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Optimal post-warranty replacement policy based on number of product failures for the second-hand product

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  • Jae-Hak Lim
  • Dong Ho Park
  • Dae Kyung Kim

Abstract

This paper deals with a post-warranty maintenance model for the second-hand product as follows. The second-hand product of age x , which is assumed to be positive, is purchased with a fixed length of non-renewing warranty, during which the product is given a fixed number of preventive maintenances periodically by the dealer. At each preventive maintenance, the failure rate of the product is adjusted to some extent for the purpose of reducing the likelihood of product failure. At the expiration of warranty, the user starts to self-maintain the product until a pre-determined number of failures occur, at which time the product is replaced by another one. For each post-warranty failure, only a minimal repair is taken to restore the failed product to its previous functioning state. This paper aims to determine an optimal number of post-warranty product failures that minimizes the expected cost rate during the second-hand product’s life cycle. To this end, we derive a formula to evaluate the expected cost rate during the second-hand product’s life cycle by assuming a certain cost structure for maintaining the product during the life-span of the product and determine an optimal number of post-warranty product failures from the user’s perspective. And we provide a numerical example to illustrate our proposed optimal maintenance model by assuming a Weibull failure distribution. The main contribution of this work is to use the number of post-warranty failures to propose a maintenance model for the second-hand product, where the number of failures is in general easier to observe than the failure times.

Suggested Citation

  • Jae-Hak Lim & Dong Ho Park & Dae Kyung Kim, 2024. "Optimal post-warranty replacement policy based on number of product failures for the second-hand product," Journal of Risk and Reliability, , vol. 238(5), pages 995-1008, October.
    • Handle: RePEc:sae:risrel:v:238:y:2024:i:5:p:995-1008
    DOI: 10.1177/1748006X231194899
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    References listed on IDEAS

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    1. Shafiee, Mahmood & Finkelstein, Maxim & Chukova, Stefanka, 2011. "On optimal upgrade level for used products under given cost structures," Reliability Engineering and System Safety, Elsevier, vol. 96(2), pages 286-291.
    2. Lijun Shang & Shubin Si & Shudong Sun & Tongdan Jin, 2018. "Optimal warranty design and post-warranty maintenance for products subject to stochastic degradation," IISE Transactions, Taylor & Francis Journals, vol. 50(10), pages 913-927, October.
    3. Minjae Park & Hoang Pham, 2011. "Maintenance and Warranty Concepts," Springer Series in Reliability Engineering, in: Hoang Pham (ed.), Safety and Risk Modeling and Its Applications, pages 101-122, Springer.
    4. Dai, Anshu & Wei, Guanzhou & Wang, Dongfan & He, Zhen & He, Shuguang, 2021. "The opportunity study of PM strategy for second-hand products sold with a two-dimensional warranty," Reliability Engineering and System Safety, Elsevier, vol. 214(C).
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    Cited by:

    1. Shang, Lijun & Liu, Baoliang & Peng, Rui, 2025. "Designing random collaborative warranty and customizing maintenance strategies for systems subject to mission cycles," Reliability Engineering and System Safety, Elsevier, vol. 257(PA).

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