On the extension of signature-based representations for coherent systems with dependent non-exchangeable components

The signature representation shows that the reliability of the system is a mixture of the reliability functions of thek-out-of-nsystems. 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.