Monte Carlo comparison of tests of exponentiality against NWBUE alternatives

In this paper we focus on the testing of exponentiality (which essentially captures no aging) against non‐monotonic aging captured by the fairly large class of new worse then better than used in expectation (NWBUE) alternatives. Three different tests are reviewed; these tests are based on three different characteristics of the NWBUE distributions, namely the moment characteristic, the scaled TTT (total time on test)‐transformation and the centered form of the scaled TTT‐transformation. They are compared with respect to size and power. The empirical size and empirical power of the tests are obtained by Monte Carlo simulations. The small sample critical points based on simulation are given for the ‘most useful’ test.