Window Fill Rate with Compound Arrival and Assembly Time

Exchangeable-item repair systems are inventory systems in which customers receive operable items in exchange of the failed items they brought. The failed items are not discarded, but instead, they are repaired on site. We consider such a system in which failed items arrival follows a Compound Poisson process and in which the item removal and installation times may be positive. For this system, we develop exact formulas for the window fill rate, that is, the probability that customers receive service within a specific time window. This service measure is appropriate in situations that customers tolerate a certain delay and therefore the system does not incur reputations costs if it completes service within this time window.