Low Cycle Fatigue (LCF) is one of most common mechanisms behind turbine blade failures. The reason is high stress concentration in notch areas, like fir-tree root groves, which can cause cyclic stress beyond the safe threshold. The stress levels strictly depend on the manufacturing accuracy of the fir-tree lock (for both fitted together: blade root and disk groove). The probabilistic study aimed at determination of stress was performed using Finite Element Method (FEM) simulation on a population of 1000 turbine models (disk + blades +friction dampers), where fir-tree lock dimensions were sampled according to the normal distribution, within limits specified in the documentation. The studies were performed for different manufacturing quality levels: 3-Sigma, 6-Sigma and 3-Sigma with tolerance ranges reduced twice. Based on the results, the probabilistic distributions, probabilities and expected ranges of values could be determined for: material plastification, stress, strain, LCF lifetime, etc. The study has shown how each tooth of the root is loaded and how wide a stress range should be expected in each groove. That gives information on how the definition of tolerances should be modified to make the construction more optimal, more robust, with lower likelihood of damage, taking into account the cost-quality balance. It also shows how the Six Sigma philosophy can improve the safety of the construction, its repeatability and predictability. Additionally, the presented numerical study is a few orders of magnitude more cost- and time-effective than experiment.