Approximate evaluations of various reliability measures for computer networks and distributed systems are derived using a uniform approach that finds set path-strings for the favorable events of interest. The path-strings are processed by a reliability evaluation algorithm based on paths and cutsets. During each iteration of the algorithm, lower bounds and upper bounds are computed. Using the improved symbolic reliability algorithm (ISYREL), the first k paths in the kth iteration are used to compute the reliability measure of interest. An advantage of this approach is that the result of k th iteration provides a lower bound from which an upper bound can be calculated, consuming only one additional path in each iteration. This process can be stopped when enough accuracy has been obtained or when enough computation power has been invested.