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Optimization problems and maintenance policy for a parallel computing system with dependent components

Author

Listed:
  • Junyuan Wang

    (Nanjing University of Aeronautics and Astronautics
    China Jiliang University)

  • Lubing Wang

    (Nanjing University of Aeronautics and Astronautics)

  • Xufeng Zhao

    (Nanjing University of Aeronautics and Astronautics
    Wenzhou University)

  • Zhouqian Miao

    (China Jiliang University)

Abstract

This paper proposes the generalized maintenance policies for a computing system when the copula functions model the interdependency. In this paper, the dependence between the components has been modeled by three copula functions. We deal with random maintenance policies for repairable parallel systems with n dependent or independent components. Firstly, we discuss the maintenance first and last policies for parallel systems composed of dependent components. We consider the random maintenance policy for parallel systems that are dependent and attempt to find the optimal maintenance time by considering the copula framework. The expected cost rate is considered as objective function to minimize. For each policy, the optimal maintenance time that minimizes the mean cost rate is analyzed and discussed numerically. And we study the effects of model parameters on the optimal maintenance policy and compare the copula. The findings of the paper extend the results in the literature from system with independent components to dependent components. Numerical results are presented for components lifetime follow Weilbull distribution. Therefore manager can use the results to formulate the optimal decision problem of their parallel systems with dependent components.

Suggested Citation

  • Junyuan Wang & Lubing Wang & Xufeng Zhao & Zhouqian Miao, 2025. "Optimization problems and maintenance policy for a parallel computing system with dependent components," Annals of Operations Research, Springer, vol. 349(1), pages 339-364, June.
  • Handle: RePEc:spr:annopr:v:349:y:2025:i:1:d:10.1007_s10479-024-06065-7
    DOI: 10.1007/s10479-024-06065-7
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    References listed on IDEAS

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    1. Khac Tuan Huynh & Inma T. Castro & Anne Barros & Christophe Bérenguer, 2012. "Modeling age-based maintenance strategies with minimal repairs for systems subject to competing failure modes due to degradation and shocks," Post-Print hal-00790729, HAL.
    2. Toshio Nakagawa, 2014. "Random Maintenance Policies," Springer Series in Reliability Engineering, Springer, edition 127, number 978-1-4471-6575-0, July.
    3. Xufeng Zhao & Mingchih Chen & Toshio Nakagawa, 2022. "Periodic replacement policies with shortage and excess costs," Annals of Operations Research, Springer, vol. 311(1), pages 469-487, April.
    4. Yang, Li & Ye, Zhi-sheng & Lee, Chi-Guhn & Yang, Su-fen & Peng, Rui, 2019. "A two-phase preventive maintenance policy considering imperfect repair and postponed replacement," European Journal of Operational Research, Elsevier, vol. 274(3), pages 966-977.
    5. Ying-Kui Gu & Chao-Jun Fan & Ling-Qiang Liang & Jun Zhang, 2022. "Reliability calculation method based on the Copula function for mechanical systems with dependent failure," Annals of Operations Research, Springer, vol. 311(1), pages 99-116, April.
    6. Liu, Biyu & Pang, Jie & Yang, Haidong & Zhao, Yilin, 2024. "Optimal condition-based maintenance policy for leased equipment considering hybrid preventive maintenance and periodic inspection," Reliability Engineering and System Safety, Elsevier, vol. 242(C).
    7. Zhao, Xufeng & Chen, Mingchih & Nakagawa, Toshio, 2016. "Replacement policies for a parallel system with shortage and excess costs," Reliability Engineering and System Safety, Elsevier, vol. 150(C), pages 89-95.
    8. Shen, Yilan & Zhang, Xi & Shi, Leyuan, 2022. "Joint optimization of production and maintenance for a serial–parallel hybrid two-stage production system," Reliability Engineering and System Safety, Elsevier, vol. 226(C).
    9. Huynh, K.T. & Castro, I.T. & Barros, A. & Bérenguer, C., 2012. "Modeling age-based maintenance strategies with minimal repairs for systems subject to competing failure modes due to degradation and shocks," European Journal of Operational Research, Elsevier, vol. 218(1), pages 140-151.
    10. Chien, Yu-Hung & Sheu, Shey-Huei, 2006. "Extended optimal age-replacement policy with minimal repair of a system subject to shocks," European Journal of Operational Research, Elsevier, vol. 174(1), pages 169-181, October.
    11. Rommert Dekker & Ralph Wildeman & Frank Duyn Schouten, 1997. "A review of multi-component maintenance models with economic dependence," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 45(3), pages 411-435, October.
    12. Xufeng Zhao & Toshio Nakagawa, 2018. "Advanced Maintenance Policies for Shock and Damage Models," Springer Series in Reliability Engineering, Springer, number 978-3-319-70456-2, July.
    13. Edoardo Berton & Lorenzo Mercuri, 2021. "An Efficient Unified Approach for Spread Option Pricing in a Copula Market Model," Papers 2112.11968, arXiv.org, revised Feb 2023.
    14. Mingchih Chen & Xufeng Zhao & Toshio Nakagawa, 2019. "Replacement policies with general models," Annals of Operations Research, Springer, vol. 277(1), pages 47-61, June.
    15. Xufeng Zhao & Satoshi Mizutani & Mingchih Chen & Toshio Nakagawa, 2022. "Preventive replacement policies for parallel systems with deviation costs between replacement and failure," Annals of Operations Research, Springer, vol. 312(1), pages 533-551, May.
    16. Aseem K. Mishra & Divya Shrivastava & Devesh Tarasia & Abdur Rahim, 2022. "Joint optimization of production scheduling and group preventive maintenance planning in multi-machine systems," Annals of Operations Research, Springer, vol. 316(1), pages 401-444, September.
    17. 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).
    18. Zhao, Xufeng & Nakagawa, Toshio, 2012. "Optimization problems of replacement first or last in reliability theory," European Journal of Operational Research, Elsevier, vol. 223(1), pages 141-149.
    19. 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).
    20. Toshio Nakagawa, 2008. "Advanced Reliability Models and Maintenance Policies," Springer Series in Reliability Engineering, Springer, number 978-1-84800-294-4, July.
    21. Xu, Jun & Liang, Zhenglin & Li, Yan-Fu & Wang, Kaibo, 2021. "Generalized condition-based maintenance optimization for multi-component systems considering stochastic dependency and imperfect maintenance," Reliability Engineering and System Safety, Elsevier, vol. 211(C).
    22. Toshio Nakagawa, 2005. "Maintenance Theory of Reliability," Springer Series in Reliability Engineering, Springer, number 978-1-84628-221-8, July.
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