A performance-based warranty for products subject to competing hard and soft failures

Xiaolin Wang, Bin Liu, Xiujie Zhao

Research output: Journal article publicationJournal articleAcademic researchpeer-review

9 Citations (Scopus)


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.

Original languageEnglish
Article number107974
JournalInternational Journal of Production Economics
Publication statusPublished - Mar 2021


  • Competing risks
  • Performance deterioration
  • Warranty
  • Warranty policy design

ASJC Scopus subject areas

  • Business, Management and Accounting(all)
  • Economics and Econometrics
  • Management Science and Operations Research
  • Industrial and Manufacturing Engineering

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