Types of signature analysis in reliability based on Hilbert series. (March 2017)

• Record Type: Journal Article
• Authors: Mohammadi, Fatemeh; Sáenz-de-Cabezón, Eduardo; Wynn, Henry P.
• Is Part Of: Journal of symbolic computation. Volume 79(2017)Part 1
• Page Start: 140
• Page End: 155
• Publication Date: 2017-03
• Subjects: Algebraic reliability -- Signature analysis -- Monomial ideals -- Hilbert series -- lcm-filtration; Mathematics -- Data processing -- Periodicals; Numerical analysis -- Data processing -- Periodicals; Automatic programming (Computer science) -- Periodicals; Mathématiques -- Informatique -- Périodiques; Analyse numérique -- Informatique -- Périodiques; Programmation automatique -- Périodiques; Automatic programming (Computer science); Mathematics -- Data processing; Numerical analysis -- Data processing; Periodicals; Electronic journals; 510.285
• DOI: 10.1016/j.jsc.2016.08.010
• Languages: English
• ISSNs: 0747-7171

Abstract

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.