Complex components in gas turbines and aero engines have to withstand extreme operating conditions over long lifetimes. Due to manufacturing and operation material properties as well as operating loads are subject to scatter and uncertainties. As a result of that those components don’t show a deterministic lifetime, but rather a lifetime distribution. To calculate the lifetime distribution and to quantify the component’s reliability, stochastic methods are being developed. Based on semi-analytical algorithms those methods are capable to calculate the very small failure probabilities which are necessary for gas turbines and aero engines.