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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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    1. Kuo, Ching-Chang & Ke, Jau-Chuan, 2016. "Comparative analysis of standby systems with unreliable server and switching failure," Reliability Engineering and System Safety, Elsevier, vol. 145(C), pages 74-82.
    2. Lee, Yutae, 2017. "Comments on “Comparative analysis of standby systems with unreliable server and switching failure†[Relib Eng Syst Saf 2016; 145: 74–82]," Reliability Engineering and System Safety, Elsevier, vol. 160(C), pages 98-100.
    3. Yuan, Li & Xu, Jian, 2011. "An optimal replacement policy for a repairable system based on its repairman having vacations," Reliability Engineering and System Safety, Elsevier, vol. 96(7), pages 868-875.
    4. Ke, Jau-Chuan & Liu, Tzu-Hsin & Yang, Dong-Yuh, 2018. "Modeling of machine interference problem with unreliable repairman and standbys imperfect switchover," Reliability Engineering and System Safety, Elsevier, vol. 174(C), pages 12-18.
    5. Shweta Upadhyaya, 2016. "Queueing systems with vacation: an overview," International Journal of Mathematics in Operational Research, Inderscience Enterprises Ltd, vol. 9(2), pages 167-213.
    6. Tao Li & Liyuan Zhang & Shan Gao, 2016. "Performance of an M/M/1 Retrial Queue with Working Vacation Interruption and Classical Retrial Policy," Advances in Operations Research, Hindawi, vol. 2016, pages 1-9, May.
    7. Jeongsim Kim & Bara Kim, 2016. "A survey of retrial queueing systems," Annals of Operations Research, Springer, vol. 247(1), pages 3-36, December.
    8. Liu, Baoliang & Cui, Lirong & Wen, Yanqing & Shen, Jingyuan, 2015. "A cold standby repairable system with working vacations and vacation interruption following Markovian arrival process," Reliability Engineering and System Safety, Elsevier, vol. 142(C), pages 1-8.
    9. Yu, Miaomiao & Tang, Yinghui & Liu, Liping & Cheng, Jiang, 2013. "A phase-type geometric process repair model with spare device procurement and repairman’s multiple vacations," European Journal of Operational Research, Elsevier, vol. 225(2), pages 310-323.
    10. A. Krishnamoorthy & P. Ushakumari, 1999. "Reliability of ak-out-of-n system with repair and retrial of failed units," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 7(2), pages 293-304, December.
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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. 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).
    5. 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).
    6. 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.
    7. 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).
    8. 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).
    9. 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.
    10. 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).
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    12. 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).
    13. 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).
    14. 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).
    15. 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).
    16. 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).
    17. 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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