Repeated significance test procedure for testing against new better than used of specified age

In life testing and clinical trials observations are available over a period of time. In those cases a sequential or multistage test might be appropriate. One alternative is to develop non-parametric repeated significance test (RST) procedure discussed in detail by Sen (1978). It is pointed out that from time and cost consideration the RST is more desirable and it is no less efficient than the terminal test in asymptotic sense. Alam and Basu (1990) developed RST for testing exponentiality against new better than used alternative. Recently, Pandit and Shirke (2006) considered the problem of testing exponentiality against increasing failure rate alternatives using non-parametric RST procedure. In this paper, we have developed RST procedure for testing exponentiality against NBU-t0 alternatives based on a U-statistic with a kernel of degree two which is proposed for this problem with fixed sample size by Hollander, Park and Proschan (1986). The asymptotic null distribution of this procedure is studied. The estimates of the expected sample size and power of the test procedure are obtained using simulation experiments for Weibull, Linear failure rate and Exponentiated exponential distributions as alternatives. The study shows that there is considerable amount of saving with respect to the number of observations required to arrive at a decision