Some control charts for the process mean and variance based on Downton's estimator

Abstract

The EWMA (exponentially weighted moving average) control chart is a good alternative to the Shewhart chart in the detection of small shifts. The EWMA charts for the sample means and sample ranges are constructed based on the assumption that the data used in the computation of the limits are outlier free. In most real life situations, outliers will occur in the data used in computing the limits. Since the EWMA chart is a weighted average of all past and current observations, it is insensitive to outliers. The detection of outliers using EWMA charts for the process mean and variance becomes even more difficult if the average sample range, R_, is used in the computation of the limits because the sample range, R, is easily influenced by outliers so that the limits will be stretched. In this paper, the use of Downton's estimator in setting up the limits of the EWMA charts for the process mean (EWMAMD) and the process variance (EWMAVD) is proposed. Monte Carlo simulations using SAS (statistical analysis system) version 8 are conducted to show that the new EWMA charts have higher probabilities in detecting outliers while maintaining the same rates of type-I errors compared to the standard EWMA chart.