Abstract
The present paper considers a system in which components stochastically deteriorate with age. When the component fails, it is repaired with a specified repair time distribution or left as it is until the next planned replacement opportunity. As a result of this action, an idle time occurs and the cost is incurred during the idle time. The optimal policy which minimizes the total expected cost is derived and the critical point in time to distinguish the above two actions is found by the method of dynamic programming. Some simple examples are discussed to illustrate our model.
