In this article we introduce new classes of life distributions namely new better (worse) than used in expectation
at specific age t0 NBUE-t0 (NWUE-t0) and harmonic new better (worse) than used in expectation at specific
age t0 HNBUE-t0 (HNWUE-t0). The closure properties under various reliability operations such as convolution,
mixture, mixing and the homogeneous Poisson shock model of these classes are studied. Furthermore,
nonparametric tests are proposed to test exponentiality versus the NBUE-t0 and HNBUE-t0 classes. The critical
values and the powers of this tests are calculated to assess the performance of the tests. It is shown that the
proposed tests have high efficiencies for some commonly used distributions in reliability. Sets of real data are
used as examples to elucidate the use of the proposed tests for practical problems