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<p>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.</p>

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

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年5月19日

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  • Mohammad Saber Fallahnezhad,
  • Masoud Amini

摘要

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.