A simple and effective scanning rule for a multi-channel system

We consider a multi-channel system in which one apparatus makes a sequence of observations, one at a time. By means of scanning, i.e. selecting a channel to be analyzed at any instant and deciding to stop at some stage, it is required to determine the channel in which there is the signal with prescribed constraints on error probabilities. A simple scanning rule, based on a cyclic application of a sequential probability ratio test (SPRT) is proposed for this problem. It is proved that in the case of Brownian motion, the expected scanning rime of this rule is equal to the one of the optimal scanning rule (which is known only for this case). The simple structure of this rule permits to obtain corrected Brownian approximations for its characteristics in the case of exponential family of distributions. The same procedure is used in multi-channel change point problem.