ON PERFORMANCE OF METHODS FOR STATISTICAL SURVEILLANCE

Abstract

Statistical surveillance is used to detect a change in a process. It might for example be a change of the level of a characteristic of an economic time series or a change of heart rate in intensive care. An alarm is triggered when there is enough evidence of a change. When surveillance is used in practice it is necessary to know the characteristics of the method, in order to know which action that is appropriate at an alarm. The average run length, the probability of a false alarm, the probability of successful detection and the predictive value of an alarm are measures that are used when comparing the performance of different methods for statistical surveillance. In the first paper a detailed comparison between two important methods, the Exponentially Weighted Moving Average and the CUSUM, is made. Some consequences of using only the average run length as the measure of performance are demonstrated. Differences between the methods are discussed in regard to the measures mentioned above. The second paper is focused on the predictive value of an alarm, that is the relative frequency of motivated alarms among all alarms. The interpretation of an alarm is difficult to make if the predictive value of an alarm varies with time. Thus conditions for a constant predictive value of an alarm are studied. The Shewhart methods and some Moving Average methods are discussed and some general differences in performance are pointed out. Three different types of Exponentially Weighted Average are discussed and some differences established. It is further stated that if a Fast Initial Response feature is added to a method, this will in general lower the level of the predictive value of an alarm in the beginning of the surveillance. The increased probability of alarm in the beginning might thus be useless.