Optimal ordering of observations for fast sequential detection

The effect of the ordering of independent and non-identical observations on the average number of samples needed to make a decision in a sequential binary hypothesis test is analyzed in this paper. We show that among all permutations of ordering of the observations, the average sample number (ASN) is minimum for the order in which the area under the receiver operating characteristic (ROC) curve for each of the non-identically distributed observations is monotonically decreasing. The claim is verified by computing the ASN of a generalized sequential probability ratio test (GSPRT) for different orderings of observations, which are independent and non-identical Gaussian random variables, using a combination of analytical and numerical techniques.