Fault Tree Analysis (FTA) is a wellestablished technique to analyze the safety risks of a system. Two specific prominent FTA methods, largely applied in the aerospace field, are the socalled 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. The paper presents several improvements applied to both approaches in order to upgrade the computing performance. Firstly, 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. Secondly, 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.