Optimal Repair of a Series System

A single repairman maintains a series system whose components have exponential failure and repair distributions. It is desired to assign the repairman to maximize the expected total discounted working time or average working time for the system. Whenever the failure rates of all components are equal, the time to repair the system from any initial state is stochastically independent of the operating policy. The Laplace transform of time to repair the system and the long-run average time that the system works are explicitly available. For the two-component series system the repair time is stochastically minimized if the failed component with longest expected lifetime is always under repair. This is true even if the repairman experiences random periods of time during which repair is not allowed. For an n-component series system the policy that always repairs the failed component with longest expected lifetime stochastically minimizes the repair time over the class of policies, that repair failed components in a predetermined order. We apply the results to a queuing system.