This paper presents a new computational procedure for the quantification of fault trees containing dependent basic events. The quantification procedure expands the modeling power of fault trees, by allowing such enhancements as the quantification of multiple basic events in a fault tree by connecting them to different variables in a single Bayesian Belief Network (BBN) structure. The procedure was developed to support the analysis of Hybrid Causal Logic models, which are comprised of Event Sequence Diagrams (ESD), Fault Trees, and BBNs, and which are investigated as a way of modeling of causal factors with widespread influences in risk models.

The complication posed by these types of connections between logical and quantification models is that they cause the basic events to become dependent, in the sense that the occurrence of one basic event may affect the probability of others. Such dependencies are not allowed by conventional solution methods.

This view of dependencies between events is different from the one employed by Common Cause Failure (CCF) modeling approaches, in which dependencies are considered in terms of the joint occurrence of events. Possible combinations of basic events are represented in the fault tree by so-called Common Cause Basic Events, which are quantified in such a manner that they can be treated as independent events.

The quantification procedure presented in this paper is an extension of the BDD-based quantification procedure, which was generalized to allow for basic event probabilities that are conditional on the occurrence of other events in the BDD. The procedure repeatedly queries BBN models using conventional BBN solution methods. Alternatively, the procedure allows basic events in the model to be connected to two or more states in a Markov Chain model, which would also cause the basic events to become dependent.

The results of the procedure are strictly in accordance with the rules of Probability Theory, which follows directly from the formulation of the quantification rule on which the procedure is based.