New classes of life distributions called new better (worse) than used at age $t_0$ in Laplace transform order, NBUL- $t_0$(NWUL - $t_0$) are introduced. For the classes NBUL - $t_0$(NWUL - $t_0$), preservation under convolution, mixture, mixing and the homogeneous Poisson shock model are studied. In the sequel, we obtain a test for $H_0$ : F is exponential versus $H_1$ : F is NBUL - $t_0$ and not exponential. The critical values and the powers of this test are calculated to assess the performance of the test. It is shown that the proposed test has high efficiencies for some commonly used distributions in reliability. Sets of real data are used as examples to elucidate the use of the proposed test for practical problems.