Classification of life distributions in multivariate models

In reliability theory, lifetimes of systems and components are frequently studied through univariate concepts of ageing. By considering suitable multivariate generalizations of the univariate ageing properties, some multivariate ageing classes of life distributions are defined. Properties of these classes with their equivalent definitions and chain of implications are presented along with a few characterizing properties. These results are useful for obtaining reliability bounds (when component lives are independent) at the early stage of product design. Also for model selection, characterization results can be important. Moreover, the underlying mathematical treatment is univariate when viewed through conditional distributions