  We introduce some new generalized stochastic orderings (in the spirit of
relative ageing) which compare probability distributions with the exponential
distribution.
  These orderings are useful to understand the phenomenon of positive ageing
classes and also helpful to guide the practitioners when there are crossing
hazard rates and/or crossing mean residual lives. We study some
characterizations of these orderings. Inter-relations among these orderings
have also been discussed.
