Common-Cause Failures (CCF) impose severe consequences on a complex system’s reliability and overall performance. A more realistic assessment, therefore, of the survivability of the system requires an adequate consideration of these failures. The survival signature approach opens up a new and efficient way to compute system reliability, given its ability to segregate the structural and probabilistic attributes of the system. Traditional survival signature-based approaches assume the failure of one component to have no effect on the survival of the others. This assumption, however, is flawed for most realistic systems, given the existence of various forms of couplings between components. This paper, therefore, presents a novel and general survival signature-based simulation approach for non-repairable complex systems. We have used Monte Carlo Simulation to enhance the easy propagation of CCF across the complex system, instead of an analytical approach, which currently is impossible. In real application world, however, due to lack of knowledge or data about the behaviour of a certain component, its parameters can only be reported with a certain level of confidence, normally expressed as an interval. In order to deal with the imprecision, the double loop Monte Carlo simulation methodology which bases on the survival signature is used to analyse the complex system with CCF. The numerical examples are presented in the end to show the applicability of the approach.