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Reliability and availability analysis of a retrial system with mixed standbys and an unreliable repair facility

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  • Gao, Shan
  • Wang, Jinting

Abstract

We study a K-out-of-M+W+C: G mixed standby system with an unreliable repair facility, in which there are M primary operating components, W warm standby components and C cold standby components. The life times of primary components and warm components are assumed to be exponentially distributed random variables. The repair facility is performed preventive maintenance (PM) when it is idle, and it is subject to breakdowns when it repairs a failed component (called as active breakdowns). Upon arrival, a failed component is repaired immediately if the repair facility is found free, and the failed component enters a retrial orbit for seeking repair service after some time later if the repair facility is found busy, under PM, or under repair. By adopting a Markov process approach and solving equations of statistical equilibrium in matrix form, we obtain the system steady-state availability of the machine system, the steady-state availability and the expected busy cycle of the repair facility. Furthermore, we obtain the reliability function and the mean time to the failure (MTTF) of the system by using Laplace transform method. Numerical examples are presented to show the effects of system parameters on the reliability function, steady-state availability and MTTF and to analyze the optimization problem of the cost-effectiveness ratio.

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  • 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).
    • Handle: RePEc:eee:reensy:v:205:y:2021:i:c:s0951832020307407
    DOI: 10.1016/j.ress.2020.107240
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    References listed on IDEAS

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    1. Yonit Barron, 2015. "Group replacement policies for a repairable cold standby system with fixed lead times," IISE Transactions, Taylor & Francis Journals, vol. 47(10), pages 1139-1151, October.
    2. Wu‐Lin Chen, 2018. "System reliability analysis of retrial machine repair systems with warm standbys and a single server of working breakdown and recovery policy," Systems Engineering, John Wiley & Sons, vol. 21(1), pages 59-69, January.
    3. Gao, Shan & Wang, Jinting, 2014. "Performance and reliability analysis of an M/G/1-G retrial queue with orbital search and non-persistent customers," European Journal of Operational Research, Elsevier, vol. 236(2), pages 561-572.
    4. Gupta, Diwakar & Gunalay, Yavuz & Srinivasan, Mandyam M., 2001. "The relationship between preventive maintenance and manufacturing system performance," European Journal of Operational Research, Elsevier, vol. 132(1), pages 146-162, July.
    5. Yonit Barron & Uri Yechiali, 2017. "Generalized control-limit preventive repair policies for deteriorating cold and warm standby Markovian systems," IISE Transactions, Taylor & Francis Journals, vol. 49(11), pages 1031-1049, November.
    6. Barron, Yonit & Frostig, Esther & Levikson, Benny, 2006. "Analysis of R out of N systems with several repairmen, exponential life times and phase type repair times: An algorithmic approach," European Journal of Operational Research, Elsevier, vol. 169(1), pages 202-225, February.
    7. Reza Ahmadi, 2014. "Optimal maintenance scheduling for a complex manufacturing system subject to deterioration," Annals of Operations Research, Springer, vol. 217(1), pages 1-29, June.
    8. 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.
    9. Samira Taleb & Amar Aissani, 2016. "Preventive maintenance in an unreliable M/G/1 retrial queue with persistent and impatient customers," Annals of Operations Research, Springer, vol. 247(1), pages 291-317, December.
    10. Awi Federgruen & Kut C. So, 1990. "Optimal Maintenance Policies for Single-Server Queueing Systems Subject to Breakdowns," Operations Research, INFORMS, vol. 38(2), pages 330-343, April.
    11. Young K. Yoo, 2011. "Operating characteristics of a failure counting group replacement policy," International Journal of Systems Science, Taylor & Francis Journals, vol. 42(3), pages 499-506.
    12. Levitin, Gregory & Amari, Suprasad V., 2010. "Approximation algorithm for evaluating time-to-failure distribution of k-out-of-n system with shared standby elements," Reliability Engineering and System Safety, Elsevier, vol. 95(4), pages 396-401.
    13. Zhang, Tieling & Xie, Min & Horigome, Michio, 2006. "Availability and reliability of k-out-of-(M+N):G warm standby systems," Reliability Engineering and System Safety, Elsevier, vol. 91(4), pages 381-387.
    14. Yonit Barron, 2018. "Group maintenance policies for an R-out-of-N system with phase-type distribution," Annals of Operations Research, Springer, vol. 261(1), pages 79-105, February.
    15. 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.
    16. Levitin, Gregory & Xing, Liudong & Dai, Yuanshun, 2014. "Cold vs. hot standby mission operation cost minimization for 1-out-of-N systems," European Journal of Operational Research, Elsevier, vol. 234(1), pages 155-162.
    17. 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.
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    Cited by:

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    4. 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).
    5. Cheng, Dawei & Lu, Zhong & Zhou, Jia & Liang, Xihui, 2023. "An optimizing maintenance policy for airborne redundant systems operating with faults by using Markov process and NSGA-II," Reliability Engineering and System Safety, Elsevier, vol. 236(C).
    6. 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).
    7. 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).
    8. 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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