Developing an optimal warranty policy model for products with multiple failure modes by considering mixture distribution

Modern industrial products often experience multiple failure modes with different economic consequences, such as repairable failures and repair/replacement failures. However, most existing warranty optimization models assume a single failure mode, which limits their applicability in practice. This paper develops an optimal warranty period model for repairable products subject to multiple failure modes by employing a statistical mixture distribution to model the time-to-failure process. The proposed model integrates heterogeneous failure behaviors into a unified life-cycle cost framework and determines the optimal warranty period by minimizing the expected life-cycle cost rate from the manufacturer’s perspective. Unlike traditional models that assume fixed warranty costs, this study explicitly distinguishes between different failure types and their associated repair or replacement costs. A numerical example is provided to illustrate the applicability of the proposed approach, and the model is numerically validated using Maple 2024. The results demonstrate that the mixture-based failure modeling framework provides greater flexibility and realism compared to conventional single-mode warranty models.