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ALGEBRAIC RELIABILITY OF MULTI-STATE k-OUT-OF-n SYSTEMS

Published online by Cambridge University Press:  02 June 2020

Patricia Pascual-Ortigosa ,
Eduardo Sáenz-de-Cabezón Open the ORCID record for Eduardo Sáenz-de-Cabezón [Opens in a new window]  and
Henry P. Wynn
Patricia Pascual-Ortigosa
Affiliation:
Departamento de Matemáticas y Computación, Universidad de La Rioja, La Rioja, Spain E-mail: eduardo.saenz-de-cabezon@unirioja.es
Eduardo Sáenz-de-Cabezón
Affiliation:
Departamento de Matemáticas y Computación, Universidad de La Rioja, La Rioja, Spain E-mail: eduardo.saenz-de-cabezon@unirioja.es
Henry P. Wynn
Affiliation:
Department of Statistics, London School of Economics, London, UK
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Abstract

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In this paper, we review different definitions that multi-state k-out-of-n systems have received along the literature and study them in a unified way using the algebra of monomial ideals. We thus obtain formulas and algorithms to compute their reliability and bounds for it. We provide formulas and computer experiments for simple and generalized multi-state k-out-of-n systems and for binary k-out-of-n systems with multi-state components.

Keywords

applied probabilityreliability theory
Type
Research Article
Information
Probability in the Engineering and Informational Sciences , Volume 35 , Issue 4 , October 2021 , pp. 903 - 927
Copyright
Copyright © The Author(s), 2020. Published by Cambridge University Press

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