Monomial ideals and the Scarf complex for coherent systems in reliability theory.

DOI10.1214/009053604000000373zbMath1105.90312arXivmath/0406527OpenAlexW3103308720WikidataQ61855896 ScholiaQ61855896MaRDI QIDQ1879939

Henry P. Wynn, Beatrice Giglio

Publication date: 15 September 2004

Published in: The Annals of Statistics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0406527

zbMATH Keywords

network reliabilitymonomial idealscoherent systemsinclusion-exclusionScarf complexmultistate systems

Mathematics Subject Classification ID

Partial orders, general (06A06) Reliability, availability, maintenance, inspection in operations research (90B25)

Related Items (10)

Mincut ideals of two-terminal networks ⋮ Polarization and depolarization of monomial ideals with application to multi-state system reliability ⋮ Computational algebraic algorithms for the reliability of generalized \(k\)-out-of-\(n\) and related systems ⋮ Lattice conditional independence models and Hibi ideals ⋮ Stochastic orderings for discrete random variables ⋮ The reliability importance of components and prime implicants in coherent and non-coherent systems including total-order interactions ⋮ The Algebraic Method in Tree Percolation ⋮ Combinatorial and Geometric View of the System Reliability Theory ⋮ Betti numbers and minimal free resolutions for multi-state system reliability bounds ⋮ Divisors on graphs, orientations, syzygies, and system reliability

Cites Work

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• A Unified Formula for Analysis of Some Network Reliability Problems
• Multistate coherent systems
• New Topological Formula and Rapid Algorithm for Reliability Analysis of Complex Networks
• Engineering Reliability
• Reliable circuits using less reliable relays

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