A shock model for the maintenance problem of a repairable system

In this paper, a shock model for the maintenance problem of a repairable system is studied. Assume that shocks will arrive according to a Poisson process. If the interarrival time of two successive shocks is less than a threshold, then the system will fail. For a deteriorating system, we assume that the successive threshold values are geometrically nondecreasing after repair, and the consecutive repair times after failure form an increasing geometric process. For an improving system, we assume that the successive threshold values are geometrically decreasing after repair, and the consecutive repair times after failure form a decreasing geometric process. A replacement policy N is adopted by which we shall replace the system by an identical new one at the time following the Nth failure. Then for each of the deteriorating system and improving system, an optimal policy N ∗ for minimizing the long-run average cost per unit time is determined explicitly.