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

Author

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  • 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. 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.
    2. 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.
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    4. Xiaoyan Zhu & Way Kuo, 2014. "Importance measures in reliability and mathematical programming," Annals of Operations Research, Springer, vol. 212(1), pages 241-267, January.
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