Semi-copulas and Interpretations of Coincidences between Stochastic Dependence and Ageing

We provide probabilistic explanations of equivalences, between conditions of positive dependence and of univariate ageing, that have been pointed out in the literature. To this purpose we consider bivariate survival functions and properties of them that are respectively invariant under distortions or increasing transformations of their arguments. Bivariate Schur-constant survival models have an important role in our discussion