• ARMA (p, q) processes;
  • statistical process control;
  • change point detection;
  • change point diagnostics;
  • quality control;
  • special cause identification


Statistical process control charts are intended to assist operators in detecting process changes. If a process change does occur, the control chart should detect the change quickly. Owing to the recent advancements in data retrieval and storage technologies, today's industrial processes are becoming increasingly autocorrelated. As a result, in this paper we investigate a process-monitoring tool for autocorrelated processes that quickly responds to process mean shifts regardless of the magnitude of the change, while supplying useful diagnostic information upon signaling. A likelihood ratio approach was used to develop a phase II control chart for a permanent step change in the mean of an ARMA (p, q) (autoregressive-moving average) process. Monte Carlo simulation was used to evaluate the average run length (ARL) performance of this chart relative to that of the more recently proposed ARMA chart. Results indicate that the proposed chart responds more quickly to process mean shifts, relative to the ARMA chart, while supplying useful diagnostic information, including the maximum likelihood estimates of the time and the magnitude of the process shift. These crucial change point diagnostics can greatly enhance the special cause investigation. Copyright © 2010 John Wiley & Sons, Ltd.