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Reliability and availability analysis of standby systems with working vacations and retrial of failed components

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  • Yang, Dong-Yuh
  • Tsao, Chih-Lung

Abstract

In this paper, we consider a repairable system consisting of M primary components, S spare components, and a repairman. In cases where none of the components in the system is failed, the repairman leaves the system for multiple vacations. During a vacation period, the repairman lowers the repair rate rather than halting repairs together. The system does not include a waiting space. If a failed component finds the repairman free upon arrival, then it immediately occupies the repairman and is being repaired. If a failed component does not find a free repairman upon arrival, then it leaves the service area to join the retrial group (orbit) to try again for a repair. For this system, the matrix-analytic method is used to compute the steady-state availability. We develop the reliability function and mean-time-to-failure (MTTF) based on the Laplace transform technique. Numerical examples are given to assess the effects of system parameters on the system reliability, MTTF, and steady-state availability.

Suggested Citation

  • Yang, Dong-Yuh & Tsao, Chih-Lung, 2019. "Reliability and availability analysis of standby systems with working vacations and retrial of failed components," Reliability Engineering and System Safety, Elsevier, vol. 182(C), pages 46-55.
    • Handle: RePEc:eee:reensy:v:182:y:2019:i:c:p:46-55
    DOI: 10.1016/j.ress.2018.09.020
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    Cited by:

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    3. Levitin, Gregory & Finkelstein, Maxim & Dai, Yuanshun, 2021. "Optimization of cyclic preventive replacement in homogeneous warm-standby system with reusable elements exposed to shocks," Reliability Engineering and System Safety, Elsevier, vol. 207(C).
    4. Finkelstein, Maxim & Cha, Ji Hwan & Langston, Amy, 2022. "Optimal preventive switching of components in degrading systems," Reliability Engineering and System Safety, Elsevier, vol. 219(C).
    5. Li, Mingjia & Hu, Linmin & Peng, Rui & Bai, Zhuoxin, 2021. "Reliability modeling for repairable circular consecutive-k-out-of-n: F systems with retrial feature," Reliability Engineering and System Safety, Elsevier, vol. 216(C).
    6. Li, Yan & Zhang, Wei & Liu, Baoliang & Wang, Xiaofeng, 2024. "Availability and maintenance strategy under time-varying environments for redundant repairable systems with PH distributions," Reliability Engineering and System Safety, Elsevier, vol. 246(C).
    7. Wang, Kuo-Hsiung & Wu, Chia-Huang & Yen, Tseng-Chang, 2022. "Comparative cost-benefit analysis of four retrial systems with preventive maintenance and unreliable service station," Reliability Engineering and System Safety, Elsevier, vol. 221(C).
    8. Gao, Shan & Wang, Jinting & Zhang, Jie, 2023. "Reliability analysis of a redundant series system with common cause failures and delayed vacation," Reliability Engineering and System Safety, Elsevier, vol. 239(C).
    9. Li, Mingjia & Hu, Linmin & Wu, Shaomin & Zhao, Bing & Wang, Yan, 2023. "Reliability assessment for consecutive-k-out-of-n: F retrial systems under Poisson shocks," Applied Mathematics and Computation, Elsevier, vol. 448(C).
    10. Wu, Chia-Huang & Yen, Tseng-Chang & Wang, Kuo-Hsiung, 2021. "Availability and Comparison of Four Retrial Systems with Imperfect Coverage and General Repair Times," Reliability Engineering and System Safety, Elsevier, vol. 212(C).
    11. Gao, Shan & Wang, Jinting, 2021. "Reliability and availability analysis of a retrial system with mixed standbys and an unreliable repair facility," Reliability Engineering and System Safety, Elsevier, vol. 205(C).
    12. Levitin, Gregory & Finkelstein, Maxim & Dai, Yuanshun, 2020. "Optimal preventive replacement policy for homogeneous cold standby systems with reusable elements," Reliability Engineering and System Safety, Elsevier, vol. 204(C).
    13. Gabi Hanukov & Shraga Shoval, 2023. "A Model for a Vacation Queuing Policy Considering Server’s Deterioration and Recovery," Mathematics, MDPI, vol. 11(12), pages 1-21, June.
    14. Kumar, Pankaj & Jain, Madhu, 2020. "Reliability analysis of a multi-component machining system with service interruption, imperfect coverage, and reboot," Reliability Engineering and System Safety, Elsevier, vol. 202(C).
    15. Gao, Shan, 2023. "Reliability analysis and optimization for a redundant system with dependent failures and variable repair rates," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 208(C), pages 637-659.
    16. Levitin, Gregory & Finkelstein, Maxim & Dai, Yuanshun, 2021. "Optimal shock-driven switching strategies with elements reuse in heterogeneous warm-standby systems," Reliability Engineering and System Safety, Elsevier, vol. 210(C).
    17. Wang, Yan & Hu, Linmin & Yang, Li & Li, Jing, 2022. "Reliability modeling and analysis for linear consecutive-k-out-of-n: F retrial systems with two maintenance activities," Reliability Engineering and System Safety, Elsevier, vol. 226(C).
    18. Yang, Dong-Yuh & Wu, Chia-Huang, 2021. "Evaluation of the availability and reliability of a standby repairable system incorporating imperfect switchovers and working breakdowns," Reliability Engineering and System Safety, Elsevier, vol. 207(C).
    19. Yu, Xiaoyun & Hu, Linmin & Ma, Mengrao, 2023. "Reliability measures of discrete time k-out-of-n: G retrial systems based on Bernoulli shocks," Reliability Engineering and System Safety, Elsevier, vol. 239(C).

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