In recent years, probabilistic methods have become increasingly important in engineering applications. They allow a quantification of the impact of the variability of components on result values. In this thesis, existing probabilistic methods are analyzed and new ones are introduced to improve their performance, especially in the context of the probabilistic analyses of jet engine components. A major focus of the thesis is on the analysis of sampling methods, especially with regard to the resulting surrogate model quality. For this purpose, Latinized Particle Sampling is introduced as a new method in which the realizations of the sample are considered as charged particles. This new method is then compared with existing sampling methods. Another focus is on sensitivity analysis with correlated input variables. Established methods such as the Sobol indices or Shapley values cannot reliably identify input variables without functional influence in such cases. Therefore, the modified coefficient of importance is introduced as a new sensitivity measure. Finally, the discussed methods are applied to the analysis of compressor blades subject to manufacturing variability and their advantage is demonstrated.

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