Optimal Repairman Allocation—Asymptotic Results - Smith, Donald R. (Management Science, 1978)
We consider a single repairman who maintains a coherent system of n components. Each component works for and is repaired in random periods of time with exponential distribution independent of the behavior of other components. We try to find a policy for assignment of the repairman which maximizes the long run probability that the system functions. Although the general problem is quite complicated, highly reliable and highly unreliable systems can be solved easily by asymptotic techniques. These techniques express ergodic probabilities and expected passage times between states in power series of an asymptotic parameter when the policy employed is in a class of potentially optimal policies. As an example, the highly reliable optimal actions are obtained for the k of n system which includes both series and parallel systems.