A New Approach to Moments Inequalities for NRBU and RNBU Classes With Hypothesis Testing Applications

In this article, new moment inequalities are derived for new renewal better than used (NRBU) and renewal new better than used (RNBU) classes of life distributions demonstrateing that if the mean life is finite for any of them, then all higher order moments exist. Next, based on these inequalities, new testing procedures for testing exponentiality against any one of the above classes are introduced and studied showing that they are simpler than most earlier ones and hold high efficiency for some commonly used alternatives and compared the two testes relative to the tests of Mahmoud et al (2002) and (2003). The power and critical values of the proposed statistic are calculated. Real examples are presented to elucidate the use of the proposed tests for practical reliability analysis. Finally,the problem in case of right censored data is also handled with some applications. Abstract-new renewal better than used (NRBU), renewal new better than used (RNBU), moments, U -Statistic, life testing, efficiency, Monte Carlo method, power and censored data.new renewal better than used (NRBU), renewal new better than used (RNBU), moments, U -Statistic, life testing, efficiency, Monte Carlo method, power and censored data.