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February 2004 A generalized EWMA control chart and its comparison with the optimal EWMA, CUSUM and GLR schemes
Dong Han, Fugee Tsung
Ann. Statist. 32(1): 316-339 (February 2004). DOI: 10.1214/aos/1079120139

Abstract

It is known that both the optimal exponentially weighted moving average (EWMA) and cumulative sum (CUSUM) control charts are based on a given reference value $\delta$, which, for the CUSUM chart, is the magnitude of a shift in the mean to be detected quickly. In this paper a generalized EWMA control chart (GEWMA) which does not depend on $\delta$ is proposed for detecting the mean shift. We compare theoretically the GEWMA control chart with the optimal EWMA, CUSUM and the generalized likelihood ratio (GLR) control charts. The results of the comparison in which the in-control average run length approaches infinity show that the GEWMA control chart is better than the optimal EWMA control chart in detecting a mean shift of any size and is also better than the CUSUM control chart in detecting the mean shift which is not in the interval $(0.7842\delta ,1.3798\delta )$. Moreover, the GLR control chart has the best performance in detecting mean shift among the four control charts except when detecting a particular mean shift $\delta,$ when the in-control average run length approaches infinity.

Citation

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Dong Han. Fugee Tsung. "A generalized EWMA control chart and its comparison with the optimal EWMA, CUSUM and GLR schemes." Ann. Statist. 32 (1) 316 - 339, February 2004. https://doi.org/10.1214/aos/1079120139

Information

Published: February 2004
First available in Project Euclid: 12 March 2004

zbMATH: 1105.62385
MathSciNet: MR2051010
Digital Object Identifier: 10.1214/aos/1079120139

Subjects:
Primary: 62L10
Secondary: 62N10

Rights: Copyright © 2004 Institute of Mathematical Statistics

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Vol.32 • No. 1 • February 2004
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