Computational algebraic algorithms for the reliability of generalized \(k\)-out-of-\(n\) and related systems

DOI10.1016/j.matcom.2010.07.028zbMath1242.65022OpenAlexW2053254496WikidataQ60246176 ScholiaQ60246176MaRDI QIDQ417960

Eduardo Sáenz-de-Cabezón, Henry P. Wynn

Publication date: 14 May 2012

Published in: Mathematics and Computers in Simulation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.matcom.2010.07.028

zbMATH Keywords

numerical examplesmonomial idealsminimal free resolutionsk-out-of-n systemssystem reliabilty

Mathematics Subject Classification ID

Reliability, availability, maintenance, inspection in operations research (90B25) Reliability and life testing (62N05)

Related Items

ALGEBRAIC RELIABILITY OF MULTI-STATE k-OUT-OF-n SYSTEMS, Types of signature analysis in reliability based on Hilbert series, Support posets of some monomial ideals, Mincut ideals of two-terminal networks, Polarization and depolarization of monomial ideals with application to multi-state system reliability, Computing availability for redundant flow systems, Complexity of some graph-based bounds on the probability of a union of events, The Algebraic Method in Tree Percolation

Uses Software

• CoCoA
• CoCoALib

Cites Work

• Betti numbers and minimal free resolutions for multi-state system reliability bounds
• Improved Bonferroni inequalities via abstract tubes. Inequalities and identities of inclusion-exclusion type
• The exact distribution of the \(k\)-tuple statistic for sequence homology
• Monomial ideals and the Scarf complex for coherent systems in reliability theory.
• Multi-Component Systems and Structures and Their Reliability
• Percolation
• On a generalizedk-out-of-nsystem and its reliability
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