A log-normal delta-shock maintenance model for a deteriorating system

In this paper, a delta-shock maintenance model for a deteriorating system is studied. Assume that shocks arrive according to a renewal process, the inter-arrival time of shocks has a lognormal distribution. Whenever an inter-arrival time of shocks is less than a threshold, the system will fail. A replacement policy N is adopted by which the system will be replaced by an identical new one at the time following the Nth failure. Then the long-run average cost per unit time is evaluated and an analytic expression for the optimal replacement policy N* is given.