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Reliability and importance measures for m-consecutive-k, l-out-of-n system with non-homogeneous Markov-dependent components

Author

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  • Zhu, Xiaoyan
  • Boushaba, Mahmoud
  • Coit, David W.
  • Benyahia, Azzeddine

Abstract

We study an m-consecutive-k, l-out-of-n system with non-homogenous Markov-dependent components. The m-consecutive-k, l-out-of-n:F system fails if and only if there are at least m runs of k consecutive failed components and each of the runs may have at most l components overlapping with the previous run of k consecutive failed components. Using probability generating function method, we derive closed-form formulas for the reliability of the m-consecutive-k, l-out-of-n:F system, the marginal reliability importance measure of a single component, and the joint reliability importance measure of two or more components when components are non-homogenous Markov-dependent. We also extend these results into an analogous m-consecutive-k, l-out-of-n:G system, which is developed by considering consecutive working components. The results can be simplified to the situations of the homogenous Markov-dependent components and the independent components. We present a practical application in quality control and related numerical examples that demonstrate the use of derived formulas and provide the insights on the m-consecutive-k, l-out-of-n system and the importance measures.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:reensy:v:167:y:2017:i:c:p:1-9
    DOI: 10.1016/j.ress.2017.05.023
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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. Zhu, Xiaoyan & Fu, Yuqiang & Yuan, Tao & Wu, Xinying, 2017. "Birnbaum importance based heuristics for multi-type component assignment problems," Reliability Engineering and System Safety, Elsevier, vol. 165(C), pages 209-221.
    3. Do Van, Phuc & Barros, Anne & Bérenguer, Christophe, 2008. "Reliability importance analysis of Markovian systems at steady state using perturbation analysis," Reliability Engineering and System Safety, Elsevier, vol. 93(11), pages 1605-1615.
    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. Yun, Won-Young & Kim, Gui-Rae & Yamamoto, Hisashi, 2007. "Economic design of a circular consecutive-k-out-of-n:F system with (k-1)-step Markov dependence," Reliability Engineering and System Safety, Elsevier, vol. 92(4), pages 464-478.
    6. 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.
    7. 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.
    8. Xiaoyan Zhu & Way Kuo, 2014. "Importance measures in reliability and mathematical programming," Annals of Operations Research, Springer, vol. 212(1), pages 241-267, January.
    9. Contini, Sergio & Matuzas, Vaidas, 2011. "New methods to determine the importance measures of initiating and enabling events in fault tree analysis," Reliability Engineering and System Safety, Elsevier, vol. 96(7), pages 775-784.
    10. Do Van, Phuc & Barros, Anne & Bérenguer, Christophe, 2010. "From differential to difference importance measures for Markov reliability models," European Journal of Operational Research, Elsevier, vol. 204(3), pages 513-521, August.
    11. Serkan Eryilmaz, 2012. "m-consecutive-k-out-of-n:F system with overlapping runs: signature-based reliability analysis," International Journal of Operational Research, Inderscience Enterprises Ltd, vol. 15(1), pages 64-73.
    12. Dutuit, Yves & Rauzy, Antoine, 2015. "On the extension of Importance Measures to complex components," Reliability Engineering and System Safety, Elsevier, vol. 142(C), pages 161-168.
    13. 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.
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    3. 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).
    4. Yin, Juan & Cui, Lirong, 2021. "Reliability for consecutive-k-out-of-n: F systems with shared components between adjacent subsystems," Reliability Engineering and System Safety, Elsevier, vol. 210(C).
    5. Eryilmaz, Serkan & Ozkut, Murat, 2020. "Optimization problems for a parallel system with multiple types of dependent components," Reliability Engineering and System Safety, Elsevier, vol. 199(C).
    6. 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.
    7. Eryilmaz, Serkan, 2020. "Age-based preventive maintenance for coherent systems with applications to consecutive-k-out-of-n and related systems," Reliability Engineering and System Safety, Elsevier, vol. 204(C).
    8. Yin, Juan & Cui, Lirong & Balakrishnan, Narayanaswamy, 2022. "Reliability of consecutive-(k,l)-out-of-n: F systems with shared components under non-homogeneous Markov dependence," Reliability Engineering and System Safety, Elsevier, vol. 224(C).
    9. Zhang, Nan & Fouladirad, Mitra & Barros, Anne, 2019. "Reliability-based measures and prognostic analysis of a K-out-of-N system in a random environment," European Journal of Operational Research, Elsevier, vol. 272(3), pages 1120-1131.
    10. Endharta, Alfonsus Julanto & Yun, Won Young & Ko, Young Myoung, 2018. "Reliability evaluation of circular k-out-of-n: G balanced systems through minimal path sets," Reliability Engineering and System Safety, Elsevier, vol. 180(C), pages 226-236.
    11. Lin, Cong & Zeng, Zhaoyang & Zhou, Yan & Xu, Ming & Ren, Zhanyong, 2019. "A lower bound of reliability calculating method for lattice system with non-homogeneous components," Reliability Engineering and System Safety, Elsevier, vol. 188(C), pages 36-46.

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