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Replacement Costs Under Warranty: Cost Moments and Time Variability

Author

Listed:
  • Yves Balcer

    (University of Wisconsin, Madison, Wisconsin)

  • Izzet Sahin

    (University of Wisconsin, Milwaukee, Wisconsin)

Abstract

We consider a product that is sold under one of the two common warranty policies. Under the “pro rata” warranty policy, a failed item is replaced by a new one or is repaired at a cost prorated to the age of the failed item. Under the “free replacement” warranty policy, replacements or repairs during the warranty period are provided by the supplier free of charge to the buyer. Assuming that successive failure times form a renewal process, we derive moments of the total replacement cost for both policies during the product life cycle (0, t ]. We also provide an extension to time-varying failure time distributions in the case of the pro rata warranty policy.

Suggested Citation

  • Yves Balcer & Izzet Sahin, 1986. "Replacement Costs Under Warranty: Cost Moments and Time Variability," Operations Research, INFORMS, vol. 34(4), pages 554-559, August.
    • Handle: RePEc:inm:oropre:v:34:y:1986:i:4:p:554-559
    DOI: 10.1287/opre.34.4.554
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    Citations

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    Cited by:

    1. Marlin U. Thomas & Sridevi S. Rao, 1999. "Warranty Economic Decision Models: A Summary and Some Suggested Directions for Future Research," Operations Research, INFORMS, vol. 47(6), pages 807-820, December.
    2. Mitra, Amitava & Patankar, Jayprakash G., 1997. "Market share and warranty costs for renewable warranty programs," International Journal of Production Economics, Elsevier, vol. 50(2-3), pages 155-168, June.
    3. Polatoglu, Hakan & Sahin, Izzet, 1998. "Probability distributions of cost, revenue and profit over a warranty cycle," European Journal of Operational Research, Elsevier, vol. 108(1), pages 170-183, July.
    4. J-A Chen & Y-H Chien, 2007. "Optimal age-replacement policy for renewing warranted products," Journal of Risk and Reliability, , vol. 221(4), pages 229-237, December.
    5. Chien, Yu-Hung, 2010. "Optimal age for preventive replacement under a combined fully renewable free replacement with a pro-rata warranty," International Journal of Production Economics, Elsevier, vol. 124(1), pages 198-205, March.
    6. Hui Chen & Jie Chen & Yangyang Lai & Xiaoqi Yu & Lijun Shang & Rui Peng & Baoliang Liu, 2024. "Discrete Random Renewable Replacements after the Expiration of Collaborative Preventive Maintenance Warranty," Mathematics, MDPI, vol. 12(18), pages 1-21, September.
    7. Chun, Young Hak & Tang, Kwei, 1995. "Determining the optimal warranty price based on the producer's and customers' risk preferences," European Journal of Operational Research, Elsevier, vol. 85(1), pages 97-110, August.
    8. K Sahyouni & R C Savaskan & M S Daskin, 2010. "The effect of lifetime buys on warranty repair operations," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 61(5), pages 790-803, May.
    9. Kunpeng Li & Suman Mallik & Dilip Chhajed, 2012. "Design of Extended Warranties in Supply Chains under Additive Demand," Production and Operations Management, Production and Operations Management Society, vol. 21(4), pages 730-746, July.
    10. Izzet Sahin & Hakan Polatoglu, 1995. "Distributions of manufacturer's and user's replacement costs under warranty," Naval Research Logistics (NRL), John Wiley & Sons, vol. 42(8), pages 1233-1250, December.
    11. Lu, Zhen & Shang, Jennifer, 2019. "Warranty mechanism for pre-owned tech products: Collaboration between E-tailers and online warranty provider," International Journal of Production Economics, Elsevier, vol. 211(C), pages 119-131.
    12. Lianmin Zhang & Lei Guan & Daniel Zhuoyu Long & Houcai Shen & Huajun Tang, 2023. "Who is better off by selling extended warranties in the supply chain: the manufacturer, the retailer, or both?," Annals of Operations Research, Springer, vol. 328(2), pages 1557-1583, September.
    13. Li, Kunpeng & Chhajed, Dilip & Mallik, Suman, 2005. "Design of Extended Warranties in Supply Chains," Working Papers 05-0128, University of Illinois at Urbana-Champaign, College of Business.
    14. Edward P. C. Kao & Marion Spokony Smith, 1992. "On excess‐, current‐, and total‐life distributions of phase‐type renewal processes," Naval Research Logistics (NRL), John Wiley & Sons, vol. 39(6), pages 789-799, October.
    15. Herbert Moskowitz & Young Hak Chun, 1994. "A poisson regression model for two‐attribute warranty policies," Naval Research Logistics (NRL), John Wiley & Sons, vol. 41(3), pages 355-376, April.
    16. Chien, Yu-Hung, 2008. "A general age-replacement model with minimal repair under renewing free-replacement warranty," European Journal of Operational Research, Elsevier, vol. 186(3), pages 1046-1058, May.
    17. Lam, Yeh & Kwok Wai Lam, Peggo, 2001. "An extended warranty policy with options open to consumers," European Journal of Operational Research, Elsevier, vol. 131(3), pages 514-529, June.
    18. Kao, Edward P. C. & Smith, Marion Spokony, 1996. "Computational approximations of renewal process relating to a warranty problem: The case of phase-type lifetimes," European Journal of Operational Research, Elsevier, vol. 90(1), pages 156-170, April.

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