Optimal design of the adaptive EWMA chart for the mean based on median run length and expected median run length

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 (ARL) 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 (MRL) provides a more meaningful interpretation than the ARL. In this paper, the MRL is used as an alternative performance criterion, and the AEWMA X¯ chart is optimized for a wide range of mean shifts using zero and steady state modes. Comparative results show that the suggested AEWMA X¯ chart offers a more balanced protection for detecting both small and large shifts in the process mean than the classical EWMA X¯ chart, in terms of the MRL performance. The construction of the MRL-based AEWMA X¯ chart is also illustrated using an example, and it is compared with competing charts.