The effect of natural and man made disasters on critical infrastructures are substantial, as evident from recent history. Break downs of critical systems such as electrical power grids, water supply networks, communication networks or transportation can have dire consequences on the availability of aid in such a crisis. That is why, reliability analyses of these networks are of paramount importance. Two important factors must taken into consideration during reliability analysis. First, the networks are subject to complex interdependencies and must not be treated as individual units. Second, the reliability analysis is typically based on some form of data and or expert knowledge. However, this information is rarely precise or even available. Therefore, it is important to account for different kinds of uncertainties, namely aleatory uncertainty and epistemic uncertainty. Aleatory uncertainty represents the natural randomness in a process, while epistemic uncertainty represents vaguness or lack of knowledge in the model. In this work we present an approach to the numerical reliability analysis of complex networks and systems extending a previously developed method based on Monte Carlo simulation and survival signature. The extended method treats both kinds of uncertainties, thus, yielding better results. We show how Monte Carlo simulation controls aleatory uncertainty and apply sets of distributions (probability boxes) to treat epistemic uncertainties in component failures. In this framework, dependencies are modelled using copulas. Copulas possess the unique property of decoupling the odelling of the univariate margins from the modelling of the dependence structure for continuous multivariate distributions. Analoguous to the p-boxes we use sets of copulas to include imprecision in the dependencies. Finally, the method is applied to an example system of coupled networks.