Comparisons of renewable warranties

Two types of warranties are commonly applied. There are replacement-free warranty and pro-rata warranty. The third warranty is the mixing of the above two. That is it has a replacement-free stage followed by a pro-rata stage. In addition to the above classification, warranties can also be renewable or nonrenewable. No matter which warranty is used, it always incurs certain cost to the manufacturer. Moreover, often manufacturers want to improve the quality of products by burn-in before delivering them to consumers, and this incurs an extra cost. This article considers the random costs for both burn-in and renewable warranty, and derives the mean warranty cost. Then the mean costs corresponding to pure replacement-free warranty, mixing renewable warranty, and pure pro-rata warranty are compared. Furthermore, the mean costs under the same warranty policy associated with different lifetime distributions of products are also compared.