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New reliability bounds for coherent systems

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  • Y-C Hsieh

    (National Huwei Institute of Technology, Huwei)

Abstract

In 1970, Esary and Proschan proposed simple formulae for the system reliability lower bound and system reliability upper bound. Their formulae of reliability bounds have been classic and have been incorporated into almost all recent textbooks on reliability. In this paper, we decompose a coherent system into several consecutive-k-out-of-n : F(G) systems, and then based upon their exact formulae for system reliabilities, we develop new formulae for both reliability lower bound and reliability upper bound for the coherent system. In addition, we show that the new proposed reliability bounds are superior to those of Esary and Proschan for all coherent systems when the minimal cut/path sets have elements in common. Numerical results are reported, compared and discussed for various systems.

Suggested Citation

  • Y-C Hsieh, 2003. "New reliability bounds for coherent systems," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 54(9), pages 995-1001, September.
    • Handle: RePEc:pal:jorsoc:v:54:y:2003:i:9:d:10.1057_palgrave.jors.2601598
    DOI: 10.1057/palgrave.jors.2601598
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    References listed on IDEAS

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    1. Dharmadhikari, Avinash & Kulathinal, S. B. & Mandrekar, Vidyadhar, 2002. "An algorithm for the estimation of minimal cut and path sets from field failure data," Statistics & Probability Letters, Elsevier, vol. 58(1), pages 1-11, May.
    2. Fu, J. C. & Koutras, M. V., 1995. "Reliability bounds for coherent structures with independent components," Statistics & Probability Letters, Elsevier, vol. 22(2), pages 137-148, February.
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    4. Endre Boros & András Prékopa, 1989. "Closed Form Two-Sided Bounds for Probabilities that At Least r and Exactly r Out of n Events Occur," Mathematics of Operations Research, INFORMS, vol. 14(2), pages 317-342, May.
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    6. Koutras, M. V. & Papastavridis, S. G. & Petakos, K. I., 1996. "Bounds for coherent reliability structures," Statistics & Probability Letters, Elsevier, vol. 26(3), pages 285-292, February.
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    Cited by:

    1. Zaigraev, Alexander & Kaniovski, Serguei, 2010. "Exact bounds on the probability of at least k successes in n exchangeable Bernoulli trials as a function of correlation coefficients," Statistics & Probability Letters, Elsevier, vol. 80(13-14), pages 1079-1084, July.

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