Abstract
In this paper, comparison between the life distribution of a new unit with that of the remaining life or a used unit in the increasing convex order leads us to introduce a new class of life distributions which we call new better than used in increasing convex average order and denote by NBUCA. This class includes as subclasses the new better than used, NBU and the new better than used in increasing convex ordering, NBUC. Several properties of this class are presented, including the preservation under convolution, random maxima, mixing and formation of coherent structures. Stochastic comparisons of the excess lifetime at different times of a renewal process when the interarrival times belong to the NBUCA class are established. We provide also some applications of Poisson shock models. Finally testing exponentially against NBUCA is presented.