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Reliability bounds for coherent structures with independent components

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  • Fu, J. C.
  • Koutras, M. V.

Abstract

In this article a minimal path upper bound and a minimal cut lower bound on the reliability of a coherent system are derived for the case of independent (but not necessarily identical) components. Coupling these bounds with the classical Esary and Proschan's (1963) bounds, some limit theorems are established for the reliability of large coherent systems under quite general conditions.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:stapro:v:22:y:1995:i:2:p:137-148
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    References listed on IDEAS

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    1. Stavros Papastavridis & Markos Koutras, 1992. "Consecutive k-out-of-n systems with maintenance," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 44(4), pages 605-612, December.
    2. James Fu & Markos Koutras, 1994. "Poisson approximations for 2-dimensional patterns," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 46(1), pages 179-192, March.
    3. M. Chao & James Fu, 1989. "A limit theorem of certain repairable systems," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 41(4), pages 809-818, December.
    4. Markos V. Koutras & Stavros G. Papastavridis, 1993. "Application of the stein‐chen method for bounds and limit theorems in the reliability of coherent structures," Naval Research Logistics (NRL), John Wiley & Sons, vol. 40(5), pages 617-631, August.
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    Cited by:

    1. Michael V. Boutsikas & Markos V. Koutras, 2002. "On a class of multiple failure mode systems," Naval Research Logistics (NRL), John Wiley & Sons, vol. 49(2), pages 167-185, March.
    2. Kordecki, Wojciech, 1997. "Reliability bounds for multistage structures with independent components," Statistics & Probability Letters, Elsevier, vol. 34(1), pages 43-51, May.
    3. Koutras, M. V. & Tsitmidelis, S. & Zissimopoulos, V., 2003. "Evaluation of reliability bounds by set covering models," Statistics & Probability Letters, Elsevier, vol. 61(2), pages 163-175, January.
    4. 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.
    5. Michael V. Boutsikas & Markos V. Koutras, 2000. "Reliability Approximation for Markov Chain Imbeddable Systems," Methodology and Computing in Applied Probability, Springer, vol. 2(4), pages 393-411, December.

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