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.