On digraphs, fault trees, and cut sets

Abstract Digraphs are an attractive tool for analyzing cause-effect relations in complex systems. This paper develops a new method for obtaining all minimal combinations of conditions which can cause a specified deviation at a node in a digraph (in general, these combinations are the minimal cut sets). The digraph structure is represented by a set of conditions and node-state relation pairs. Based on this representation, the method first obtains all possible disturbance propagation paths (‘disturbance situations’). Then, the method identifies control loop malfunction conditions, which can nullify the disturbance situation (‘corrective-related control loops’). The method enumerates lists of conditions and node states and checks their consistency. The combination of conditions which cause a specified deviation is expressed by a logical AND combination of disturbance situation conditions and the related control loop malfunctions. Minimal combinations of conditions are obtained by comparing abnormal conditions. As long as the analysis of the disturbance effect on control loops, and the control loop interactions, are correct, consistency of the minimal conditions is guaranteed. Analysis of control loop interactions, and classification of disturbances to control loops are necessary for a consistent and complete identification of system failure modes. Using examples from the literature, it is shown that fully automated fault tree synthesis methods give questionable and/or incomplete results. Caveat emptor.