The concept of the system signature has quickly become a popular tool for analysis and assessment of system reliability. A good introduction and overview to the topic is provided by Samaniego's excellent book `System Signatures and their Applications in Engineering Reliability' (Springer, 2007). However, signatures can only really be used for systems with a single type of component, as all the lifetimes of the components must be exchangeable random quantities (well, one can do a bit more, but it quickly becomes very complicated). Hence, while this work is of theoretic interest, its practical value for real systems is limited, as these tend to have components of multiple types. Also, reliability analysis for networks can typically not be based on the signature, as networks tend to have at least two different kinds of components (`nodes' and `links').
To overcome this major drawback of the system signature, we have recently presented an alternative, called the `Survival Signature'. For systems with a single type of component this is directly related to the signature, hence comes with the same opportunities and advantages. Crucially, the survival signature is straightforwardly generalized, as introduced, to systems with multiple types of components. Recently, Samaniego and Navarro called the survival signature a breakthrough result and used it for comparison of systems (On comparing coherent systems with heterogeneous components, in: Advances in Applied Probability 48, 2016 88-111).
The first paper, introducing the survival signature, was presented at the 2012 DepCoS-Relcomex conference in Poland, following a kind invitation by Prof Wojtek Zamojski, it is published in: `Complex Systems and Dependability', Springer, 2012 (pp. 115-130) and available here. If you are interested in any further work on the survival signature then please contact me.