The class of better mean residual life at age t0

The conditional mean remaining life of an item of age t is called the mean residual life (MRL) at age t. In this paper we introduce a better mean residual life at t₀ (BMRL-t₀) class of life distributions, where the MRL decreases initially during [0, t₀] and then for t ≥ t₀ the MRL at time t is not greater than the MRL at t₀. It is shown that the BMRL-t₀ class contains the DMRL class, but it is a proper subclass of the NBUE class. The dual class of worse mean residual life at t₀(WMRL-t₀) is defined by reversing the direction of inequality. Some characteristics of these two classes are presented. We also develop the tests of exponentiality against the BMRL-t₀(WMRL-t₀) alternatives.