Evaluations of some exponentially weighted moving average methods

Abstract

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 onesided 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 are considered such as the expected delay, the ARLI, the probability of successful detection and the predictive value of an alarm to give a broad picture of the features of the methods. Results are presented both for a fixed ARLO and a fixed probability of a false alarm. The differences highlight the essential problem of how to define comparability between surveillance methods. The results are from a large-scale simulation study. Special attention is given to the effect on the confidence in the final results by the stochastic variation in the calibration of the methods. 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 many respects.