There are many real-world systems, such as transportation systems, power distribution networks, and communication systems, which are modeled as binary-state networks (BSN). Hence, reliability evaluation of BSNs is essential in system performance assessment. Evaluating the exact reliability of BSNs is an NP-hard/#P-hard problem, and computing its approximated value often requires a trade-off between precision and computational cost, which are main challenges in reliability evaluation of BSNs. Here, we study twenty machine learning (ML) models under three reliability intervals, including the full domain 0.0, 1.0, the high-reliability interval 0.9, 1.0, and the ultra-high-reliability range 0.99, 1.0. Our results indicate that when the reliability of the system’s components is not less than 0.9, the overall network reliability converges to values close to one, which implies computational simplifications in large systems with highly reliable components. Moreover, the results show that the method’s performance is notably related to the dataset size. Among the 20 studied ML methods, artificial neural networks (ANN) provide strong results for the cases with limited samples (fewer than m2, where m is the number of arcs in the network), and polynomial regression (PR) outperforms other methods in cases with a large enough number of samples (not less than m2 samples). For instance, ANN achieves a test mean squared error of 7.24 × 10−5 in a case with 30,000 samples, whereas PR attains 5.61 × 10−5 for the case with 40,000 samples, which illustrates PR is more accurate than ANN. Nevertheless, both ANN and PR outperform the standard Monte Carlo simulation. These results provide practical guidance to choose better methods based on data availability.
Yeh et al. (2026) studied this question.