Sequential procedures for two-sample problem based on early failures from ranked set samples

Abstract

In this article, a class of sequential precedence tests based on ranked set samples (RSS-SPT) with different sequential rank schemes and different α-spending is proposed. The exact null distributions of the proposed RSS-SPT test statistics are derived and the corresponding critical values are tabulated. The performance of the class of RSS-SPT is evaluated in terms of their the power values and their efficiencies by means of the expected stopping location, expected number of failures, and expected total experimental time consumed. The exact power functions and efficiencies of different test procedures under the Lehmann alternative are derived. The performance of RSS-SPT is compared with the nonsequential precedence test based on ranked set samples under the Lehmann alternative based on exact calculation and under the location-shift alternative using Monte Carlo simulations. Conclusions and recommendations are provided based on the numerical results.