In this article, a test statistic for testing exponentiality versus a used better than aged in Laplace transform ordering class of life distribution based on a U-statistic is proposed. Pitman’s asymptotic efficiencies of the test are calculated and compared to other tests. The percentiles of this test statistic are tabulated for censored and non-censored data, and the powers of this test are estimated for some famously alternative distributions in reliability, such as the Weibull, Makeham, linear failure rate, and Gamma distributions. Finally, examples in different areas are used as practical applications of the proposed test.