Hotelling's T 2 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 T 2. 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 (τ) in the process. Here we investigate a delay measure for the bivariate situation. Generally, the measure depends on both change times (i.e. τ1 and τ2). We show that, for a bivariate situation using the T 2 method, the delay only depends on τ1 and τ2 through the distance τ1–τ2.