Hotelling´s T2 Method in Multivariate On-line Surveillance. On the Delay of an Alarm

A system for detecting changes in an on-going process is needed in many situations. On-line monitoring (surveillance) is used in early detection of disease outbreaks, of patients at risk and of financial instability. By continually monitoring one or several indicators, we can, early, detect a change in the processes of interest. There are several suggested methods for multivariate surveillance, one of which is the Hotelling’s T2. Since one aim in surveillance is quick detection of a change, it is important to use evaluation measures that reflect the timeliness of an alarm. One suggested measure is the expected delay of an alarm, in relation to the time of change () in the process. Here we investigate a delay measure for the bivariate situation. Generally, the measure depends on both change times (i.e. 1 and 2). We show that, for a bivariate situation using the T2 method, the delay only depends on 1 and 2 through the distance 1-2.