Types of signature analysis in reliability based on Hilbert series

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

LSE Research Online Documents on Economics from London School of Economics and Political Science, LSE Library

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.

JEL-codes: C1 (search for similar items in EconPapers)
Date: 2016-08-11
New Economics Papers: this item is included in nep-cmp
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Published in Journal of Symbolic Computation, 11, August, 2016, 79(1), pp. 140-155. ISSN: 0747-7171

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Persistent link: https://EconPapers.repec.org/RePEc:ehl:lserod:67529

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