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Efficient multicut enumeration of k -out-of- n:F and consecutive k -out-of- n:F systems

Author

Listed:
  • Mohammadi, Fatemeh
  • Saenz-de-Cabezon, Eduardo
  • Wynn, Henry P.

Abstract

We study multiple simultaneous cut events for k-out-of-n:F and linear consecutive k-out-of-n:F systems in which each component has a constant failure probability. We list the multicuts of these systems and describe the structural differences between them. Our approach, based on combinatorial commutative algebra, allows complete enumeration of the sets of multicuts for both kinds of systems. We also analyze the computational issues of multicut enumeration and reliability computations

Suggested Citation

  • Mohammadi, Fatemeh & Saenz-de-Cabezon, Eduardo & Wynn, Henry P., 2018. "Efficient multicut enumeration of k -out-of- n:F and consecutive k -out-of- n:F systems," LSE Research Online Documents on Economics 86460, London School of Economics and Political Science, LSE Library.
    • Handle: RePEc:ehl:lserod:86460
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    File URL: http://eprints.lse.ac.uk/86460/
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    References listed on IDEAS

    as
    1. Borgonovo, Emanuele & Aliee, Hananeh & Glaß, Michael & Teich, Jürgen, 2016. "A new time-independent reliability importance measure," European Journal of Operational Research, Elsevier, vol. 254(2), pages 427-442.
    2. S Eryilmaz, 2010. "Review of recent advances in reliability of consecutive k-out-of-n and related systems," Journal of Risk and Reliability, , vol. 224(3), pages 225-237, September.
    3. Sáenz-de-Cabezón, Eduardo & Wynn, Henry P., 2011. "Computational algebraic algorithms for the reliability of generalized k-out-of-n and related systems," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 82(1), pages 68-78.
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    Cited by:

    1. Marilena Jianu & Leonard Dăuş & Vlad-Florin Drăgoi & Valeriu Beiu, 2023. "The Roots of the Reliability Polynomials of Circular Consecutive- k -out-of- n :F Systems," Mathematics, MDPI, vol. 11(20), pages 1-12, October.

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    More about this item

    Keywords

    k-out-of-n; consecutive k-out-of-n; multiple failures; multi cuts; algebraic reliability; monomial ideals; Hilbert series;
    All these keywords.

    JEL classification:

    • C1 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General

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