Optimal policy for a general repair replacement model: Average reward case

For a general repair replacement model, two types of replacement policy are studied. Replacement policy T replaces the system at time T since the installation or last replacement, while replacement policy N replaces the system at the time of Nth failure. Let T* and N* be the optimal among all policies T and N respectively. Under the expected average reward criterion, then it is shown that the optimal policy N* is at least as good as the optimal policy T*. Furthermore, for a monotone process model, the optimal policy N* is determined explicitly through two different approaches.