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A linear m-consecutive-k-out-of-n system with sparse d of non-homogeneous Markov-dependent components

Author

Listed:
  • Xiaoyan Zhu
  • Mahmoud Boushaba
  • Abdelmoumene Boulahia
  • Xian Zhao

Abstract

Consider non-homogeneous Markov-dependent components in an m -consecutive- k -out-of- n :F (G) system with sparse d , which consists of n linearly ordered components. Two failed components are consecutive with sparse d if and if there are at most d working components between the two failed components, and the m -consecutive- k -out-of- n :F system with sparse d fails if and if there exist at least m non-overlapping runs of k consecutive failed components with sparse d for 1 ⩽ d ⩽ n − k . We use conditional probability generating function method to derive uniform closed-form formulas for system reliability, marginal reliability importance measure, and joint reliability importance measure for such the F system and the corresponding G system. We present numerical examples to demonstrate the use of the formulas. Along with the work in this article, we summarize the work on consecutive- k systems of Markov-dependent components in terms of system reliability, marginal reliability importance, and joint reliability importance.

Suggested Citation

  • Xiaoyan Zhu & Mahmoud Boushaba & Abdelmoumene Boulahia & Xian Zhao, 2019. "A linear m-consecutive-k-out-of-n system with sparse d of non-homogeneous Markov-dependent components," Journal of Risk and Reliability, , vol. 233(3), pages 328-337, June.
    • Handle: RePEc:sae:risrel:v:233:y:2019:i:3:p:328-337
    DOI: 10.1177/1748006X18776189
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    References listed on IDEAS

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    1. Xiaoyan Zhu & Qingzhu Yao & Way Kuo, 2012. "Patterns of the Birnbaum importance in linear consecutive--out-of- systems," IISE Transactions, Taylor & Francis Journals, vol. 44(4), pages 277-290.
    2. K. K. Kamalja & R. L. Shinde, 2014. "On the Reliability of (n, f, k) and 〈n, f, k〉 Systems," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 43(8), pages 1649-1665, April.
    3. G.Y. Tütüncü & S. Eryilmaz, 2009. "Reliability evaluation of linear consecutive-weighted-k-out-of-n : F System," Post-Print hal-00569519, HAL.
    4. Xiaoyan Zhu & Mahmoud Boushaba, 2017. "A linear weighted system for non-homogeneous Markov-dependent components," IISE Transactions, Taylor & Francis Journals, vol. 49(7), pages 722-736, July.
    5. Zhao, Xian & Wang, Xiaoyue & Sun, Ge, 2015. "Start-up demonstration tests with sparse connection," European Journal of Operational Research, Elsevier, vol. 243(3), pages 865-873.
    6. Barlow, Richard E. & Proschan, Frank, 1975. "Importance of system components and fault tree events," Stochastic Processes and their Applications, Elsevier, vol. 3(2), pages 153-173, April.
    7. Zhu, Xiaoyan & Boushaba, Mahmoud & Coit, David W. & Benyahia, Azzeddine, 2017. "Reliability and importance measures for m-consecutive-k, l-out-of-n system with non-homogeneous Markov-dependent components," Reliability Engineering and System Safety, Elsevier, vol. 167(C), pages 1-9.
    8. Qingzhu Yao & Xiaoyan Zhu & Way Kuo, 2014. "A Birnbaum-importance based genetic local search algorithm for component assignment problems," Annals of Operations Research, Springer, vol. 212(1), pages 185-200, January.
    9. Qingzhu Yao & Xiaoyan Zhu & Way Kuo, 2011. "Heuristics for component assignment problems based on the Birnbaum importance," IISE Transactions, Taylor & Francis Journals, vol. 43(9), pages 633-646.
    10. Xiaoyan Zhu & Way Kuo, 2014. "Importance measures in reliability and mathematical programming," Annals of Operations Research, Springer, vol. 212(1), pages 241-267, January.
    11. Serkan Eryilmaz & G. Yazgi Tutuncu, 2009. "RELIABILITY EVALUATION OF LINEAR CONSECUTIVE-WEIGHTED-k-OUT-OF-n:F SYSTEM," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 26(06), pages 805-816.
    12. Gao, Xueli & Cui, Lirong & Li, Jinlin, 2007. "Analysis for joint importance of components in a coherent system," European Journal of Operational Research, Elsevier, vol. 182(1), pages 282-299, October.
    13. M. Koutras, 1997. "Waiting Time Distributions Associated with Runs of Fixed Length in Two-State Markov Chains," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 49(1), pages 123-139, March.
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    1. Liu, Qiang & Zhang, Hailin, 2022. "Reliability evaluation of weighted voting system based on D–S evidence theory," Reliability Engineering and System Safety, Elsevier, vol. 217(C).

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