Reliability of thermal barrier coatings (TBCs) of turbine blades and vanes is gaining importance, because the continuous improvement of gas turbine efficiency and CO2 reduction requires an increase in turbine inlet temperatures. To predict the reliable operation of TBCs, lifetime tests using selected material systems have to be conducted. Tests under real operating conditions are often difficult to realise and too time-consuming, since the expected lifetime of several years exceeds the time available for further technological development. To overcome this dilemma, accelerated tests are performed under more severe loading conditions and lifetimes are extrapolated from acceleration to use conditions. Due to the natural variance in the lifetime test data, extrapolation to use conditions is prone to statistical uncertainty. For a reliable lifetime prediction, it is essential to take these uncertainties into account. Probabilistic methods have to be used for this purpose. In the present paper, a Bayesian approach is selected for the probabilistic analysis of the extrapolation uncertainty. This approach is based on the well-known likelihood function, but makes different use of it compared to a classical statistical approach. The first advantage of the Bayesian approach is that it does not suffer from sample size limitations. Since life tests are expensive and time-consuming, the number of available data is generally limited, leading to large uncertainties and making classical statistical procedures questionable, because they are usually based on large sample approximations. As a second advantage, the Bayesian approach allows to eliminate nuisance parameters, which contribute to the lifetime prediction uncertainty, but are not interesting in its own respect. The presented example of using a Bayesian approach is the analysis of cyclic oxidation test data; a commonly used lifetime test for TBC systems. The lifetime of coated specimens is determined under overload conditions for several temperature levels above the operating temperature and the lifetime under use conditions is extrapolated from these data. In a first (analysis) step it is shown, how the uncertainties in the expected lifetime at the various test temperatures can be quantified using Bayesian credibility intervals. In the second (prediction) step, the uncertainty in the extrapolated lifetime is assessed by using an Arrhenius-type acceleration model. It is shown that neglecting the uncertainty in the Arrhenius activation energy leads to a pronounced underestimation of the uncertainty in the extrapolated lifetime.

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