Performance Analysis of Exponentially Weighted Moving Average Charts When Parameters Are Estimated

The exponentially weighted moving average (EWMA) control chart is typically designed assuming that standards are given for the process parameters. In practice, the parameters are rarely known, and control charts are constructed using estimates in place of the parameters. This practice can affect the control chart's run-length performance in both in- and out-of-control situations. Specifically, estimation can lead to substantially more frequent false alarms and yet reduce the sensitivity of the chart to detecting process changes. In this article, the run-length distribution of the EWMA chart with estimated parameters is derived. The effect of estimation on the performance of the chart is discussed in a variety of practical scenarios.