From Reliability Block Diagrams to Fault Tree Circuits

Reliability block diagrams (RBDs) depict the functional relationships between components comprising a system, whereas Bayesian networks (BNs) represent probabilistic relationships between uncertain variables. Previous research has described how one can transform an RBD into a BN. In parallel, developments in the artificial intelligence literature have shown how a BN can be transformed into another graphical representation, an arithmetic circuit, which can subsequently be used for efficient inference. In this paper, we introduce a new graphical representation that we call a fault tree circuit, which is a special kind of arithmetic circuit constructed specifically for an RBD. A fault tree circuit can be constructed directly from an RBD and is more efficient than an arithmetic circuit that is compiled from the BN corresponding to that RBD. We develop several methods for fault tree circuits, highlighting how they can aid the analyst in efficient diagnosis, sensitivity analysis, and decision support for many typical reliability problems. The circuit framework can complement tools that are popular in the reliability analysis community. We use a simple pump system example to illustrate the concepts.