Robust residual control chart for contaminated time series: A solution to the effects of outlier-driven parameter misestimation on the control chart performance

Abstract

Control charts have typically been constructed using estimators obtained under assumptions of data independence and a given distribution of data. Here, I deal with cases in which neither of these conditions are satisfied. In particular, I consider the case of data obtained from a first-order autoregressive (AR(1)) time series model that have been contaminated by outlying process observations. I first analyze the effects of contaminations on the accuracy of estimation of parameters and control limits, and thus on the performance of time-series control charts. Next, I present a novel design for a robust control chart suitable for autocorrelated observations that is robust against the effects of contaminations. The proposed chart is based on an innovative approach to parameter estimation of autocorrelated data based on our previously developed Iteratively Robust Filtered Fast- estimation method. This chart is shown to outperform the classical control charts’ ability to detect structural changes, including changes in the process mean and in the variance of errors. This improvement in performance, as measured by Average Run Length and Mean Squared Deviation, is verified in a simulation study. This method has clear potential to improve control charts for applications whereby the data being monitored is both autocorrelated and contaminated.