Copula is one of the widely used techniques to describe the dependency structure between components of a system. Among all existing copulas, the family of Archimedean copulas is the popular one due to its wide range of capturing the dependency structures. In this paper, we consider the systems that are formed by dependent and identically distributed components, where the dependency structures are described by Archimedean copulas. We study some stochastic comparisons results for series, parallel, and general $r$-out-of-$n$ systems. Furthermore, we investigate whether a system of used components performs better than a used system with respect to different stochastic orders. Furthermore, some aging properties of these systems have been studied. Finally, some numerical examples are given to illustrate the proposed results.

Copula 是描述系统组件之间依赖结构的广泛使用的技术之一。在所有现有的 copula 中，阿基米德 copula 家族因其广泛的捕获依赖结构而成为流行的一种。在本文中，我们考虑由依赖和同分布的组件形成的系统，其中依赖结构由阿基米德连接函数描述。我们研究了串联、并联和一般$r$ -out-of- $n$的一些随机比较结果系统。此外，我们还研究了使用过的组件系统在不同随机顺序方面是否比使用过的系统表现更好。此外，还研究了这些系统的一些老化特性。最后，给出了一些数值例子来说明所提出的结果。