In this paper, test statistic for testing exponentiality versus exponential better than used in Laplace transform order based
on goodness of fit approach is discussed. Pitman's asymptotic efficiencies of our test are calculated and compared with other
tests. The percentiles of this test are tabulated. The powers of the test are estimated for famously used distributions in aging
problems. In case of censored data our test is applied and the percentiles are calculated and tabulated. Finally, examples in
different fields are used as practical applications for the proposed test.