Optimal repair allocation in a series system expected discounted operation time criterion

Consider a series system with n repairable components maintained by a single repairman. The following assumptions are made. Component failure and repair times are independent, exponentially distributed, random variables. Component failures can occur even while the system is not functioning and it is possible to reassign the repairman among failed components instantaneously. It is shown that the policy which always assigns the repairman to the failed component with the smallest failure rate among the failed ones maximizes the expected discounted system operation time irrespective of the values of the repair rates and the discount rate