Types of signature analysis in reliability based on Hilbert series

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 and signature. 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.
Type de document :
Communication dans un congrès
MEGA'2015 (Special Issue), Jun 2015, Trento, Italy
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https://hal.inria.fr/hal-01350785
Contributeur : Alain Monteil <>
Soumis le : lundi 1 août 2016 - 17:00:37
Dernière modification le : samedi 16 décembre 2017 - 07:18:04

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  • HAL Id : hal-01350785, version 1
  • ARXIV : 1510.04427

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Fatemeh Mohammadi, Eduardo Sáenz-De-Cabezón, Henry P. Wynn. Types of signature analysis in reliability based on Hilbert series. MEGA'2015 (Special Issue), Jun 2015, Trento, Italy. 〈hal-01350785〉

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