The exact calculation of all-terminal network reliability is an NP-hard problem, with computational effort growing exponentially with the number of nodes and links in a network. Because of the impracticality of calculating all-terminal network reliability for networks of moderate to large size, Monte Carlo simulation methods to estimate network reliability and upper and lower bounds to bound reliability have been used as alternatives. In this study, an artificial neural, network (ANN) is used to estimate all-terminal network reliability for networks with both homogeneous and heterogeneous link reliablity. Two forms of design methods for generating training data sets for networks with homogeneous and heterogeneous link reliability are compared. These are experimental design and randomized design.