Optimal Replacement Policy Based on the Number of Down Times

In this paper a cold standby system consisting of two identical components (first component in working state and second one in the cold standby state) and one repairman is studied. A replacement policy is considered which is based on the number of down times in a renewal cycle. The problem is to determine an optimal policy with respect to the the long run reward per unit time. An explicit expression of the long run reward per unit time is derived and illustrated by a numerical example.