Testing exponentiality has long been an interesting issue in statistical inferences. This article is based on a modified measure of distance between two distributions. New measure is similar Kullback Leibler divergence and it is related to the Lin Wong divergence applied on the residual lifetime data. Modified measure, a consistent test statistic for testing the hypothesis of exponentiality against some alternatives is developed. In order to estimate the divergence, we first consider a method similar to Vasicek's method for estimating the Shannon entropy. Then, critical values of the test are computed by Monte Carlo simulation. Finally, we found that the powers differences between the proposed test and other tests. It is shown that the proposed test is better than other tests of exponentiality, when hazard rate function is increasing. Finally, the use of the proposed test is shown in two illustrative examples.

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