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Modeling of machine interference problem with unreliable repairman and standbys imperfect switchover

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  • Ke, Jau-Chuan
  • Liu, Tzu-Hsin
  • Yang, Dong-Yuh

Abstract

This investigation is concerned with an M/G/1 machine interference problem with imperfect switchover of standbys, in which an unreliable repairman maintains a group of machines. An unreliable repairman means that the repairman is typically subject to unpredictable breakdowns. The time between two consecutive breakdowns follows an exponential distribution, and recovery time of the unreliable repairman follows a general distribution. The lifetime of operating/standby machines and the repair time of failed machines are exponentially and generally distributed, respectively. Using the method of supplementary variable, the stationary probability distribution is obtained. We develop some performance measures and system reliability indices. Furthermore, the cost effectiveness maximization is also discussed. Finally, a cost model is proposed to find the optimal numbers of operating and standby substations, which minimize the average cost per unit time.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:reensy:v:174:y:2018:i:c:p:12-18
    DOI: 10.1016/j.ress.2018.01.013
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    References listed on IDEAS

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    1. Haque, Lani & Armstrong, Michael J., 2007. "A survey of the machine interference problem," European Journal of Operational Research, Elsevier, vol. 179(2), pages 469-482, June.
    2. 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.
    3. M. Jain & Sulekha Rani, 2013. "Availability analysis for repairable system with warm standby, switching failure and reboot delay," International Journal of Mathematics in Operational Research, Inderscience Enterprises Ltd, vol. 5(1), pages 19-39.
    4. Levitin, Gregory & Jia, Heping & Ding, Yi & Song, Yonghua & Dai, Yuanshun, 2017. "Reliability of multi-state systems with free access to repairable standby elements," Reliability Engineering and System Safety, Elsevier, vol. 167(C), pages 192-197.
    5. 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.
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    Citations

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    Cited by:

    1. 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.
    2. Jain, Madhu & Kumar, Pankaj & Singh, Mayank & Gupta, Ritu, 2024. "Cost optimization and reliability analysis of fault tolerant system with service interruption and reboot," Reliability Engineering and System Safety, Elsevier, vol. 249(C).
    3. 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).
    4. Zhu, Tiefeng, 2020. "Reliability estimation for two-parameter Weibull distribution under block censoring," Reliability Engineering and System Safety, Elsevier, vol. 203(C).
    5. 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).
    6. 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).
    7. 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).

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