A stochastic model on an additional warranty service contract

In general, a newly purchased item or system is warranted for a specific period. When the system fails during the warranty period, it is repaired free of charge. Even if the system is repairable, there exist some warranty services under which the manufacturer replaces the failed system during the warranty period. This study considers a case where a manufacturer offers an additional warranty service under which the failed system is replaced by a new one for its first failure, but minimal repairs are carried out to the system for its succeeding failures before the warranty expires. In this paper, we propose a mathematical model for setting a suitable charge of such an additional warranty service. Numerical examples assuming a personal computer are also presented.