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Optimal preventive maintenance for repairable products with three types of failures sold under a renewable hybrid FRW/PRW policy

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  • Safaei, Fatemeh
  • Taghipour, Sharareh

Abstract

This paper proposes the optimal preventive maintenance policy for products under a warranty policy, which combines fully renewable free replacement warranty (FRW) and pro-rata warranty (PRW). Replacement age is divided into three separate periods: within FRW, during PRW and post-warranty. Moreover, it is assumed the product is subject to three types of failures arriving according to a non-homogeneous Poisson process. The first type can be fixed by minimal repair, and the third type is a catastrophic failure that results in product replacement. If the failure is of the second type and the product is at age t, it is either minimally repaired with probability p(t) or replaced by a new one with probability 1−p(t). The aim of this study is to develop the long-run expected cost rate for both warranted and non-warranted repairable products as well as to derive the optimal replacement time such that the incurred costs are minimized. The proposed approach provides valuable information for the product customers, managers, or engineers to make better decisions about the preventive replacement time of such products. The proposed model covers some preventive maintenance policies in the existing literature. Numerical computations are also performed to investigate the effect of the model’s parameters on the optimal solutions. Eventually, a real-life application is discussed to demonstrate the applicability of the proposed policy.

Suggested Citation

  • 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).
    • Handle: RePEc:eee:reensy:v:223:y:2022:i:c:s0951832022000679
    DOI: 10.1016/j.ress.2022.108392
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    1. Shafiee, Mahmood & Chukova, Stefanka, 2013. "Maintenance models in warranty: A literature review," European Journal of Operational Research, Elsevier, vol. 229(3), pages 561-572.
    2. Azimpoor, Samareh & Taghipour, Sharareh, 2021. "Joint inspection and product quality optimization for a system with delayed failure," Reliability Engineering and System Safety, Elsevier, vol. 215(C).
    3. 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.
    4. Zhou, Taotao & Droguett, Enrique López & Modarres, Mohammad, 2020. "A common cause failure model for components under age-related degradation," Reliability Engineering and System Safety, Elsevier, vol. 195(C).
    5. Xiaolin Wang & Chun Su, 2016. "A two-dimensional preventive maintenance strategy for items sold with warranty," International Journal of Production Research, Taylor & Francis Journals, vol. 54(19), pages 5901-5915, October.
    6. Zhao, Xiujie & He, Shuguang & Xie, Min, 2018. "Utilizing experimental degradation data for warranty cost optimization under imperfect repair," Reliability Engineering and System Safety, Elsevier, vol. 177(C), pages 108-119.
    7. Yun, Won Young & Murthy, D.N.P. & Jack, N., 2008. "Warranty servicing with imperfect repair," International Journal of Production Economics, Elsevier, vol. 111(1), pages 159-169, January.
    8. 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.
    9. Madhu Jain & Ritu Gupta, 2014. "Availability analysis of repairable redundant system with three types of failures subject to common cause failure," International Journal of Mathematics in Operational Research, Inderscience Enterprises Ltd, vol. 6(3), pages 271-296.
    10. Murthy, D. N. P. & Djamaludin, I., 2002. "New product warranty: A literature review," International Journal of Production Economics, Elsevier, vol. 79(3), pages 231-260, October.
    11. Wang, Jinting & Zhou, Zhuang & Peng, Hao, 2017. "Flexible decision models for a two-dimensional warranty policy with periodic preventive maintenance," Reliability Engineering and System Safety, Elsevier, vol. 162(C), pages 14-27.
    12. Chun Su & Xiaotian Yang, 2021. "Two-stage renewing warranty policy with the threshold of maintenance times," International Journal of Production Research, Taylor & Francis Journals, vol. 59(20), pages 6210-6222, October.
    13. 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.
    14. Chien, Yu-Hung & Zhang, Zhe George & Yin, Xiaoling, 2019. "On optimal preventive-maintenance policy for generalized Polya process repairable products under free-repair warranty," European Journal of Operational Research, Elsevier, vol. 279(1), pages 68-78.
    15. Safaei, Fatemeh & Ahmadi, Jafar & Balakrishnan, N., 2019. "A repair and replacement policy for repairable systems based on probability and mean of profits," Reliability Engineering and System Safety, Elsevier, vol. 183(C), pages 143-152.
