On the Maintenance of Systems Composed of Highly Reliable Components

We consider the dynamic repair allocation problem for a general multi-component system that is maintained by a limited number of repairmen. Component functioning and repair times are exponentially distributed random variables with known parameters. At most one repairman may be assigned to a failed component and it is possible to reassign a repairman from one failed component to another instantaneously. The objective is to determine repair allocation policies that maximize a measure of performance of the system such as the expected discounted system operation time or the availability of the system. We consider systems composed of highly reliable, i.e., small failure rates, components and study asymptotic techniques for the determination of optimal policies. In the final section we find asymptotically optimal policies for the series, parallel, and a system composed of parallel subsystems connected in series.