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Component importance for linear consecutive‐ k ‐Out‐of‐ n and m ‐Consecutive‐ k ‐Out‐of‐ n systems with exchangeable components

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  • Serkan Eryilmaz

Abstract

Measuring the relative importance of components in a mechanical system is useful for various purposes. In this article, we study Birnbaum and Barlow‐Proschan importance measures for two frequently studied system designs: linear consecutive k ‐out‐of‐ n and m ‐consecutive‐ k ‐out‐of‐ n systems. We obtain explicit expressions for the component importance measures for systems consisting of exchangeable components. We illustrate the results for a system whose components have a Lomax type lifetime distribution. © 2013 Wiley Periodicals, Inc. Naval Research Logistics, 2013

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  • Serkan Eryilmaz, 2013. "Component importance for linear consecutive‐ k ‐Out‐of‐ n and m ‐Consecutive‐ k ‐Out‐of‐ n systems with exchangeable components," Naval Research Logistics (NRL), John Wiley & Sons, vol. 60(4), pages 313-320, June.
    • Handle: RePEc:wly:navres:v:60:y:2013:i:4:p:313-320
    DOI: 10.1002/nav.21535
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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. David A. Butler, 1977. "Technical Note—An Importance Ranking for System Components Based upon Cuts," Operations Research, INFORMS, vol. 25(5), pages 874-879, October.
    3. Iyer, Srinivas, 1992. "The Barlow-Proschan importance and its generalizations with dependent components," Stochastic Processes and their Applications, Elsevier, vol. 42(2), pages 353-359, September.
    4. Xie, Min, 1987. "On some importance measures of system components," Stochastic Processes and their Applications, Elsevier, vol. 25, pages 273-280.
    5. Bent Natvig, 2011. "Measures of Component Importance in Nonrepairable and Repairable Multistate Strongly Coherent Systems," Methodology and Computing in Applied Probability, Springer, vol. 13(3), pages 523-547, September.
    6. Eryilmaz, Serkan & Kan, Cihangir & Akici, Fatih, 2009. "Consecutive k-within-m-out-of-n:F system with exchangeable components," MPRA Paper 26838, University Library of Munich, Germany.
    7. Stathis Chadjiconstantinidis & Markos V. Koutras, 1999. "Measures of component importance for markov chain imbeddable reliability structures," Naval Research Logistics (NRL), John Wiley & Sons, vol. 46(6), pages 613-639, September.
    8. Jorge Navarro & Francisco J. Samaniego & N. Balakrishnan & Debasis Bhattacharya, 2008. "On the application and extension of system signatures in engineering reliability," Naval Research Logistics (NRL), John Wiley & Sons, vol. 55(4), pages 313-327, June.
    9. Hsun-Wen Chang & R.J. Chen & F.K. Hwang, 2002. "The Structural Birnbaum Importance of Consecutive-k Systems," Journal of Combinatorial Optimization, Springer, vol. 6(2), pages 183-197, June.
    10. Jorge Navarro & Rafael Rubio, 2011. "A note on necessary and sufficient conditions for ordering properties of coherent systems with exchangeable components," Naval Research Logistics (NRL), John Wiley & Sons, vol. 58(5), pages 478-489, August.
    11. Natvig, Bent, 1979. "A suggestion of a new measure of importance of system components," Stochastic Processes and their Applications, Elsevier, vol. 9(3), pages 319-330, December.
    12. Mingjian Zuo & Way Kuo, 1990. "Design and performance analysis of consecutive‐K‐out‐of‐n structure," Naval Research Logistics (NRL), John Wiley & Sons, vol. 37(2), pages 203-230, April.
    13. Andrews, J.D., 2008. "Birnbaum and criticality measures of component contribution to the failure of phased missions," Reliability Engineering and System Safety, Elsevier, vol. 93(12), pages 1861-1866.
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