Abstract
The Adaptive Exponentially Weighted Moving Average (AEWMA) chart, which combines the Shewhart and classical EWMA schemes, is usually designed using the Average Run Length () as the criterion to be optimized. The shape of the run length distribution is known to change according to the magnitude of the shift in the process mean, ranging from highly skewed when the process is in-control or nearly to approximately symmetric when the shift is large. Therefore, the Median Run Length (
) provides a more meaningful interpretation than the
. In this paper, the
is used as an alternative performance criterion, and the AEWMA
chart is optimized for a wide range of mean shifts using zero and steady state modes. Comparative results show that the suggested AEWMA
chart offers a more balanced protection for detecting both small and large shifts in the process mean than the classical EWMA
chart, in terms of the
performance. The construction of the
-based AEWMA
chart is also illustrated using an example, and it is compared with competing charts.
Acknowledgements
The authors express their sincere thanks to the editor and the reviewers for their helpful suggestions and comments.
Notes
No potential conflict of interest was reported by the authors.