Abstract This article studies a performance-based warranty for products subject to competing hard and soft failures. The two failure modes are competing in the sense that either one, on a “whichever-comes-first” basis, can cause the product to fail. A performance-based warranty not only covers the repair or replacement of any defect, but also guarantees the minimum performance level throughout the warranty period. In this article, we propose three compensation policies—that is, free replacement, penalty, and full refund, when a product’s performance fails to meet the guaranteed level. The expected warranty servicing costs for the three policies are derived, based on the competing risks concept. A warranty design problem is further formulated to simultaneously determine the optimal product price, warranty length, and performance guarantee level so as to maximize the manufacturer’s total profit. Numerical studies are conducted to demonstrate and compare the three performance-based compensation policies. It is shown that the full refund policy always leads to the lowest total profit, whereas neither of the other two policies can dominate each other in all scenarios. In particular, the free replacement policy results in a higher total profit than the penalty policy when the replacement cost is low, the penalty cost coefficient is high, and/or the product reliability is high.

中文翻译：

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对受竞争性硬和软故障影响的产品提供基于性能的保修

摘要 本文研究了针对竞争性软硬件故障的产品的基于性能的保修。这两种故障模式在某种意义上是相互竞争的，在“以先到者为准”的基础上，任何一种都可能导致产品出现故障。基于性能的保修不仅涵盖任何缺陷的维修或更换，而且还保证整个保修期内的最低性能水平。在这篇文章中，我们提出了三种补偿政策——当产品性能未达到保证水平时，即免费更换、罚款和全额退款。三个保单的预期保修服务成本是根据相互竞争的风险概念推导出来的。进一步制定保修设计问题，同时确定最优产品价格、保修期限、和性能保证水平，从而使制造商的总利润最大化。进行了数值研究来证明和比较三种基于绩效的薪酬政策。结果表明，全额退款政策总是导致总利润最低，而其他两种政策在所有情况下都不能相互支配。特别是，当更换成本低、惩罚成本系数高和/或产品可靠性高时，免费更换政策比惩罚政策产生更高的总利润。而其他两种策略都不能在所有情况下相互支配。特别是，当更换成本低、惩罚成本系数高和/或产品可靠性高时，免费更换政策比惩罚政策产生更高的总利润。而其他两种策略都不能在所有情况下相互支配。特别是，当更换成本低、惩罚成本系数高和/或产品可靠性高时，免费更换政策比惩罚政策产生更高的总利润。