EWMA and CUSUM control charts in the presence of correlation
In Statistical Process Control, it is usually assumed that observations taken from the process at different times are independent with a constant mean and with variation due only to measurement error. In many processes this assumption of independence is not satisfied. The lack of independence of observations taken at different times may have a significant effect on the properties of a process monitoring technique.
A first order autoregressive process which is observed subject to measurement error is considered. Integral equation, Markov chain and simulation approaches are used to evaluate the average run length (ARL) of exponentially weighted moving average (EWMA) and one-sided cumulative sum (CUSUM) control charts used to monitor the process. The effects of correlation and measurement error on the ARL's of the control charts are studied for a process which is in control and for a process which has undergone a shift in mean level away from the target value. Methods of estimation of the parameters of the process are examined, and tables are given to assist in the design of EWMA and CUSUM control charts for AR(1) processes. Examples of designing an EWMA and a CUSUM chart for an AR(1) process are presented.