IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v10y2022i10p1644-d813548.html
   My bibliography  Save this article

Post-Warranty Replacement Models for the Product under a Hybrid Warranty

Author

Listed:
  • Lijun Shang

    (School of Quality Management and Standardization, Foshan University, Foshan 528000, China)

  • Guojun Shang

    (Gao Tou Yao Coal Mine, North United Power Corporation, Ordos 014323, China)

  • Yongjun Du

    (School of Economics and Management, Lanzhou University of Technology, Lanzhou 730050, China)

  • Qingan Qiu

    (School of Management & Economics, Beijing Institute of Technology, Beijing 100081, China)

  • Li Yang

    (School of Reliability and Systems Engineering, Beihang University, Beijing 100191, China)

  • Qinglai Dong

    (School of Mathematics & Computer Science, Yan’an University, Yan’an 716000, China)

Abstract

In this article, by considering both a limited number of failure replacements and a limited number of random working cycles as warranty terms, a hybrid warranty (HW) is designed from the manufacturer’s point of view to warrant the product that does successive projects at random working cycles. The warranty cost produced by HW is derived and analyzed. By defining that HW warrants the product, two types of post-warranty replacement models are investigated from the consumer’s point of view to ensure the reliability of the product through HW, i.e., customized post-warranty replacement and uniform post-warranty replacement. Depreciation expense is integrated into each post-warranty replacement. The expected cost rate model is presented for each post-warranty replacement and some special cases are obtained by setting parameters in the expected cost rate. Finally, sensitivities on both HW and post-warranty replacements are analyzed in numerical experiments. It is shown that when a limited number of failure replacements or/and a limited number of random working cycles are introduced to a warranty, the warranty cost can be reduced; and the performance of the uniform post-warranty replacement is superior to the customized post-warranty replacement.

