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

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

Reliability Engineering and System Safety, 2017, vol. 167, issue C, 1-9

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.

Keywords: m-Consecutive-k, l-out-of-n system; Markov-dependent components; System reliability; Marginal reliability importance; Joint reliability importance (search for similar items in EconPapers)
Date: 2017
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Citations: View citations in EconPapers (11)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:reensy:v:167:y:2017:i:c:p:1-9

DOI: 10.1016/j.ress.2017.05.023

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