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In this paper a new test statistic for testing exponentiality against renewal new better than used in Laplace transform order(RNBUL) based on goodness of fit is studied. selected critical values are tabulated for sample size 5(5)50. Pitman’s asymptotic efficiencies of the test and Pitman’s asymptotic relative efficiencies (PARE) are calculated . The power of this test are estimated for some famous alternatives distributions in reliability such as Wiebull, linear failure rate (LFR) and Gamma distributions. The problem in case of right censored data is also handled. Finally, some applications to elucidate the usefulness of the proposed test in reliability analysis are discussed.

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