Suggested Citation

  • Lijun Shang & Guojun Shang & Yongjun Du & Qingan Qiu & Li Yang & Qinglai Dong, 2022. "Post-Warranty Replacement Models for the Product under a Hybrid Warranty," Mathematics, MDPI, vol. 10(10), pages 1-18, May.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:10:p:1644-:d:813548
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/10/10/1644/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/10/10/1644/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. 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.
    2. Su, Chun & Wang, Xiaolin, 2016. "A two-stage preventive maintenance optimization model incorporating two-dimensional extended warranty," Reliability Engineering and System Safety, Elsevier, vol. 155(C), pages 169-178.
    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. Park, Minjae & Jung, Ki Mun & Park, Dong Ho, 2018. "Optimization of periodic preventive maintenance policy following the expiration of two-dimensional warranty," Reliability Engineering and System Safety, Elsevier, vol. 170(C), pages 1-9.
    5. 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.
    6. Sarah Marshall & Richard Arnold & Stefanka Chukova & Yu Hayakawa, 2018. "Warranty cost analysis: Increasing warranty repair times," Applied Stochastic Models in Business and Industry, John Wiley & Sons, vol. 34(4), pages 544-561, July.
    7. Chen, Cheng-Kang & Lo, Chih-Chung & Weng, Tzu-Chun, 2017. "Optimal production run length and warranty period for an imperfect production system under selling price dependent on warranty period," European Journal of Operational Research, Elsevier, vol. 259(2), pages 401-412.
    8. Cha, Ji Hwan & Finkelstein, Maxim & Levitin, Gregory, 2021. "Optimal warranty policy with inspection for heterogeneous, stochastically degrading items," European Journal of Operational Research, Elsevier, vol. 289(3), pages 1142-1152.
    9. Ye, Zhi-Sheng & Murthy, D.N. Pra, 2016. "Warranty menu design for a two-dimensional warranty," Reliability Engineering and System Safety, Elsevier, vol. 155(C), pages 21-29.
    10. Bei Wu & Brenda Ivette Garcia Maya & Nikolaos Limnios, 2021. "Using Semi-Markov Chains to Solve Semi-Markov Processes," Methodology and Computing in Applied Probability, Springer, vol. 23(4), pages 1419-1431, December.
    11. 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.
    12. Huang, Yeu-Shiang & Gau, Wei-Yo & Ho, Jyh-Wen, 2015. "Cost analysis of two-dimensional warranty for products with periodic preventive maintenance," Reliability Engineering and System Safety, Elsevier, vol. 134(C), pages 51-58.
    13. Luo, Ming & Wu, Shaomin, 2019. "A comprehensive analysis of warranty claims and optimal policies," European Journal of Operational Research, Elsevier, vol. 276(1), pages 144-159.
    14. Qiu, Qingan & Kou, Meng & Chen, Ke & Deng, Qiao & Kang, Fengming & Lin, Cong, 2021. "Optimal stopping problems for mission oriented systems considering time redundancy," Reliability Engineering and System Safety, Elsevier, vol. 205(C).
    15. Sheu, Shey-Huei & Liu, Tzu-Hsin & Zhang, Zhe-George, 2019. "Extended optimal preventive replacement policies with random working cycle," Reliability Engineering and System Safety, Elsevier, vol. 188(C), pages 398-415.
    16. 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.
    17. Zhao, Xian & Sun, Jinglei & Qiu, Qingan & Chen, Ke, 2021. "Optimal inspection and mission abort policies for systems subject to degradation," European Journal of Operational Research, Elsevier, vol. 292(2), pages 610-621.
    18. Wang, Jingjing & Qiu, Qingan & Wang, Huanhuan, 2021. "Joint optimization of condition-based and age-based replacement policy and inventory policy for a two-unit series system," Reliability Engineering and System Safety, Elsevier, vol. 205(C).
    19. Zhang, Zihan & Yang, Li, 2020. "Postponed maintenance scheduling integrating state variation and environmental impact," Reliability Engineering and System Safety, Elsevier, vol. 202(C).
    20. Darghouth, M.N. & Ait-kadi, D. & Chelbi, A., 2017. "Joint optimization of design, warranty and price for products sold with maintenance service contracts," Reliability Engineering and System Safety, Elsevier, vol. 165(C), pages 197-208.
    21. Qiu, Qingan & Cui, Lirong, 2019. "Gamma process based optimal mission abort policy," Reliability Engineering and System Safety, Elsevier, vol. 190(C), pages 1-1.
    22. Luo, Ming & Wu, Shaomin, 2018. "A value-at-risk approach to optimisation of warranty policy," European Journal of Operational Research, Elsevier, vol. 267(2), pages 513-522.
    23. Wei Xie & Lijuan Shen & Yuanguang Zhong, 2017. "Two-dimensional aggregate warranty demand forecasting under sales uncertainty," IISE Transactions, Taylor & Francis Journals, vol. 49(5), pages 553-565, May.
