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, Azzeddine Benyahia

Research output: Contribution to journalArticlepeer-review

24 Scopus citations

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.

Original languageEnglish (US)
Pages (from-to)1-9
Number of pages9
JournalReliability Engineering and System Safety
Volume167
DOIs
StatePublished - Nov 1 2017

All Science Journal Classification (ASJC) codes

  • Safety, Risk, Reliability and Quality
  • Industrial and Manufacturing Engineering

Keywords

  • Joint reliability importance
  • Marginal reliability importance
  • Markov-dependent components
  • System reliability
  • m-Consecutive-k, l-out-of-n system

Fingerprint

Dive into the research topics of 'Reliability and importance measures for m-consecutive-k, l-out-of-n system with non-homogeneous Markov-dependent components'. Together they form a unique fingerprint.

Cite this