Comparison with a standard via fully sequential procedures

We develop fully sequential procedures for comparison with a standard. The goal is to find systems whose expected performance measures are larger or smaller than a single system referred to as a standard and, if there is any, to find the one with the largest or smallest performance. The general formulation of comparison with a standard gives the standard a special status and tries to protect it when its performance is better than or even equal to performance measures of all the other alternatives. Therefore, the problem cannot be formulated as the selection of the best and a specialized procedure is required. Our procedures allow for unequal variances across systems, the use of common random numbers, and known or unknown expected performance of the standard. Experimental results are provided to compare the efficiency of the procedure with other existing procedures.

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