Test for new better than used in convex ordering

Class of life distributions which are new better than used in convex ordering (NBUC) is dealt with. A probabilistic characterization is introduced to measure the degree of NBUC-ness. A nonparametric procedure is also developed to test the exponentiality against the strict NBUC property, therein, the theory of U-statistics and jackknife is utilized to establish the asymptotic normality of the test statistic. Furthermore, Edgeworth expansion and bootstrap are employed to improve the accuracy of the approximation. Some numerical simulations on the power are presented as a demonstration for the proposed procedure.