The reliability of critical infrastructures, such as power distribution networks, is of key importance for modern societies. The reliability of such complex systems can, in principle, be assessed by Monte Carlo simulation. However, the size and complexity of these systems, and the rarity of the failure events, can make the calculations quite demanding. Survival signature can help to address this issue, as it allows modelling the structure of the system separately from the probabilistic modelling for the reliability assessment. However, the survival signature calculation of complex, multi-component systems for their reliability assessment suffers from the curse of dimensionality, and both analytical calculation and Monte Carlo Simulation (MCS) are not feasible in practice. Then, in this work, we propose a novel approach to approximate the survival signature of a system, which stands on the use of entropy to drive the sampling by MCS towards non-trivial system structure configurations, so as to save computational cost. The approach is exemplified by calculating the reliability of a generic synthetic multi-component network and the feasibility of its application is shown on a real-world network.