Testing renewal new better than used life distributions based on U-test

New test-statistic for testing exponentiality against renewal new better than used (RNBU) class of life distribution based on U-statistic is studied. Selected critical values are tabulated for sample size n = 5(5)50. The Pitman asymptotic efficiency (PAE) of the test is calculated and compared with, the (PAE) of the test for new renewal better than used (NRBU) class of life distribution [see M.A.W. Mahmoud, S.M. EL-arishy, L.S. Diab, A non-parametric test of new renewal better than used class of life distributions, in: Proceedings of the International Conference on Mathematics Trends and Developments, Cairo, Egypt, vol. 4, 2002, pp. 191-203]. The power of the test is estimated by simulation at 0.05 significant level. A real example is given to elucidate the use of the proposed test. The problem in case of right-censored data is also handled.