Aggregate Discounted Warranty Cost Forecast for a New Product Considering Stochastic Sales

Most commercial products are sold with a warranty. Product repairs during the warranty period are often free of charge, and contribute significantly to the costs of a manufacturer. Estimation of the warranty costs is important for the manufacturer to prepare sufficient warranty reserves for future claims. Because products are often sold to customers intermittently, the total number of sold units under warranty varies over time, which presents difficulties in forecasting the warranty costs over time. In this study, we consider the stochastic sales process, and derive the expectation and variance of the aggregate discounted warranty costs within a given period of time. By taking the variation of the warranty costs into consideration, the result can be used in the preparation of a conservative warranty reserve for a new product. The discounted life-cycle warranty cost is a special case of our model, and it can also be determined from our result. Numerical results show the applicability of our model in estimating periodic discounted warranty costs, and preparing both short-term and long-term warranty reserves.