Optimal Upgrade Policy for Used Products Sold with Two-dimensional Warranty

Chun Su, Xiaolin Wang

Research output: Journal article publicationJournal articleAcademic researchpeer-review

33 Citations (Scopus)


In this paper, a pre-sale upgrade model is developed for repairable used products sold with two-dimensional warranty policies. Two kinds of two-dimensional warranty regions are considered, that is, rectangular and L-shaped regions. The marginal approach is used to describe the effect of age and usage on product reliability by treating usage as a random function of age. The optimal upgrade policy is determined to minimize the dealer's total expected servicing cost which is the sum of upgrade cost and warranty servicing cost. Analytical properties of the optimal solutions are also investigated. Furthermore, a five-step approach is presented to design flexible warranty contracts with optimized upgrade policies for used products, which allow customers to choose the most suitable warranty plans among the available options offered by the dealer. Numerical example and sensitivity analysis are provided to demonstrate the proposed models. This study provides the dealers of used products with useful guidelines on designing flexible and optimized warranty contracts.

Original languageEnglish
Pages (from-to)2889-2899
Number of pages11
JournalQuality and Reliability Engineering International
Issue number8
Publication statusPublished - 1 Dec 2016
Externally publishedYes


  • flexible warranty
  • two-dimensional warranty
  • upgrade
  • used products

ASJC Scopus subject areas

  • Safety, Risk, Reliability and Quality
  • Management Science and Operations Research


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