  Testing of various classes of life distributions has been addressed in the
literature for more than 45 years. In this paper, we consider the problem of
testing exponentiality (which essentially implies no ageing) against positive
ageing which is captured by the fairly large class of new better than used in
expectation (NBUE) distributions. These tests of exponentiality against NBUE
alternatives are discussed and compared. The empirical size of the tests is
obtained by simulations. Power comparisons for different popular alternatives
are done using Monte Carlo simulations. These comparisons are made for both
small and large sample sizes. The paper concludes with a discussion in which
suggestions are made regarding the choices of the test when a particular
alternative is suspected.
