Cusum charts for monitoring an autocorrelated process

Control charts for process monitoring have traditionally been designed and evaluated under the assumption that observations on the process output at d ifferent times are independent. However, autocorrelation may be present in many processes, and may have a strong impact on the properties of control c harts. This paper investigates CUSUM control charts for monitoring the proc ess mean for the situation in which observations from the process can be mo deled as an AR(1) process plus an additional random error. CUSUM charts bas ed on plotting the residuals from model forecasts, or on plotting the origi nal observations, are considered. CUSUM charts based on the original observ ations perform as well as CUSUM charts of residuals, except in the case in which the level of autocorrelation is high and the shift in the process mea n is large. A method for designing the CUSUM chart of the observations in t he presence of autocorrelation is given. The CUSUM charts are compared to S hewhart and EWMA charts based on the residuals or on the original observati ons. The CUSUM and EWMA charts perform similarly in terms of the ability to detect shifts in the process mean.