A test for the bidirectional stochastic order with an application to quality control theory

A test for the bidirectional stochastic ordering is developed in this paper. The main properties of such a test are investigated. The asymptotic distribution of the statistic of the test is obtained under conditions which allow the construction of critical regions with a specific level of significance. It is also proved that the test is consistent on the whole set of alternatives. An application of such a test to quality control theory is developed.