A bivariate optimal replacement policy for a repairable system

In this paper, a repairable system consisting of one unit and a single repairman is studied. Assume that the system after repair is not as good as new. Under this assumption, a bivariate replacement policy ( T, N ) , where T is the working age and N is the number of failures of the system is studied. The problem is to determine the optimal replacement policy ( T, N )∗such that the long-run average cost per unit time is minimized. The explicit expression of the long-run average cost per unit time is derived, and the corresponding optimal replacement policy can be determined analytically or numerically. Finally, under some conditions, we show that the policy ( T, N ) ∗ is better than policies N∗ or T∗.