Identifying and resolving circular logic in fault trees

Circular logic is an instance of dependency repetition that may occur in a multi-system fault tree. These occurrences must be resolved before a solution to the fault tree can be obtained. Circular logic frequently occurs in time-dependent interrelationships among auxiliary systems which are dependent on one another. The basic problem arises when System A requires System B for startup/initial operation, while in the long-term System B then requires System A for continued operation. These instances of circular logic often do not appear in the fault tree for a single system but instead become apparent when the models are linked. As a result the resolution of these logic loops can delay the quantification process. Therefore, a coordinated effort was implemented to identify and break circular logic before quantification began for the AP1000®[1] plant PRA. This paper presents the method applied to identify and resolve circular logic in the AP1000^® plant PRA. The method developed involved a process of first automating the identification of circular logic loops within the model via software application. Next, a careful mapping analysis was used to determine the appropriate place to break the loops consistent with the supporting requirements included in the ASME/ANS PRA Standard (Reference 1). The requirements state that the loops must be resolved without introducing unnecessary conservatisms or non-conservatisms. This flexible method enabled identification of circular logic loops prior to the completion of support system modeling and without extensive support from support system analysts. The circular logic analyst was able to use the developed software application to determine if the identified changes correctly eliminated circular logic before the changes were introduced to the actual system models allowing the system modeling to continue uninterrupted. The results of the method show that approximately seventy support system transfers were either created or modified from their original versions to break all of the circular logic loops within the model. These loops identified were consistent with the expected traditional circular logic paths such as component cooling water/compressed air systems and diesel backed heating, ventilation and conditioning (HVAC) systems.