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Evaluation of reliability bounds by set covering models

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  • Koutras, M. V.
  • Tsitmidelis, S.
  • Zissimopoulos, V.

Abstract

In the present article, we deal with the problem of developing a systematic procedure for evaluating the general reliability bounds developed recently by Fu and Koutras (Statist. Probab. Lett. 22 (1995) 137). More specifically, we prove that, the identification of the optimal bounds can be achieved by transforming the set-theoretic and probabilistic conditions associated with the bounds to an equivalent set covering problem (SC). As a consequence, available solution algorithms for the SC (exact or heuristic) can be exploited to derive very tough approximation intervals for a general system's reliability at very competitive computer times as compared to the respective exact reliability evaluation algorithms.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:stapro:v:61:y:2003:i:2:p:163-175
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    References listed on IDEAS

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    1. 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.
    2. Wim Hordijk & Peter F. Stadler, 1998. "Amplitude Spectra of Fitness Landscapes," Working Papers 98-02-021, Santa Fe Institute.
    3. Beasley, J. E. & Chu, P. C., 1996. "A genetic algorithm for the set covering problem," European Journal of Operational Research, Elsevier, vol. 94(2), pages 392-404, October.
    4. Wim Hordijk & Peter F. Stadler, 1998. "Amplitude Spectra of Fitness Landscapes," Advances in Complex Systems (ACS), World Scientific Publishing Co. Pte. Ltd., vol. 1(01), pages 39-66.
    5. Marshall L. Fisher & Pradeep Kedia, 1990. "Optimal Solution of Set Covering/Partitioning Problems Using Dual Heuristics," Management Science, INFORMS, vol. 36(6), pages 674-688, June.
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