Replacement Policies for Periodic Damage Models

A new periodic damage model is proposed in this paper, where the damage produced by shocks is only measured at periodic times, without considering the stochastic shocks and the cumulative process of damage in discrete times. We model five replacement policies for the periodic damage models using three approaches of whichever triggering event occurs first, whichever triggering event occurs last, and replacing over a planned measure, which are named as replacement first, replacement last, over-damage replacement, over-damage replacement first, and over-damage replacement last, respectively. In analytical ways, we obtain their optimum replacement policies to minimize the expected cost rates and compare them to find which model is more economical. Finally, numerical examples are given to illustrate the validity of the presented models.