A nonparametric procedure based on early failures for selecting the best population using a test for equality

In this paper, we first propose a nonparametric test based on early failures for the equality of two lifetime distributions against two alternatives regarding the best population. This procedure makes use of the precedence statistic which can determine the difference between populations based on early (100q%) failures. Hence, this procedure can be useful in life-testing experiments in biological as well as industrial settings. First, we propose the test procedure and derive the null distribution of the test statistic in the two-sample case with equal or unequal sample sizes. We also present the exact probability of correct selection under the Lehmann alternative. Then, we generalize the test procedure to the k-sample case. Critical values for some sample sizes are presented. Next, we examine the performance of this test procedure under a location-shift alternative through Monte Carlo simulations. An example is presented to illustrate our test procedure with selecting the best population as an objective. Finally, we make a few concluding remarks and some suggestions for the choice of q.