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Customized Random Maintenance Policies After the Expiration of a Renewal Repair–Replacement Warranty with Random Charge

Author

Listed:
  • Lin Zhao

    (College of Economics and Management, Changzhou Institute of Technology, Changzhou 213032, China)

  • Lijun Shang

    (School of Management, Foshan University, Foshan 528225, China)

  • Baoliang Liu

    (College of Mathematics and Statistics, Shanxi Datong University, Datong 037009, China)

Abstract

Driven by the trend of integrating monitored data into reliability management to explore innovative and practical approaches for managing reliability, researchers in the industry–university–research community have proposed random warranties. Existing random warranties use the limited mission cycle as a warranty-expiry limit instead of a measurement tool for controlling costs. This either shortens the warranty period for consumers or increases costs for manufacturers. To tackle these issues, this paper integrates mission cycles into the reliability management during the warranty stage and defines and models a renewal repair–replacement warranty with random charge (RRRW-RC) to manage the warranty-stage reliability of products. In the RRRW-RC, the limited mission cycles, acting as a usage limit, are used as a measurement tool to recover the fractional replacement cost within the warranty stage. This is designed to compensate manufacturers for replacement losses without shorting the warranty period, thus achieving the goal of reducing the warranty costs and not shortening the warranty period. The RRRW-RC can classify the usage habits of consumers into the heavy usage type and light usage type. Therefore, based on the usage classification results generated by the RRRW-RC, this paper also customizes two random maintenance policies to manage the post-warranty reliability of products. The first policy includes preventive/corrective replacement and “whichever occurs first,” and is thus referred to as customized bivariate random maintenance first (CBRMF). By revising “whichever occurs first” to “whichever occurs last,” the second policy is similarly represented and is called customized bivariate random maintenance last (CBRML). The policies defined above are modeled in terms of cost and time measures or cost rates, and their derivative policies are presented and modeled by setting parameter values. Numerical investigations are carried out to explore the management insights hidden in the proposed policies. Numerical investigations reveal that, by setting the failure number at an appropriate value, the warranty cost of the RRRW-RC can be minimized and its warranty period can be extended.

Suggested Citation

  • Lin Zhao & Lijun Shang & Baoliang Liu, 2024. "Customized Random Maintenance Policies After the Expiration of a Renewal Repair–Replacement Warranty with Random Charge," Mathematics, MDPI, vol. 13(1), pages 1-24, December.
  • Handle: RePEc:gam:jmathe:v:13:y:2024:i:1:p:70-:d:1555064
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    References listed on IDEAS

