Section \[IndContext\] formalizes the problem in the framework of an industrial application to aircraft industry. In Section \[revLit\], a short survey of extreme quantiles estimation and of existing designs of experiment are studied as well as their applicability to extreme quantiles estimation. Then, a new procedure is proposed in Section \[Splitting\] and elaborated for a Generalized Pareto model. An estimation procedure is detailed and evaluated in Section \[EstimationProc\]. Then an alternative Weibull model for the design proposed is presented in Section \[WeibullModel\]. Lastly, Sections \[model\_selection\_missp\] and \[Perspectives\] provide a few ideas discussing model selection and behavior under misspecification as well as hints about extensions of the models studied beforehand.

Industrial challenge {#IndContext}
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Estimation of minimal allowable stress in material fatigue
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In aircraft industry, one major challenge is the characterization of extreme behaviors of materials used to design engine pieces. Especially, we will consider extreme risks associated with fatigue wear, which is a very classical type of damage suffered by engines during flights. It consists in the progressive weakening of a material due to the application of cyclic loadings a large number of times that can lead to its failure. As shown in Figure [cyclefatigue]{}, a loading cycle is 