In this fourth blok we describe some engineering applications. We start with a fatigue model and derive, step by step, the model without arbitrary assumptions. In this case a comaptibility assumption, the weakest link principle and extreme value theory are sufficient to derive the functional form of the S-N curve and the Weibull model. When incorporating min and max stresses, another compatibility condition allows to extend the previous model. Next, we derive a crack-.grow model, using also a similar compatibility condition and extreme value analysis. Finally, both models are linked by using the failure curve, providing a very interesting link, not previosly obtained, in which we can move from S-N curves to derive the crack-grow curve model and vice versa.