A general family of NBU classes of life distributions

In this paper we introduce and study a family of new better than used ageing notions parameterized by a function hh. The new better than used (NBU), the new better than used of a specified age t0(NBU-t0) and the new better than used in total time on test transform order (NBUT), are special cases of this new family. We study some properties of the new family, and we give some applications of it in actuarial science, reliability theory and statistics.