Survival signature can be useful for the reliability assessment of critical infrastructures. However, analytical calculation and Monte Carlo Simulation (MCS) are not feasible for approximating the survival signature of large infrastructures, because of the complexity and computational demand due to the large number of components. In this case, efficient and accurate approximations are sought. In this paper we formulate the survival signature approximation problem as a missing data problem. An ensemble of artificial neural networks (ANNs) is trained on a set of survival signatures obtained by MCS. The ensemble of trained ANNs is, then, used to retrieve the missing values of the survival signature. A numerical example is worked out and recommendations are given to design the ensemble of ANNs for large-scale, real-world infrastructures. The electricity grid of Great Britain, the New England power grid (IEEE 39-Bus Case), the reduced Berlin metro system and the approximated American Power System (IEEE 118-Bus Case) are, then, eventually, analyzed as particular case studies.