Asymptotically Optimum Sample Size for Quickest Detection

A method is presented for selecting the asymptotically optimum sample size M for detecting a sudden change in the statistics of an observed process. The test statistic is assumed to be a sum of M consecutive values of some single sample detector and the optimization criterion is to minimize the mean time to detection MD for a given mean time between false alarms MF. It is shown that for large MF and MD the solution can be expressed as a function of the single variable √MFß (or alternatively √MDß) where ß is a measure of the signal-to-noise ratio (SNR).