Optimal repair and replacement in markovian systems

A deteriorating system is inspected at equally spaced points in time. After each inspection a repair to a better state or a full replacement are possible. We introduce a generalized control limit policy and show that, under reasonable conditions on the system's law of evolution and on the operating, repair and replacement costs, this policy is optimal for the expected total discounted cost, as well as for the (long-run) average cost criteria. Furthermore, we allow for uncertain repair actions (that may even end up in a worse state), and show that the generalized control limit rule is still optimal. The work extends, generalizes and unifies many models in the area of optimal control of repairable systems