Performance and Robustness of Control Charting Methods for Autocorrelated Data

Statistical process control (SPC) has been used to achieve and maintain control of various processes in industry (Stoumbos, Reynolds, Ryan, and Woodall 2000). The control chart is a primary SPC tool to monitor process variability and promote quality improvement by means of detecting process shifts requiring corrective actions. As a graphical monitor, control charts generally contain a centerline and two other horizontal lines called control limits, the width of which is often proportional to the standard deviation of the charted statistic. If a point plots outside the control limits, the process is declared not to be in a state of control. Since the advent of Shewhart charts, many control charts have been developed to monitor, control, and improve processes. Traditional control charts such as x-bar charts, CUSUM (cumulative sum) charts, and exponentially weighted moving average (EWMA) charts assume the independence of observations over time. With significant advances in measurement and data collection technology, however, measurements are taken at increasingly higher rates and are more likely to be autocorrelated (Montgomery and Woodall 1997; Woodall and Montgomery 1999). This leads to a significant deterioration of traditional control chart performance, a phenomenon that has been discussed by Johnson and Bagshaw (1974), Bagshaw and Johnson (1975), Harris and Ross (1991), Alwan (1992), Woodall and Faltin (1993), and many others. Positive autocorrelation typically increases the variance of the charted statistic so that the control limits determined under the independence assumption are too narrow, giving a higher-than-expected number of false alarms. Goldsmith and Whitefield (1961) revealed this relation between the nature of autocorrelation and the false alarm rate for CUSUM charts. There are two primary classes of approaches for control charting in the presence of autocorrelation: Applying traditional control charts to the original autocorrelated data with the control limits adjusted to account