A Modified Play-the-Winner Rule for Sequential Trials

Abstract

The two-arm bandit type of Play-the-Winner rule is modified to sample simultaneously the two competing sequences of trials until the first “failure” occurs. Then the sequence without a failure is sampled until it fails, and the process is repeated. This modification leads to the direct application of the sequential probability ratio test on two paired geometric variables. A further modification leads to a scheme which avoids overshooting the stopping boundaries and reduces the total sample size. Exact formulas for the boundary limits, operating characteristics and ASN function for the proposed methods are presented.