The improvement of efficiency has always been the aim of jet engine design, as it enhances performance and reduces fuel consumption and, therefore, environmental impact and costs. The turbine entry temperature is one of the most influential factors on the performance and has significantly increased over the years. The trend to push it towards new extremes represents a huge challenge for turbine blades, especially those of the first stage high-pressure turbine, which must be provided with a complex cooling system in order to withstand the high thermal loads. Potential malfunctions of the cooling system, such as the blockage of the cooling holes, have to be included in the design since they can lead to an overheating of the blade and a potential failure of the entire turbine.