Application of logic regression to assess the importance of interactions between components in a network

Logic regression (LR), not to be confused with logistic regression, is a well-known alternative tree-based method and powerful statistical learning technique that can be used to classify a binary response using Boolean combinations of binary predictors. In our case, given the binary states of the components of a network and its corresponding operating or failed status, LR can quantify the importance of the interactions of components according to their predictive capabilities (strength for classification). Meaning that, unlike traditional approaches in the reliability field, a completely different assumption is used. This paper shows the application of logic regression in six networks. Each example is characterized by a matrix representing the status of each component and a vector showing the corresponding network status. These data are analytically derived or using simulation procedures. The results show that LR could be considered as an additional assessment tool, where the most important effects (single or interactions) of components emerge naturally as a result of an optimization problem. As a byproduct, LR is also able to detect possible minimal cut/path sets.