    24. Qiu, Qingan & Cui, Lirong & Wu, Bei, 2020. "Dynamic mission abort policy for systems operating in a controllable environment with self-healing mechanism," Reliability Engineering and System Safety, Elsevier, vol. 203(C).
    25. Hooti, Fatemeh & Ahmadi, Jafar & Longobardi, Maria, 2020. "Optimal extended warranty length with limited number of repairs in the warranty period," Reliability Engineering and System Safety, Elsevier, vol. 203(C).
    26. Liu, Peng & Wang, Guanjun & Su, Peng, 2021. "Optimal maintenance strategies for warranty products with limited repair time and limited repair number," Reliability Engineering and System Safety, Elsevier, vol. 210(C).
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Shang, Lijun & Liu, Baoliang & Qiu, Qingan & Yang, Li & Du, Yongjun, 2023. "Designing warranty and maintenance policies for products subject to random working cycles," Reliability Engineering and System Safety, Elsevier, vol. 234(C).
    2. Yongjun Du & Lijun Shang & Qingan Qiu & Li Yang, 2022. "Optimum Post-Warranty Maintenance Policies for Products with Random Working Cycles," Mathematics, MDPI, vol. 10(10), pages 1-16, May.
    3. Lijun Shang & Yongjun Du & Cang Wu & Chengye Ma, 2022. "A Bivariate Optimal Random Replacement Model for the Warranted Product with Job Cycles," Mathematics, MDPI, vol. 10(13), pages 1-16, June.
    4. Lijun Shang & Guojun Shang & Qingan Qiu, 2022. "A Bivariate Post-Warranty Maintenance Model for the Product under a 2D Warranty," Mathematics, MDPI, vol. 10(12), pages 1-18, June.
    5. Lijun Shang & Xiguang Yu & Yongjun Du & Anquan Zou & Qingan Qiu, 2022. "An Optimal Random Hybrid Maintenance Policy of Systems under a Warranty with Rebate and Charge," Mathematics, MDPI, vol. 10(18), pages 1-19, September.
    6. Lijun Shang & Xiguang Yu & Liying Wang & Yongjun Du, 2022. "Design of Random Warranty and Maintenance Policy: From a Perspective of the Life Cycle," Mathematics, MDPI, vol. 10(20), pages 1-22, October.
    7. Wang, Xiaolin & Li, Lishuai & Xie, Min, 2020. "An unpunctual preventive maintenance policy under two-dimensional warranty," European Journal of Operational Research, Elsevier, vol. 282(1), pages 304-318.
    8. Zhu, Ying & Xia, Tangbin & Chen, Zhen & Pan, Ershun & Xi, Lifeng, 2022. "Optimal maintenance service strategy for OEM entering competitive MRO market under opposite patterns," Reliability Engineering and System Safety, Elsevier, vol. 217(C).
    9. Safaei, Fatemeh & Taghipour, Sharareh, 2022. "Optimal preventive maintenance for repairable products with three types of failures sold under a renewable hybrid FRW/PRW policy," Reliability Engineering and System Safety, Elsevier, vol. 223(C).
    10. 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).
    11. Yaguang Wu, 2023. "Optimal Stopping and Loading Rules Considering Multiple Attempts and Task Success Criteria," Mathematics, MDPI, vol. 11(4), pages 1-17, February.
    12. Liu, Bin & Shen, Lijuan & Xu, Jianyu & Zhao, Xiujie, 2020. "A complimentary extended warranty: Profit analysis and pricing strategy," International Journal of Production Economics, Elsevier, vol. 229(C).
    13. Luo, Ming & Wu, Shaomin, 2019. "A comprehensive analysis of warranty claims and optimal policies," European Journal of Operational Research, Elsevier, vol. 276(1), pages 144-159.
    14. Liu, Lujie & Yang, Jun, 2023. "A dynamic mission abort policy for the swarm executing missions and its solution method by tailored deep reinforcement learning," Reliability Engineering and System Safety, Elsevier, vol. 234(C).
    15. Chengye Ma & Yongjun Du & Lijun Shang & Li Yang & Kaiye Gao, 2023. "Random Maintenance Strategy Modeling of Warranted Products with Reliability Heterogeneity," Sustainability, MDPI, vol. 15(18), pages 1-19, September.
    16. Ke Chen & Xian Zhao & Qingan Qiu, 2022. "Optimal Task Abort and Maintenance Policies Considering Time Redundancy," Mathematics, MDPI, vol. 10(9), pages 1-16, April.
    17. Zhao, Xian & Dai, Ying & Qiu, Qingan & Wu, Yaguang, 2022. "Joint optimization of mission aborts and allocation of standby components considering mission loss," Reliability Engineering and System Safety, Elsevier, vol. 225(C).
    18. Zhao, Xian & Liu, Haoran & Wu, Yaguang & Qiu, Qingan, 2023. "Joint optimization of mission abort and system structure considering dynamic tasks," Reliability Engineering and System Safety, Elsevier, vol. 234(C).
    19. 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.
    20. Levitin, Gregory & Xing, Liudong & Dai, Yuanshun, 2023. "Optimal task sequencing and aborting in multi-attempt multi-task missions with a limited number of attempts," Reliability Engineering and System Safety, Elsevier, vol. 236(C).

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:gam:jmathe:v:10:y:2022:i:10:p:1644-:d:813548. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.