Characterizations of Some Aging Notions by Means of the Dispersion-type or Dilation-type Variability Orders

Some aging notions （ILR, IFR, DMRL, IFR（2） and their duals） are characterized in terms of the dispersion-type or dilation-type variability orders, using the residual lifetime of the underlying random variable. As one application of the main results, the aging notions IFR and DMRLS and their duals are also characterized by using the residual lifetimes of k-out-of-n systems. These results extend and strengthen some known characterizations in the literature.