Reward optimization of a repairable system

This paper analyzes a system subject to repairable and non-repairable failures. Non-repairable failures lead to replacement of the system. Repairable failures, first lead to repair but they lead to replacement after a fixed number of repairs. Operating and repair times follow phase type distributions (PH-distributions) and the pattern of the operating times is modelled by a geometric process. In this context, the problem is to find the optimal number of repairs, which maximizes the long-run average reward per unit time. To this end, the optimal number is determined and it is obtained by efficient numerical procedures.