Culling methods for minimal cut sets including dependencies

Binary Decision Diagrams (BDDs) are widely used in reliability analysis as an efficient representation of the Boolean logic underlying Fault and Event Tree models. More recently, BDDs have become a core component of the Dynamic and Dependent Tree Theory (D² T²), where they enable the inclusion of dependencies within traditional Fault/Event Tree frameworks. Despite their advantages, the construction of BDDs from large tree models can be challenging and, in some cases, infeasible. Although several mitigation strategies have been proposed, existing approaches do not account for dependencies, limiting their applicability to D² T² analyses. This study proposes novel algorithms for identifying and culling Fault Tree minimal cut sets and for constructing BDDs from them while explicitly accounting for dependencies between basic events. By integrating culling criteria based on order, probability, and frequency within a framework that explicitly accounts for event dependencies, the proposed approach enables the generation of BDDs regardless of model complexity, thereby ensuring the applicability of D² T² to large and complex Fault Tree models.

Keywords: Binary Decision Diagrams, Dynamic and Dependent Tree Theory, Fault Trees, Minimal Cut Sets, Dependencies, Culling.