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Reliability and Residual Life of Cold Standby Systems

Author

Listed:
  • Longlong Liu

    (Department of Basic Courses, Naval University of Engineering, Wuhan 430033, China)

  • Xiaochuan Ai

    (Department of Basic Courses, Naval University of Engineering, Wuhan 430033, China)

  • Jun Wu

    (School of Electronic Engineering, Naval University of Engineering, Wuhan 430033, China)

Abstract

In this study, we conduct a reliability characterisation study of cold standby systems. Utilising synthetic rectangular formulas and cold preparedness equivalent models for cold standby systems, we analyse the lifetimes of several typical configurations, including series, parallel, and k/n:m voting systems. This study proposes system equivalent models for various types of cold standby systems, all composed of components that follow the same exponential distribution. We use the equivalent model to determine the optimal timing for the use of cold spares and derive the reliability function and residual lifetime function for each type of system. To demonstrate the validity of our model, the Monte Carlo simulation is strategically designed based on the system failure rate function. The experimental results are then compared with those obtained from the numerical model, highlighting that the numerical method incurs a lower time cost.

Suggested Citation

  • Longlong Liu & Xiaochuan Ai & Jun Wu, 2024. "Reliability and Residual Life of Cold Standby Systems," Mathematics, MDPI, vol. 12(10), pages 1-22, May.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:10:p:1540-:d:1395296
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    References listed on IDEAS

    as
    1. Xiaoyu Zhang & Yiying Zhang & Rui Fang, 2020. "Allocations of cold standbys to series and parallel systems with dependent components," Applied Stochastic Models in Business and Industry, John Wiley & Sons, vol. 36(3), pages 432-451, May.
    2. Yashi Wang, 2016. "Conditional k-out-of-n systems with a cold standby component," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 45(21), pages 6253-6262, November.
    3. Achintya Roy & Nitin Gupta, 2021. "Reliability function of k-out-of-n system equipped with two cold standby components," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 50(24), pages 5759-5778, November.
    4. Ahmad Mirjalili & Mohammad Khanjari Sadegh & Majid Rezaei, 2017. "A note on the mean residual life of a coherent system with a cold standby component," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 46(20), pages 10348-10358, October.
    5. Zhipeng Weng & Jinghua Zhou & Zhengdong Zhan, 2022. "Reliability Evaluation of Standalone Microgrid Based on Sequential Monte Carlo Simulation Method," Energies, MDPI, vol. 15(18), pages 1-20, September.
    6. Eryilmaz, Serkan, 2012. "On the mean residual life of a k-out-of-n:G system with a single cold standby component," European Journal of Operational Research, Elsevier, vol. 222(2), pages 273-277.
    7. Li, Chen & Li, Xiaohu, 2023. "On k-out-of-n systems with homogeneous components and one independent cold standby redundancy," Statistics & Probability Letters, Elsevier, vol. 203(C).
    8. Wang, Chaonan & Xing, Liudong & Amari, Suprasad V., 2012. "A fast approximation method for reliability analysis of cold-standby systems," Reliability Engineering and System Safety, Elsevier, vol. 106(C), pages 119-126.
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