Journal
IEEE TRANSACTIONS ON RELIABILITY
Volume 64, Issue 1, Pages 83-93Publisher
IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
DOI: 10.1109/TR.2014.2354173
Keywords
Algebraic method; structural importance; monomial ideal; Hilbert function; enriched series systems
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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.
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