On the signature of complex system: A decomposed approach

The computation of the signature of a complex system is often challenging, as it may involve a large number of components and a complex architecture. In this study, we propose a novel approach to computing the signature of a system consisting of subsystems with shared components. The proposed approach relies on a new concept called decomposed survival signatures. This new concept can be efficiently used to compute the signature of a modular system with an arbitrary organizing structure and to provide explicit formulas for computation. Applications in cyber systems, transportation systems, and branched oil pipeline systems are highlighted.