Evaluating network reliability is essential for network management. In the case that the failure probabilities of nodes and links change in an evaluation, iterative calculation of the reliability is required. In large networks, however, this calculation takes considerable time; thus, iterative calculation cannot be done within a practical amount of time. In this paper, we present a method for generating network reliability formulas that is based on the reliability calculation method with binary decision diagrams (BDD). We show that the time taken to calculate reliability can be reduced by the formula expression in some orders of magnitude compared with the conventional BDD calculation method, which excludes the overhead of formula generation.