Generalized extreme shock models with a possibly increasing threshold

We propose a generalized extreme shock model with a possibly increasing failure threshold. While standard models assume that the crucial threshold for the system may only decrease over time, because of weakening shocks and obsolescence, we assume that, especially at the beginning of the system's life, some strengthening shocks may increase the system tolerance to large shock. This is for example the case of turbines' running-in in the field of engineering. On the basis of parametric assumptions, we provide theoretical results and derive some exact and asymptotic univariate and multivariate distributions for the model. In the last part of the paper we show how to link this new model to some nonparametric approaches proposed in the literature.