Characterization of some concepts of aging

The theory of functions of regular variation has been used to delineate the relationships between the family of age-smoothed distributions and the classical reliability classes of distributions with aging properties. Explicit characterizations of distributions which are IFRA, NBU, and DMRL were given, and the characterizations were used to prove that the class of age-smoothed distribution functions is rich containing the IFRA, NBU, and DMRL classes. Also, from a modeling point of view, these characterizations guarantee the ability to generate, at will, life distributions in these classes