Hilbert Functions in Design for Reliability

Author

Saenz-de-Cabezon, Eduardo ; Wynn, Henry P.

Author_Institution

Math. & Comput. Sci. Dept., Univ. de La Rioja, Logrono, Spain

Volume

64

Issue

1

fYear

2015

fDate

Mar-15

Firstpage

83

Lastpage

93

Abstract

The algebraic approach to the analysis of system reliability associates an algebraic object, a monomial ideal, to a coherent system (CS), and studies the reliability of the system using the Hilbert series of the monomial ideal. New capabilities of the algebraic method in system design are shown, in particular related to enumeration of working states. The algebraic method should be a useful tool in reliability, both for performing different computations on system features, and to study the structure of systems.

Keywords

Hilbert transforms; algebra; reliability theory; Hilbert functions; Hilbert series; algebraic approach; algebraic method; algebraic object; coherent system; design for reliability; monomial ideal; system design; system reliability analysis; system structure; Algebra; Cascading style sheets; Generators; Polynomials; Reliability engineering; System analysis and design; Algebraic method; Hilbert function; enriched series systems; monomial ideal; structural importance;

fLanguage

English

Journal_Title

Reliability, IEEE Transactions on

Publisher

ieee

ISSN

0018-9529

Type

jour

DOI

10.1109/TR.2014.2354173

Filename

6899708