New better than renewal-used classes of life distributions

The concept of stochastic dominance in economics is used to compare the conditional life distribution of a used device that has lived until time t>0 and its life distributions at time t=0. This comparison gives two classes of life distributions namely, the NBRU class of life distribution and its dual. Relations of these classes to existing criteria of aging and some of their closure properties under reliability operations are studied. The preservation of these aging properties for the survival probability under the homogeneous shock model process are investigated.