Revisiting the one-sided EWMA control chart

Exponential Weighted Moving Average (EWMA) control charts have been widely used in Statistical Process Control (SPC) to detect small and persistent process shifts. In theory, EWMA control limits monotonically increase over time to account for the continual growth of the EWMA statistic’s variance. However, these control limits are often assumed constant and are set to their respective asymptotic limits to simplify the process of applying and analyzing EWMA control charts. One-sided EWMA charts are often implemented when it is only desirable to detect shifts in a specific direction. When using one-sided EWMA charts, reflecting boundaries (resets) can be used to prevent the statistic from drifting too far from the chart’s control limit, which can delay shift detection. There have been several research efforts into designing and studying the performance of one-sided EWMA charts with reflecting boundaries. However, these efforts have maintained the constant control limit assumption. When implementing a reflecting boundary, the EWMA statistic’s variance is constantly being reset to zero, which may significantly affect the constant control limit assumption’s validity. The focus of this paper is to understand behavior of the one-sided EWMA control charts with constant and time-varying limit assumption through simulation studies.