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In this paper we will prove that if the life time of an item has used better than aged in an increasing concave ordering UBAC(2) ageing property and if the mean life is finite then the moment generating function exists and is finite. A new technique for testing exponentially versus UBAC(2) class of life distribution based on the moment generating function is introduced. Using simulation, critical values for censored and non-censored data, pitman’s asymptotic efficiency and power of the test for some commonly used distributions in reliability are calculated. Finally, medical applications are presented as an example to elucidate the use of the proposed test statistic for practical reliability analysis.

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