On-line monitoring is needed to detect outbreaks of diseases like influenza. Surveillance is also needed for other kinds of outbreaks, in the sense of an increasing expected value after a constant period. Information on spatial location or other variables might be available and may be utilized....

The detection of a change from a constant level to a monotonically increasing (or decreasing) regression is of special interest for the detection of outbreaks of, for example, epidemics. A maximum likelihood ratio statistic for the sequential surveillance of an “outbreak” situation is...