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Connecting copula properties with reliability properties of coherent systems
Author(s) -
Navarro Jorge,
Durante Fabrizio,
FernándezSánchez Juan
Publication year - 2020
Publication title -
applied stochastic models in business and industry
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.413
H-Index - 40
eISSN - 1526-4025
pISSN - 1524-1904
DOI - 10.1002/asmb.2579
Subject(s) - copula (linguistics) , mathematical proof , stochastic ordering , statistical physics , joint probability distribution , mathematics , computer science , econometrics , statistics , physics , geometry
Summary We connect copula properties with stochastic comparisons between order statistics ( k ‐out‐of‐ n systems) and coherent systems with dependent components. The copula dependence properties lead to marginal distribution‐free ordering properties between systems. Conversely, ordering properties of systems lead to properties (or new proofs of properties) for the baseline copulas. These relationships can be used to explain the meaning of mathematical properties and/or functional inequalities arising in the class of copulas. Some illustrative examples are provided including series and parallel systems with two or three components. The procedure introduced here can be applied to various system structures, even in high dimensions. In practice they can be used to determine various facets of dependency among the components of a system.