  Real-world applications such as the internet of things, wireless sensor
networks, smart grids, transportation networks, communication networks, social
networks, and computer grid systems are typically modeled as network
structures. Network reliability represents the success probability of a network
and it is an effective and popular metric for evaluating the performance of all
types of networks. Binary-state networks composed of binary-state (e.g.,
working or failed) components (arcs and/or nodes) are some of the most popular
network structures. The scale of networks has grown dramatically in recent
years. For example, social networks have more than a billion users.
Additionally, the reliability of components has increased as a result of both
mature and emergent technology. For highly reliable networks, it is more
practical to calculate approximated reliability, rather than exact reliability,
which is an NP-hard problem. Therefore, we propose a novel direct reliability
lower bound based on the binary addition tree algorithm to calculate
approximate reliability. The efficiency and effectiveness of the proposed
reliability bound are analyzed based on time complexity and validated through
numerical experiments.
