Connecting copula properties with reliability properties of coherent systems
Jorge Navarro, Fabrizio Durante, Juan Fernández Sánchez
Abstract
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.