Evaluations of some Exponentially Weighted Moving Average methods

Abstract

The need for statistical surveillance has been noted in many different areas, and examples of applications include the detection of an increased incidence of a disease, the detection of an increased radiation level and the detection of a turning point in a leading index for a business cycle. In all cases, preventive actions are possible if the alarm is made early. Several versions of the EWMA (Exponentially Weighted Moving Average) method for monitoring a process with the aim of detecting a shift in the mean are studied both for the one-sided and the two-sided case. The effects of using barriers for the one-sided alarm statistic are also studied. One important issue is the effect of different types of alarm limits. Different measures of evaluation, suitable in different types of applications, are considered such as the expected delay, the ARL¹, the probability of successful detection and the predictive value of an alarm, to give a broad picture of the features of the methods. Results from a large-scale simulation study are presented both for a fixed ARL0 and a fixed probability of a false alarm. It appears that important differences from an inferential point of view exist between the one- and two-sided versions of the methods. It is demonstrated that the method, usually considered as a convenient approximation, is to be preferred over the exact version in the overwhelming majority of applications.