Joint optimization of Reliability, Warranty and Price for a Product Family

Xinyang Liu, Pingfeng Wang

Research output: Chapter in Book/Report/Conference proceedingConference contribution


This paper presents a joint optimization work of reliability, warranty and price for a product family. The net profit from a fixed time length is considered as the objective to maximize, which is influenced by the product price, manufacturing cost, warranty service cost and the sales amount. A constant product price is optimized for a stable market and the price together with the provided warranty service length will determine the sales amount over time. Next, the manufacturing cost consists of research and development cost and unit product cost, which is influenced by the sales amount and reliability requirement. Besides, a free replacement policy is offered as the warranty service whose time length is optimized in the framework and the expected coverage cost is estimated to help maximize the total profit. The uniqueness of joint optimization for a product family compared with that for a single product is that apart from the tradeoff among reliability, warranty and price, product family has one more flexibility in module sharing. Therefore, apart from considering the structure of product family as an input information, module sharing decisions inside a product family are also incorporated in the optimization formulation. A case study on a family of products with different target consumer groups is conducted to illustrate the joint optimization framework. The result shows that the proposed model can help determine the optimal reliability parameters, warranty length and price to maximize the total profits. And multiple sensitivity analysis is performed to explore the design decision space with a focus on how the joint optimization would influence the product family structure. Based on the results, sales sensitivity with respect to warranty and price will influence the module sharing decision in the product family. And when two modules have different manufacturing and quality requirements, sharing them among the products will not bring benefits. Finally, the time horizon considered will also influence the module sharing benefit.

Original languageEnglish (US)
Title of host publication68th Annual Reliability and Maintainability Symposium, RAMS 2022
PublisherInstitute of Electrical and Electronics Engineers Inc.
ISBN (Electronic)9781665424325
StatePublished - 2022
Externally publishedYes
Event68th Annual Reliability and Maintainability Symposium, RAMS 2022 - Tucson, United States
Duration: Jan 24 2022Jan 27 2022

Publication series

NameProceedings - Annual Reliability and Maintainability Symposium
ISSN (Print)0149-144X


Conference68th Annual Reliability and Maintainability Symposium, RAMS 2022
Country/TerritoryUnited States


  • joint optimization
  • product family
  • reliability
  • warranty

ASJC Scopus subject areas

  • Safety, Risk, Reliability and Quality
  • General Mathematics
  • Computer Science Applications


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