Optimal replacement policy for a deteriorating system with increasing repair times

This paper considers an optimal maintenance policy for a practical and reparable deteriorating system subject to random shocks. Modeling the repair time by a geometric process and the failure mechanism by a generalized δ-shock process, we develop an explicit expression of the long-term average cost per time unit for the system under a threshold-type replacement policy. Based on this average cost function, we propose a finite search algorithm to locate the optimal replacement policy N∗ to minimize the average cost rate. We further prove that the optimal policy N∗ is unique and present some numerical examples. Many practical systems fit the model developed in this paper.