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The Structural Birnbaum Importance of Consecutive-k Systems

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Abstract

This paper is concerned with three types of structural Birnbaum importance of components in a consecutive-k system. We accomplish the following three tasks:

(i) Survey existing results, including pointing out results claimed but proofs are incomplete.

(ii) Give some new results and useful lemmas.

(iii) Observe what are still provable and what are not with the help of extensive computing.

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References

  • Z.W. Birnbaum, “On the importance of different components in a multi component system,” in Multivariate Analysis II, P.R. Krishnaiah (Ed.), Academic: NY, 1969, pp. 581–592.

    Google Scholar 

  • G.J. Chang, L. Cui, and F.K. Hwang, “New comparisons in Birnbaum importance for the consecutive-k-out-of-n system,” Prob. Eng. Inform. Sci., vol. 13, pp. 187–192, 1999; for corrigenda, see vol. 14, p. 405, 2000.

    Google Scholar 

  • C. Derman, G.J. Lieberman, and S.M. Ross, “On the consecutive-k-out-of-n:F system,” IEEE Trans. Rel., vol. 31, pp. 57–63, 1982.

    Google Scholar 

  • D.Z. Du and F.K. Hwang, “Optimal consecutive-2-out-of-n systems,” Math. Oper. Res., vol. 11, pp. 187–191, 1986.

    Google Scholar 

  • F.K. Hwang, “Fast solutions for consecutive-k-out-of-n:F system,” IEEE Trans. Rel., vol. R-31, pp. 447–448, 1982.

    Google Scholar 

  • W. Kuo, W. Zhang, and M. Zuo, “A consecutive-k-out-of-n:G system: The mirror image of a consecutive-k-outof-n:F system,” IEEE Trans. Rel., vol. 39, pp. 244–253, 1990.

    Google Scholar 

  • F.H. Lin, W. Kuo, and F.K. Hwang, “Structural importance of consecutive-k-out-of-n systems,” Oper. Res. Lett., vol. 25, pp. 101–107, 1999.

    Google Scholar 

  • D.M. Malon, “Optimal consecutive-2-out-of-n:F component sequencing,” IEEE Trans. Rel., vol. R33, pp. 414–418, 1984.

    Google Scholar 

  • D.M. Malon, “Optimal consecutive-k-out-of-n:F component sequencing,” IEEE Trans. Rel., vol. R34, pp. 46–49, 1985.

    Google Scholar 

  • Y.L. Tong, “A rearrangement inequality for the longest run, with an application to network reliability,” J. Appl. Prob., vol. 22, pp. 386–393, 1985.

    Google Scholar 

  • R.S. Zakaria, H.A. David, and W. Kuo, “The non monotonicity of component importance measures in linear consecutive-k-out-of-n systems,” IIE Trans., vol. 24, pp. 147–154, 1992.

    Google Scholar 

  • M. Zuo, “Reliability and component importance of a consecutive-k-out-of-n system,” Microelec. Rel., vol. 33, pp. 243–258, 1993.

    Google Scholar 

  • M. Zuo and W. Kuo, “Design and performance analysis of consecutive-k-out-of-n structure,” Naval Res. Logist., vol. 37, pp. 203–230, 1990.

    Google Scholar 

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Chang, HW., Chen, R. & Hwang, F. The Structural Birnbaum Importance of Consecutive-k Systems. Journal of Combinatorial Optimization 6, 183–197 (2002). https://doi.org/10.1023/A:1013803728112

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  • DOI: https://doi.org/10.1023/A:1013803728112

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