  Network reliability analysis remains a challenge due to the increasing size
and complexity of networks. This paper presents a novel sampling method and an
active learning method for efficient and accurate network reliability
estimation under node failure and edge failure scenarios. The proposed sampling
method adopts Monte Carlo technique to sample component lifetimes and the
K-terminal spanning tree algorithm to accelerate structure function
computation. Unlike existing methods that compute only one structure function
value per sample, our method generates multiple component state vectors and
corresponding structure function values from each sample. Network reliability
is estimated based on survival signatures derived from these values. A
transformation technique extends this method to handle both node failure and
edge failure. To enhance efficiency of proposed sampling method and achieve
adaptability to network topology changes, we introduce an active learning
method utilizing a random forest (RF) classifier. This classifier directly
predicts structure function values, integrates network behaviors across diverse
topologies, and undergoes iterative refinement to enhance predictive accuracy.
Importantly, the trained RF classifier can directly predict reliability for
variant networks, a capability beyond the sampling method alone. Through
investigating several network examples and two practical applications, the
effectiveness of both proposed methods is demonstrated.