    as
    1. Wang, Xiaolin & Liu, Bin & Zhao, Xiujie, 2021. "A performance-based warranty for products subject to competing hard and soft failures," International Journal of Production Economics, Elsevier, vol. 233(C).
    2. Huang, Yeu-Shiang & Huang, Chao-Da & Ho, Jyh-Wen, 2017. "A customized two-dimensional extended warranty with preventive maintenance," European Journal of Operational Research, Elsevier, vol. 257(3), pages 971-978.
    3. Yeh, Ruey Huei & Ho, Wen-Tsung & Tseng, Sheng-Tsaing, 2000. "Optimal production run length for products sold with warranty," European Journal of Operational Research, Elsevier, vol. 120(3), pages 575-582, February.
    4. Wang, Xiaolin & Zhao, Xiujie & Liu, Bin, 2020. "Design and pricing of extended warranty menus based on the multinomial logit choice model," European Journal of Operational Research, Elsevier, vol. 287(1), pages 237-250.
    5. Wang, Yukun & Liu, Yiliu & Liu, Zixian & Li, Xiaopeng, 2017. "On reliability improvement program for second-hand products sold with a two-dimensional warranty," Reliability Engineering and System Safety, Elsevier, vol. 167(C), pages 452-463.
    6. Liu, Bin & Wu, Jun & Xie, Min, 2015. "Cost analysis for multi-component system with failure interaction under renewing free-replacement warranty," European Journal of Operational Research, Elsevier, vol. 243(3), pages 874-882.
    7. Wang, Jiantai & Zhou, Shihan & Peng, Rui & Qiu, Qingan & Yang, Li, 2023. "An inspection-based replacement planning in consideration of state-driven imperfect inspections," Reliability Engineering and System Safety, Elsevier, vol. 232(C).
    8. Lijun Shang & Baoliang Liu & Kaiye Gao & Li Yang, 2023. "Random Warranty and Replacement Models Customizing from the Perspective of Heterogeneity," Mathematics, MDPI, vol. 11(15), pages 1-22, July.
    9. Qingan Qiu & Lirong Cui & Dejing Kong, 2019. "Availability analysis and optimal inspection policy for systems with neglected down time," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 48(11), pages 2787-2809, June.
    10. Wang, Jingjing & Qiu, Qingan & Wang, Huanhuan & Lin, Cong, 2021. "Optimal condition-based preventive maintenance policy for balanced systems," Reliability Engineering and System Safety, Elsevier, vol. 211(C).
    11. Qiu, Qingan & Cui, Lirong, 2019. "Optimal mission abort policy for systems subject to random shocks based on virtual age process," Reliability Engineering and System Safety, Elsevier, vol. 189(C), pages 11-20.
    12. Qingan Qiu & Lirong Cui, 2019. "Availability analysis for general repairable systems with repair time threshold," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 48(3), pages 628-647, February.
    13. Qingan Qiu & Lirong Cui & Jingyuan Shen, 2018. "Availability and maintenance modeling for systems subject to dependent hard and soft failures," Applied Stochastic Models in Business and Industry, John Wiley & Sons, vol. 34(4), pages 513-527, July.
    14. Peng, Shizhe & Jiang, Wei & Wei, Lai & Wang, Xiao-Lin, 2022. "A new cost-sharing preventive maintenance program under two-dimensional warranty," International Journal of Production Economics, Elsevier, vol. 254(C).
    15. Zhao, Xian & Fan, Yu & Qiu, Qingan & Chen, Ke, 2021. "Multi-criteria mission abort policy for systems subject to two-stage degradation process," European Journal of Operational Research, Elsevier, vol. 295(1), pages 233-245.
    16. Peng, Rui & He, Xiaofeng & Zhong, Chao & Kou, Gang & Xiao, Hui, 2022. "Preventive maintenance for heterogeneous parallel systems with two failure modes," Reliability Engineering and System Safety, Elsevier, vol. 220(C).
    17. Karar, Ahmed Noaman & Labib, Ashraf & Jones, Dylan, 2023. "Post-warranty maintenance strategy selection using shape packages process," International Journal of Production Economics, Elsevier, vol. 255(C).
    18. Zhi‐Sheng Ye & Min Xie, 2015. "Rejoinder to ‘Stochastic modelling and analysis of degradation for highly reliable products’," Applied Stochastic Models in Business and Industry, John Wiley & Sons, vol. 31(1), pages 35-36, January.
    19. Shang, Lijun & Liu, Baoliang & Qiu, Qingan & Yang, Li, 2023. "Three-dimensional warranty and post-warranty maintenance of products with monitored mission cycles," Reliability Engineering and System Safety, Elsevier, vol. 239(C).
    20. Zhi-Sheng Ye & D.N. Murthy & Min Xie & Loon-Ching Tang, 2013. "Optimal burn-in for repairable products sold with a two-dimensional warranty," IISE Transactions, Taylor & Francis Journals, vol. 45(2), pages 164-176.
    21. Zhi‐Sheng Ye & Min Xie, 2015. "Stochastic modelling and analysis of degradation for highly reliable products," Applied Stochastic Models in Business and Industry, John Wiley & Sons, vol. 31(1), pages 16-32, January.
    22. Liu, Peng & Wang, Guanjun, 2023. "Generalized non-renewing replacement warranty policy and an age-based post-warranty maintenance strategy," European Journal of Operational Research, Elsevier, vol. 311(2), pages 567-580.
    23. Zhang, Shuyi & Zhai, Qingqing & Li, Yaqiu, 2023. "Degradation modeling and RUL prediction with Wiener process considering measurable and unobservable external impacts," Reliability Engineering and System Safety, Elsevier, vol. 231(C).
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