A Comparison of 2-CUSUM Stopping Rules for Quickest Detection of Two-Sided Alternatives in a Brownian Motion Model

This work compares the performance of all existing 2-CUSUM stopping rules used in the problem of sequential detection of a change in the drift of a Brownian motion in the case of two-sided alternatives. As a performance measure, an extended Lorden criterion is used. According to this criterion, the optimal stopping rule is an equalizer rule. This paper compares the performance of the modified drift harmonic mean 2-CUSUM equalizer rules with the performance of the best classical 2-CUSUM equalizer rule whose threshold parameters are chosen so that equalization is achieved. This comparison is made possible through the derivation of a closed-form formula for the expected value of a general classical 2-CUSUM stopping rule.