138 Functional Block Diagrams and Automated Construction of Event Trees (PSAM-0057)

Functional Block Diagrams are introduced as a graphical representation of the functional relationships among parts of a system. A functional block diagram provides the overall output (or outmost consequence) of a system as a joint event This joint event is decomposed into simpler events the outcome space of which is partitioned into subsets corresponding to the outcomes of the initial joint event. The simpler events can be further decomposed into a lower level of events where always the outcome space of the children events is partitioned according to the possible outcomes of the parent-event. A hierarchy of events is thus created with multiple levels where the events in a given level (parents) are decomposed to a number of simpler events (children) in the next level of the hierarchy. The outcome space of the children is always partitioned according to the outcomes of the parent event. This partition is expressed in terms of logical relationships connecting the outcomes of the children events with the possible outcome of the parent event.

It is demonstrated that such a functional block diagram is equivalent to an event tree with elements the events of the lowest level of the developed hierarchy of events. Furthermore, it is demonstrated that the parent —children relationships can be used to partition the branches of the event tree according to the outcomes of the top event in the hierarchy.

The methodology and the associated algorithms have been computerized in a program with a graphical user interface (GUI) which allows the user to input the functional relationships between parent and children events, corresponding probabilities for events of the lowest level and obtain at the end the quantified corresponding simplified event-tree.