Optimal burn-in for repairable products sold with a two-dimensional warranty

Warranty data analyses reveal that products sold with two-dimensional warranties may have significant infant mortalities. To deal with this problem, this article proposes and studies a new burn-in modeling approach for repairable products sold with a two-dimensional warranty. More specifically, two types of failures are characterized—i.e., normal and defect failures—and performance and cost-based burn-in models are developed under the non-renewing free-repair warranty policy. The proposed models subsume the special cases of a one-dimensional warranty, allow different failure modes to have distinct accelerated relationships, and take consumer usage heterogeneity into consideration. Under mild assumptions, it is established that the optimal burn-in usage rate should be as high as possible, provided that no extraneous failure modes are introduced. Furthermore, It is shown that the optimal burn-in duration determined from the performance-based model is not shorter than that from the cost-based model. Numerical examples are used to demonstrate the benefits of burn-in. In addition, some practical implications from a sensitivity analysis are elaborated.