A Markovian Replacement Model with a Generalization to Include Stocking

The following model is considered: A machine is inspected at the beginning of discrete time periods and its operating state (condition) is determined. After each inspection a decision upon whether or not to replace the machine at the end of the period must be made. It is shown that under certain conditions on the costs and the transition distributions the optimal policy has a simple form. A generalisation to the case where one is allowed to stock reserve machines is also given.