Funding a Warranty Reserve with Inputs After Each Sale

We consider funding an interest-bearing warranty reserve with contributions after each sale. The problem for the manufacturer is to determine the initial level of the reserve fund and the amount to be put in after each sale, so as to ensure that the reserve fund covers all the warranty liabilities with a prespecied probability over a xed period of time. We assume a non-homogeneous Poisson sales process, random warranty periods, and an exponential failure rate for items under warranty. We derive the mean and variance of the reserve level as a function of time and provide a heuristic to aid the manufacturer in its decision.