Evaluations of some Exponentially Weighted Moving Average methods

Abstract

SUMMARYSeveral 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.

Optimal Surveillance Based on Exponentially Weighted Moving Averages

“…For small values of 8 it is very slow. However, the use of the asymptotic variance is very common and it can in fact be preferred to the exact version in some aspects, see for example Sonesson (2003). This procedure will be referred to as the "asymptotic version".…”

“…Barriers avoid bad properties in the "worst possible" case when the change occurs at a time when the earlier observations least favor the detection of the change. Sonesson (2003) examined the inferential differences between two-sided, one-sided with barrier and ordinary one-sided methods. In this paper we will only deal with ordinary one-sided procedures in order to draw attention to certain optimality issues since optimality is most clearly expressed in this situation.…”

Statistical Surveillance. Optimality and Methods

“…A slight modification of the barriers used in the papers above is used by Morais and Pacheco (1998) to achieve more easily approximated ARL properties. Comparisons between one-and two-sided EWMA with and without barriers with respect to ARL and ED are reported by Sonesson (2001). While the ARL-optimal value of A is zero, as expected, for the one-sided case this is not true for the two-sided one.…”

Properties and Use of the Shewhart Method and Its Followers

“…However, in a surveillance system the error probabilities are more complicated because of the repeated decisions. A comparison between the EWMAa and the EWMAe methods, for the standard case of Section 3, can be found in Sonesson (2003), where it is concluded that the EWMAa version is preferable for most cases. EWMAe give more frequent alarms at the first time point for the same ARL 0 .…”