Three replacement models with two kinds of damage

This paper proposes three replacement policies for a modified cumulative damage model. An item receives shocks and suffers two kinds of damage: one is produced by shocks and the other increases with time at constant rate a. It fails only when the total damage exceeds a failure level K at some shock and is replaced before failure at time T, at shock N, or at damage k. The expected cost rates of three replacement policies are obtained. When shocks occur in a Poisson process, optimal T^*, N^* and k^* which minimize them are computed numerically. Finally, two extended cases where a is a function of time and K is a random variable are also considered.