  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.
