Continual surveillance aiming to detect an increased frequency of some rare event is of interest in several different situations in quality control, medicine, economics and other fields. Examples are continual surveillance of defect articles in a production process or surveillance of a business cycle. Surveillance of rare health events in general and especially surveillance of congenital malformations has been a field of unabating interest during the last decades. Since the Thalidomide episode in the early 60's, several registries of congenital malformations are in operation all over the world. The basic idea is that if a 'catastrophe' occurs an alarm should be signalled as soon as possible after the occurrence. A method developed for this situation is the Sets method that focuses on the intervals between events under surveillance, e.g. intervals between successive births of malformed babies. If a previously defined number of such intervals are 'short' an alarm is triggered. The traditional evaluation measure used when discussing the Sets method is the ARL (Average Run Length). Here, evaluation measures such as the probability of a false alarm, the probability of a successful detection and the predictive value of an alarm are derived and discussed for the Sets method. The information provided by these measures is important for the implementation and use of a system of surveillance in practice
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