Network Reliability Analysis by means of Generalized Matrix Learning Vector Quantization

We present a new approach for assessing the reliability of an error-prone system or network by using a prototype-based classification method. More specifically, reliability levels for consecutive \(k\)-out-of-\(n\) success systems and failure networks are classified using Generalized Matrix Learning Vector Quantization (GMLVQ), which provides useful information about the impact of the input probabilities on the classified reliability levels. To increase the interpretability of the learned relevance matrix in GMLVQ, we propose two graph-based visualization strategies to reveal structural patterns and relevant feature interactions, which are of considerable importance for the classification of the reliability levels. Our approach is generally applicable to any coherent system and can even be adapted to estimate the probability of any union of finitely many events, based on their individual and pairwise intersection probabilities.