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Analysis of a multi-component system with failure dependency, N-policy and vacations

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  • He, Gang
  • Wu, Wenqing
  • Zhang, Yuanyuan

Abstract

This paper studies a repairable k-out-of-n:G system with failure dependencies, N-policy and repairman’s multiple vacations. Whenever there are no broken components, the repairman leaves for a vacation which obeys a phase type distribution. Upon returning from his/her vacation, he/she takes another vacation if broken components waiting less than N. This pattern continues until at least N broken components are waiting. By using the Markov process theory, the matrix analytical method and the probabilistic properties of the phase type distribution, the availability and the rate of occurrence of failures of the system are derived in transient and stationary regimes. Further, numerical examples discuss the behavior of the system reliability measures.

Suggested Citation

  • He, Gang & Wu, Wenqing & Zhang, Yuanyuan, 2018. "Analysis of a multi-component system with failure dependency, N-policy and vacations," Operations Research Perspectives, Elsevier, vol. 5(C), pages 191-198.
    • Handle: RePEc:eee:oprepe:v:5:y:2018:i:c:p:191-198
    DOI: 10.1016/j.orp.2018.07.005
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    References listed on IDEAS

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    1. Byun, Ji-Eun & Noh, Hee-Min & Song, Junho, 2017. "Reliability growth analysis of k-out-of-N systems using matrix-based system reliability method," Reliability Engineering and System Safety, Elsevier, vol. 165(C), pages 410-421.
    2. Srinivas R. Chakravarthy & A. Krishnamoorthy & P. V. Ushakumari, 2001. "A k -out-of- n reliability system with an unreliable server and phase type repairs and services: the ( N , T ) policy," International Journal of Stochastic Analysis, Hindawi, vol. 14, pages 1-20, January.
    3. Yu, Haiyang & Chu, Chengbin & Châtelet, Ėric & Yalaoui, Farouk, 2007. "Reliability optimization of a redundant system with failure dependencies," Reliability Engineering and System Safety, Elsevier, vol. 92(12), pages 1627-1634.
    4. Joseph Abate & Ward Whitt, 1995. "Numerical Inversion of Laplace Transforms of Probability Distributions," INFORMS Journal on Computing, INFORMS, vol. 7(1), pages 36-43, February.
    5. Zhang, Yuanyuan & Wu, Wenqing & Tang, Yinghui, 2017. "Analysis of an k-out-of-n:G system with repairman’s single vacation and shut off rule," Operations Research Perspectives, Elsevier, vol. 4(C), pages 29-38.
    6. Madhu Jain & Ritu Gupta, 2012. "Load sharing M-out of-N: G system with non-identical components subject to common cause failure," International Journal of Mathematics in Operational Research, Inderscience Enterprises Ltd, vol. 4(5), pages 586-605.
    7. Khatab, A. & Nahas, N. & Nourelfath, M., 2009. "Availability of K-out-of-N:G systems with non-identical components subject to repair priorities," Reliability Engineering and System Safety, Elsevier, vol. 94(2), pages 142-151.
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    Cited by:

    1. 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.
    2. Sudeep Kumar & Ritu Gupta, 2023. "Reliability analysis of N-policy vacation based FTC system subject to standby switching failures," Operations Research and Decisions, Wroclaw University of Science and Technology, Faculty of Management, vol. 33(2), pages 53-80.
    3. 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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