The signature representation shows that the reliability of the system is a mixture of the reliability functions of the k-out-of-n systems. The first representation was obtained for systems with independent and identically distributed (IID) components and after it was extended to exchangeable (EXC) components. The purpose of the present paper is to extend it to the class of systems with identically distributed (ID) components which have a diagonal-dependent copula. We prove that this class is much larger than the class with EXC components. This extension is used to compare systems with non-EXC components.

中文翻译：

---

关于具有依赖的不可交换组件的相干系统的基于签名的表示的扩展

签名表示表明系统的可靠性是系统可靠性函数的混合ķ-在......之外-n系统。第一个表示是针对具有独立同分布 (IID) 组件的系统并在扩展到可交换 (EXC) 组件之后获得的。本文的目的是将其扩展到具有同分布 (ID) 组件的系统类，这些组件具有对角依赖的 copula。我们证明这个类比带有 EXC 组件的类要大得多。此扩展用于比较具有非 EXC 组件的系统。