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.
