The Network Design Problem with Vulnerability Constraints and Probabilistic Edge Reliability (NDPVC-PER) is an extension of the NDPVC obtained by additionally considering edge reliability. We consider the design of a telecommunication network in which every origin-destination pair is connected by a hop-constrained primal path, and by a hop-constrained backup path when certain edges in the network fail. The edge failures occur with respect to their reliability, and the network is designed by considering a minimum reliability level. Therefore, an hop-constrained backup path must be built by considering all simultaneous edge failures that have a certain probability of realization. While there exist models to solve the NDPVC without enumerating all edge subsets, edge reliability cannot be dealt with by applying the techniques applied to the NDPVC. Therefore, we develop models based on a new concept of resilient length-bounded cuts, and solve the NDPVC-PER without edge set enumerations. We perform extensive testing of the model to determine the best performing settings, and demonstrate the computational efficiency of the developed model. Our findings on these instances show that, in the dataset considered in this study, increasing the reliability level from 90% to 95% increases the average cost only by 12.4%, while increasing it from 95% to 99% level yields a cost increase of 93.9%.