Mean throughput rate in restart-upon-failure systems subject to random disruptions

Abstract

We model a manufacturing or service system processing a fixed number of tasks subject to random disruptions generated by a renewal process, such that a task has to start over from scratch if it is interrupted. We study the impact of an increase in disruption rate on the mean throughput of the system, using tools from stochastic ordering. We show that a system that is stochastically better than another does not necessarily have a higher mean throughput - the deciding factor is the hazard rate of the underlying disruption process. We prove that a system that is better than another in the sense of hazard rate ordering of time between disruptions is guaranteed to enjoy a higher average throughput.