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Types of signature analysis in reliability based on Hilbert series

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

Abstract

The present paper studies multiple failure and signature analysis of coherent systems using the theory of monomial ideals. While system reliability has been studied using Hilbert series of monomial ideals, this is not enough to understand in a deeper sense the ideal structure features that reflect the behavior of the system under multiple simultaneous failures. Therefore, we introduce the lcm-filtration of a monomial ideal, and we study the Hilbert series and resolutions of the corresponding ideals. Given a monomial ideal, we explicitly compute the resolutions for all ideals in the associated lcm-filtration, and we apply this to study coherent systems. Some computational results are shown in examples to demonstrate the usefulness of this approach and the computational issues that arise. We also study the failure distribution from a statistical point of view by means of the algebraic tools described.

Suggested Citation

  • Mohammadi, Fatemeh & Saenz-de-Cabezon, Eduardo & Wynn, Henry P., 2016. "Types of signature analysis in reliability based on Hilbert series," LSE Research Online Documents on Economics 67529, London School of Economics and Political Science, LSE Library.
    • Handle: RePEc:ehl:lserod:67529
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    File URL: http://eprints.lse.ac.uk/67529/
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    References listed on IDEAS

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    1. Ling, K. D., 1988. "On binomial distributions of order k," Statistics & Probability Letters, Elsevier, vol. 6(4), pages 247-250, March.
    2. 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.
    3. Francisco J. Samaniego, 2007. "System Signatures and their Applications in Engineering Reliability," International Series in Operations Research and Management Science, Springer, number 978-0-387-71797-5, January.
    4. Sáenz-de-Cabezón, E. & Wynn, H.P., 2014. "Measuring the robustness of a network using minimal vertex covers," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 104(C), pages 82-94.
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    • C1 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General

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