. The aim of this paper is to derive the long-run expected cost per unit time by introducing relative costs as a criterion of optimality. The optimal period T*that minimizes that cost is also discussed. A numerical example is given to illustrate the method.