Analytical and Evolutionary Methods for Finding Cut Volumes in Fault Trees Constrained by Location

Fault tree analysis (FTA) is used to find and mitigate vulnerabilities in a system based on its constituent components. Methods exist to efficiently find minimal cut sets (MCSs), which are combinations of components whose failure causes the system to fail. However, traditional FTA ignores the physical location of the components. Components that are close to each other could be defeated by a single event with a radius of effect, such as an explosion or fire. This motivates the search for techniques to identify such vulnerabilities. Adding physical locations to the fault tree structure can help identify vulnerabilities in the overall system. Using this information requires extending existing solution methods or developing entirely new methods. In this paper, two solution approaches were explored. The first executes traditional FTA software, then searches for clusters in the resulting MCS to find these vulnerabilities. The second uses an evolutionary algorithm to search directly for volumes containing components that form cut sets. Results show that the evolutionary approach provided better answers (i.e., smaller volumes) overall and is suitable to identify vulnerabilities caused by proximity of components. However, the cluster approach performed well when evaluating higher numbers of locations and may be suitable in specific situations. Potential refinements to both methods are discussed.