Effect of bivariate data's correlation on sequential tests of circular error probability

The problem of evaluating a military or GPS/GSM system's precision quality is considered in this article, where one sequentially observes bivariate normal data (Xi,Yi)'s and wants to test hypotheses on the circular error probability (CEP) or the probability of nonconforming, i.e., the probabilities of the system hitting or missing a pre-specified disk target. In such a problem, we first consider a sequential probability ratio test (SPRT) developed under the erroneous assumption of the correlation coefficient ρ=0, and investigate its properties when the true ρ≠0. It was shown that at least one of the Type I and Type II error probabilities would be larger than the required ones if the true ρ≠0, and for the detailed effects, exp{−2}≈0.1353 turns out to be a critical value for the hypothesized probability of nonconforming. Moreover, we propose several sequential tests when the correlation coefficient ρ is unknown, and among these tests, the method of generalized sequential likelihood ratio test (GSLRT) in Bangdiwala (1982) seems to work well.