  Many network applications are based on binary-state networks, where each
component has one of two states: success or failure. Efficient algorithms to
evaluate binary-state network reliability are continually being developed.
Reliability estimates the probability of the success state and is an effective
and popular evaluation technique for binary-state networks. Binary-addition
tree (BAT) algorithms are frequently used to calculate the efficiency and
reliability of binary-state networks. In this study, we propose a novel,
bounded BAT algorithm that employs three novel concepts: the first connected
vector, the last disconnected vector, and super vectors. These vectors and the
calculations of their occurrent probabilities narrow the search space and
simplify the probability calculations to reduce the run time of the algorithm.
Moreover, we show that replacing each undirected arc with two directed arcs,
which is required in traditional direct methods, is unnecessary in the proposed
algorithm. We call this novel concept the undirected vectors. The performance
of the proposed bounded BAT algorithm was verified experimentally by solving a
benchmark set of problems.
