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On a parametric model for the mean number of system repairs with applications

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  • Asadi, Majid

Abstract

In reliability engineering and other disciplines, there are many situations, in which one deals with the number of events in a time period that happen as an outcome of a stochastic process. Examples are the number of repairs of a system in an age-based block replacement and the number of repairs for a product sold under warranty in a specific period. In these circumstances, the mean number of failures (repair) plays a crucial role in assessing reliability characteristics and the optimal time of maintenance of the system. In this paper, we study a parametric function for the mean number of repairs of the system that covers a wide range of repair degrees, such as better than minimal repair, minimal repair and worse than minimal repair. Using the suggested model, we propose an approximation for the renewal function in the case that the repairs are complete. We also give applications of the proposed function in age-based block replacement and optimal warranty policy.

Suggested Citation

  • 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).
    • Handle: RePEc:eee:reensy:v:234:y:2023:i:c:s0951832023000522
    DOI: 10.1016/j.ress.2023.109137
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    1. Dheeraj Goyal & Nil Kamal Hazra & Maxim Finkelstein, 2022. "On the Time-Dependent Delta-Shock Model Governed by the Generalized PóLya Process," Methodology and Computing in Applied Probability, Springer, vol. 24(3), pages 1627-1650, September.
    2. Dui, Hongyan & Zhang, Chi & Tian, Tianzi & Wu, Shaomin, 2022. "Different costs-informed component preventive maintenance with system lifetime changes," Reliability Engineering and System Safety, Elsevier, vol. 228(C).
    3. 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).
    4. Chadjiconstantinidis, Stathis, 2023. "Some bounds for the renewal function and the variance of the renewal process," Applied Mathematics and Computation, Elsevier, vol. 436(C).
    5. Wang, Naichao & Hu, Jiawen & Ma, Lin & Xiao, Boping & Liao, Haitao, 2020. "Availability Analysis and Preventive Maintenance Planning for Systems with General Time Distributions," Reliability Engineering and System Safety, Elsevier, vol. 201(C).
    6. Hongzhou Wang & Hoang Pham, 2006. "Reliability and Optimal Maintenance," Springer Series in Reliability Engineering, Springer, number 978-1-84628-325-3, March.
    7. 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).
    8. R. Jiang, 2022. "Two approximations of renewal function for any arbitrary lifetime distribution," Annals of Operations Research, Springer, vol. 311(1), pages 151-165, April.
    9. Zhao, Xufeng & Al-Khalifa, Khalifa N. & Magid Hamouda, Abdel & Nakagawa, Toshio, 2017. "Age replacement models: A summary with new perspectives and methods," Reliability Engineering and System Safety, Elsevier, vol. 161(C), pages 95-105.
    10. Jiang, R., 2010. "A simple approximation for the renewal function with an increasing failure rate," Reliability Engineering and System Safety, Elsevier, vol. 95(9), pages 963-969.
    11. Shi, Yan & Lu, Zhenzhou & Huang, Hongzhong & Liu, Yu & Li, Yanfeng & Zio, Enrico & Zhou, Yicheng, 2022. "A new preventive maintenance strategy optimization model considering lifecycle safety," Reliability Engineering and System Safety, Elsevier, vol. 221(C).
    12. Wang, Jingjing & Miao, Yonghao, 2021. "Optimal preventive maintenance policy of the balanced system under the semi-Markov model," Reliability Engineering and System Safety, Elsevier, vol. 213(C).
    13. Marzieh Hashemi & Majid Asadi, 2021. "Optimal preventive maintenance of coherent systems: A generalized Pólya process approach," IISE Transactions, Taylor & Francis Journals, vol. 53(11), pages 1266-1280, November.
    14. Liu, Peng & Wang, Guanjun, 2022. "Minimal repair models with non-negligible repair time," Reliability Engineering and System Safety, Elsevier, vol. 217(C).
    15. de Jonge, Bram & Scarf, Philip A., 2020. "A review on maintenance optimization," European Journal of Operational Research, Elsevier, vol. 285(3), pages 805-824.
    16. Hidetoshi Konno, 2010. "On the Exact Solution of a Generalized Polya Process," Advances in Mathematical Physics, Hindawi, vol. 2010, pages 1-12, November.
    17. Sotirios Losidis & Konstadinos Politis, 2022. "Bounds for the Renewal Function and Related Quantities," Methodology and Computing in Applied Probability, Springer, vol. 24(4), pages 2647-2660, December.
    18. Richard Barlow & Larry Hunter, 1960. "Optimum Preventive Maintenance Policies," Operations Research, INFORMS, vol. 8(1), pages 90-100, February.
    19. Cha, Ji Hwan & Finkelstein, Maxim, 2016. "New shock models based on the generalized Polya process," European Journal of Operational Research, Elsevier, vol. 251(1), pages 135-141.
    20. Badía, F.G. & Berrade, M.D. & Cha, Ji Hwan & Lee, Hyunju, 2018. "Optimal replacement policy under a general failure and repair model: Minimal versus worse than old repair," Reliability Engineering and System Safety, Elsevier, vol. 180(C), pages 362-372.
    21. Toshio Nakagawa, 2005. "Maintenance Theory of Reliability," Springer Series in Reliability Engineering, Springer, number 978-1-84628-221-8, March.
    22. Jiang, R., 2020. "A novel two-fold sectional approximation of renewal function and its applications," Reliability Engineering and System Safety, Elsevier, vol. 193(C).
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