Development and Implementation of a Direct Evaluation Solution for Fault Tree Analyses Competing With Traditional Minimal Cut Sets Methods

Fault tree analysis (FTA) is a well-established technique to analyze the safety risks of a system. Two specific prominent FTA methods, largely applied in the aerospace field, are the so-called minimal cut sets (MCS), which uses an approximate evaluation of the problem, and the direct evaluation (DE) of the fault tree, which uses a top-down recursive algorithm. The first approach is only valid for small values of basic event probabilities and has historically yielded faster results than exact solutions for complex fault trees. The second one means exact solutions at a higher computational cost. This article presents several improvements applied to both approaches in order to upgrade the computing performance. First, improvements to the MCS approach have been performed, where the main idea has been to optimize the number of required permutations and to take advantage of the available information from previous solved subsets. Second, improvements to the DE approach have been applied, which deal with a reduction of the number of recursive calls through a deep search for independent events in the fault tree. This could dramatically reduce the computation time for industrial fault trees with a high number of repeated events. Additional implementation improvements have been also applied regarding hash tables, and memory access and usage, but also implementing the so-called "virtual gates", which enable limitless children on each gate. The results presented hereafter are promising, not only because they show that both approaches have been highly optimized compared to the literature, but also because a DE solution has been achieved, which can compete in time resources (and obviously in precision) with the MCS approach. These improvements are relevant when considering the industrial, and more specifically the aeronautical, implementation and application of both techniques.