Based on comparisons of the survival of the renewal variable at age t ≥ 0 with the survival of its parent variable at t = 0 a class of life distributions namely Exponential better than renewal in expectation (EBRE) is defined. The corresponding dual class (EWRE) is also introduced. In this paper, we construct test statistic based on the scaled total time on test (TTT)-transform, to test exponentiality versus EBRE class or its dual EWRE. The distribution of the test statistic is investigated via simulation for small samples. Power of the test is also estimated by simulation. An example of 40 patients of blood cancer shows the possibility of applying the derived methodology on real data situation.