An Evaluation of the Double Exponentially Weighted Moving Average Control Chart

Abstract

In this article we perform a careful investigation of the double exponentially weighted moving average (DEWMA) chart performance for monitoring the process mean. We compare the performance of this chart to the usual EWMA control chart based on zero-state and worst-case average run length (ARL) measures. We also evaluate the signal resistance measure of the DEWMA chart and compare its maximum value to that of the EWMA chart. We show that the superiority of the DEWMA chart over the simpler standard EWMA chart based on zero-state ARL performance disappears when the smoothing constant of the EWMA chart is chosen to give weights to past observations closer to those given by the DEWMA chart. Moreover, our results show that the standard EWMA chart has much better performance than the DEWMA chart in terms of worst-case ARL values, especially when small smoothing constants are used. We also demonstrate using an illustrative example that the DEWMA chart can build up an exceedingly large amount of inertia when used to monitor the process mean.

Keywords:

• Double exponential smoothing
• EWMA control chart
• Inertia
• Signal resistance
• Statistical process control
• Worst-case run length

Mathematics Subject Classification:

• 62L10
• 62P30

Acknowledgments

The authors greatly appreciate the helpful comments of the editor and an anonymous referee. Their comments have contributed substantively in the evolution of this article. The research of W. H. Woodall was partially supported by NSF Grant CMMI-0927323.