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

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dc.creatorGiglio, Beatrice
dc.creatorWynn, Henry P.
dc.date2004-06-25
dc.date.accessioned2026-07-07T08:06:24Z
dc.date.available2026-07-07T08:06:24Z
dc.descriptionA certain type of integer grid, called here an echelon grid, is an object found both in coherent systems whose components have a finite or countable number of levels and in algebraic geometry. If α=(α_1,...,α_d) is an integer vector representing the state of a system, then the corresponding algebraic object is a monomial x_1^{α_1}... x_d^{α_d} in the indeterminates x_1,..., x_d. The idea is to relate a coherent system to monomial ideals, so that the so-called Scarf complex of the monomial ideal yields an inclusion-exclusion identity for the probability of failure, which uses many fewer terms than the classical identity. Moreover in the ``general position'' case we obtain via the Scarf complex the tube bounds given by Naiman and Wynn [J. Inequal. Pure Appl. Math. (2001) 2 1-16]. Examples are given for the binary case but the full utility is for general multistate coherent systems and a comprehensive example is given.
dc.identifierhttps://arxiv.org/abs/math/0406527
dc.identifierhttp://arxiv.org/abs/math/0406527
dc.identifierAnnals of Statistics 2004, Vol. 32, No. 3, 1289-1311
dc.identifierdoi:10.1214/009053604000000373
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/130596
dc.subjectStatistics Theory
dc.subject90B25, 06A06. (Primary)
dc.titleMonomial ideals and the Scarf complex for coherent systems in reliability theory
dc.typetext

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