    16. 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).
    17. Yang, Duo & He, Zhen & He, Shuguang, 2016. "Warranty claims forecasting based on a general imperfect repair model considering usage rate," Reliability Engineering and System Safety, Elsevier, vol. 145(C), pages 147-154.
    18. 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.
    19. Yeh, Ruey Huei & Chen, Ming-Yuh & Lin, Chen-Yi, 2007. "Optimal periodic replacement policy for repairable products under free-repair warranty," European Journal of Operational Research, Elsevier, vol. 176(3), pages 1678-1686, February.
    20. Erik Tryggvi Striz Bjarnason & Sharareh Taghipour, 2016. "Periodic inspection frequency and inventory policies for a -out-of- system," IISE Transactions, Taylor & Francis Journals, vol. 48(7), pages 638-650, July.
    21. Safaei, Fatemeh & Ahmadi, Jafar & Taghipour, Sharareh, 2022. "A maintenance policy for a k-out-of-n system under enhancing the system’s operating time and safety constraints, and selling the second-hand components," Reliability Engineering and System Safety, Elsevier, vol. 218(PA).
    22. Olde Keizer, Minou C.A. & Flapper, Simme Douwe P. & Teunter, Ruud H., 2017. "Condition-based maintenance policies for systems with multiple dependent components: A review," European Journal of Operational Research, Elsevier, vol. 261(2), pages 405-420.
    23. Hao Peng & Qianmei Feng & David Coit, 2010. "Reliability and maintenance modeling for systems subject to multiple dependent competing failure processes," IISE Transactions, Taylor & Francis Journals, vol. 43(1), pages 12-22.
    24. Peng Tong & Xuefeng Song & Liu Zixian, 2017. "A maintenance strategy for two-dimensional extended warranty based on dynamic usage rate," International Journal of Production Research, Taylor & Francis Journals, vol. 55(19), pages 5743-5759, October.
    25. J. Park & T. P. Seager & P. S. C. Rao & M. Convertino & I. Linkov, 2013. "Integrating Risk and Resilience Approaches to Catastrophe Management in Engineering Systems," Risk Analysis, John Wiley & Sons, vol. 33(3), pages 356-367, March.
    26. Wu, Chin-Chun & Chou, Chao-Yu & Huang, Chikong, 2007. "Optimal burn-in time and warranty length under fully renewing combination free replacement and pro-rata warranty," Reliability Engineering and System Safety, Elsevier, vol. 92(7), pages 914-920.
    27. de Jonge, Bram & Scarf, Philip A., 2020. "A review on maintenance optimization," European Journal of Operational Research, Elsevier, vol. 285(3), pages 805-824.
    28. 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.
    29. Chien, Yu-Hung, 2019. "The optimal preventive-maintenance policy for a NHPBP repairable system under free-repair warranty," Reliability Engineering and System Safety, Elsevier, vol. 188(C), pages 444-453.
    30. 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.
    31. Safaei, Fatemeh & Châtelet, Eric & Ahmadi, Jafar, 2020. "Optimal age replacement policy for parallel and series systems with dependent components," Reliability Engineering and System Safety, Elsevier, vol. 197(C).
    32. 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.
    33. Hajipour, Yassin & Taghipour, Sharareh, 2016. "Non-periodic inspection optimization of multi-component and k-out-of-m systems," Reliability Engineering and System Safety, Elsevier, vol. 156(C), pages 228-243.
    34. 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).
    35. Aven, Terje & Castro, I.T., 2008. "A minimal repair replacement model with two types of failure and a safety constraint," European Journal of Operational Research, Elsevier, vol. 188(2), pages 506-515, July.
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    2. Asadi, Majid, 2023. "On a parametric model for the mean number of system repairs with applications," Reliability Engineering and System Safety, Elsevier, vol. 234(C).
    3. Liang, Xiaojun & Cui, Lirong & Wang, Ruiting, 2024. "Non-renewable warranty cost analysis for dependent series configuration with distinct warranty periods," Reliability Engineering and System Safety, Elsevier, vol. 246(C).
    4. Safaei, Fatemeh & Taghipour, Sharareh, 2024. "Integrated degradation-based burn-in and maintenance model for heterogeneous and highly reliable items," Reliability Engineering and System Safety, Elsevier, vol. 244(C).
    5. Li, Yao & He, Yihai & Liao, Ruoyu & Zheng, Xin & Dai, Wei, 2022. "Integrated predictive maintenance approach for multistate manufacturing system considering geometric and non-geometric defects of products," Reliability Engineering and System Safety, Elsevier, vol. 228(C).

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