Methods to Calculate Cut Volumes for Fault Trees with Dependencies Induced by Spatial Locations

Fault tree analysis (FTA) is used to find and mitigate vulnerabilities in systems based on their constituent components. Methods exist to efficiently find minimal cut sets (MCS), which are combinations of components whose failure causes the overall system to fail. However, traditional FTA ignores the physical location of the components. Components in close proximity to each other could be defeated by a single event with a radius of effect, such as an explosion or fire. Events such as the Deepwater Horizon explosion and subsequent oil spill demonstrate the potentially devastating risk posed by such spatial dependencies. This motivates the search for techniques to identify this type of vulnerability. Adding physical locations to the fault tree structure can help identify possible points of failure in the overall system caused by localized disasters. Since existing FTA methods cannot address these concerns, using this information requires extending existing solution methods or developing entirely new ones. A problem complicating research in FTA is the lack of benchmark problems for evaluating methods, especially for fault trees over one hundred components. This research presents a method of using Lindenmeyer systems (L-systems) to generate fault trees that are reproducible, capable of producing fault trees with similar properties to real-world designs, and scalable while maintaining predictable structural properties. This approach will be useful for testing and analyzing different methodologies for FTA tasks at different scales and under different conditions. Using a set of benchmark fault trees derived from L-systems, three approaches to finding these vulnerabilities were explored in this research. These approaches were compared by defining a metric called minimal cut volumes (MCV) for describing volumes of effect that defeat the system. Since no existing methods are known for solving this problem, the methods are compared to each other to evaluate performance. 1) The control method executes traditional FTA software to find minimal cut sets (MCS), then extends this approach by searching for clusters in the resulting MCS to find MCV. 2) The next method starts by searching for clusters of components in the three dimensional space, then evaluates combinations of clusters to find MCV that defeat the system. 3) The last method uses an evolutionary algorithm to search the space directly by selecting center points, then using the radius of the smallest sphere(s) as the fitness value for identifying MCV. Results generated using each method are presented. The performance of the methods are compared to the control method and their utilities evaluated accordingly