Robust CUSUM Charts for Monitoring the Process Mean and Variance

This paper considers the problem of obtaining robust control charts for detecting changes in the mean p and standard deviation a of process observations that have a continuous distribution. The standard control charts for monitoring p and a are based on the assumption that the process distribution is normal. However, the process distribution may not be normal in many situations, and using these control charts can lead to very misleading conclusions. Although some control charts for p can be tuned to be robust to non-normal distributions, the most critical problem with non-robustness is with the control chart for a. This paper investigates the performance of two CUSUM chart combinations that can be made to be robust to non-normality. One combination consists of the standard CUSUM chart for p and a CUSUM chart of absolute deviations from target for a, where these CUSUM charts are tuned to detect relatively small parameter shifts. The other combination is based on using winsorized observations in the standard CUSUM chart for p and a CUSUM chart of squared deviations from target for a. Guidance is given for selecting the design parameters and control limits of these robust CUSUM chart combinations. When the observations are actually normal, using one of these robust CUSUM chart combination will result in some reduction in the ability to detect moderate and large changes in p and a, compared with using a CUSUM chart combination that is designed specifically for the normal distribution. Copyright (C) 2009 John Wiley & Sons, Ltd.