Abstract
In this paper, we introduce a new test statistic for testing exponentiality against new better than used in the increasing convex average class of life distributions (NBUCA) based on Laplace transform. For this proposed test, the asymptotic properties are studied, and the critical values for sample size 5(1)50 are calculated. The powers of the test are also estimated by using a simulation study for commonly used distributions in reliability. The Pittman asymptotic efficiencies of this test are calculated and compared with some old tests. Finally, the test is applied to some real data. Copyright (c) 2014 John Wiley & Sons, Ltd.