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

Xiaoyan Zhu, Mahmoud Boushaba, Abdelmoumene Boulahia and Xian Zhao

Journal of Risk and Reliability, 2019, vol. 233, issue 3, 328-337

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.

Keywords: Marginal reliability importance; joint reliability importance; linear m-consecutive-k-out-of-n system with sparse d; non-homogeneous Markov-dependent components; conditional probability generating function (search for similar items in EconPapers)
Date: 2019
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Citations: View citations in EconPapers (1)

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Persistent link: https://EconPapers.repec.org/RePEc:sae:risrel:v:233:y:2019:i:3:p:328-337

DOI: 10.1177/1748006X18776189

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