In this paper, we present a new network reliability measure that is useful to evaluate performance of ad hoc networks with imperfect nodes and perfectly reliable links. An ad hoc network is modeled as undirected probabilistic graph. A specific feature of our model is that a network contains initially excessive amount of nodes to properly provide the functioning of the network. Thus, we consider the networks which carry on operating acceptably even if some of the nodes fail. The problem of calculation of the new reliability measure is NP-hard, just like problems of computing other reliability parameters. The method for calculating a new reliability measure has been obtained. It is shown that this method can be used for the optimal sink nodes placement in networks in order to obtain the most reliable version.