A Note on Testing Exponentiality Against New Better Than Used of Specified Age

In this paper the problem is investigated how to prove that after a specified time t 0 of operation the conditional survival probability of an item is less than the corresponding survival probability of a new item. This problem occurs in various areas like for instance in industry, when designing a maintenance policy. For a randomly censored sample, test statistics are derived for testing the null hypothesis that a new item has stochastically the same residual life length as does a used item of specified age t 0 versus the alternative hypothesis that a new item has stochastically a longer residual life length as does a used item of specified age t 0. The tests are based on the asymptotic distribution of the test statistics and selected using the Pitman asymptotic relative efficacy. Since small samples are prevailing in reliability testing, further research is needed, which omits the asymptotic derivation.