Asymptotic Performance of a Multichart CUSUM Test Under False Alarm Probability Constraint

Traditionally the false alarm rate in change point detection problems is measured by the mean time to false detection (or between false alarms). The large values of the mean time to false alarm, however, do not generally guarantee small values of the false alarm probability in a fixed time interval for any possible location of this interval. In this paper we consider a multichannel (multi-population) change point detection problem under a non-traditional false alarm probability constraint, which is desirable for a variety of applications. It is shown that in the multichart CUSUM test this constraint is easy to control. Furthermore, the proposed multichart CUSUM test is shown to be uniformly asymptotically optimal when the false alarm probability is small: it minimizes an average detection delay, or more generally, any positive moment of the stopping time distribution for any point of change.