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.

中文翻译：

---

连接copula属性与相干系统的可靠性属性

我们将 copula 属性与顺序统计之间的随机比较联系起来（k -out-of- n系统）和具有相关组件的相干系统。copula 依赖属性导致系统之间的边缘无分布排序属性。相反，系统的排序属性会导致基线 copula 的属性（或新的属性证明）。这些关系可以用来解释数学性质和/或联结类中出现的函数不等式的含义。提供了一些说明性示例，包括具有两个或三个组件的串联和并联系统。这里介绍的过程可以应用于各种系统结构，即使是高维。在实践中，它们可用于确定系统组件之间依赖关系的各个方面。