A Log-normal δ-Shock maintenance model for a deteriorating system

In this paper,a δ-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 log-normal 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.