On Some Characterizations to NBRULC Class with Hypotheses Testing Application

In this paper, we investigate the probabilistic characteristics for new better than renewal used in Laplace transform in increasing convex order class, the closure properties under various reliability operations such as convolution, mixture, homogeneous Poisson shock model are studied. A new hypothesis test is constructed to test exponentiality against, based on U-statistic. Pitman’s asymptptic efficiency of the test are studied and compared with other tests. The percentiles of this test statistic are tabulated and the power of the new test statistics are calculated in case of censored and non-censored data. Finally, the right-censored data problem is given in some medical and engineering science applications to evaluate the performances of our test