A Weighted CUSUM Chart for Detecting Patterned Mean Shifts

摘要

Most conventional control charts focus on detecting a constant mean shift. In reality, however, it is often important to deal with situations where the mean of the monitoring sequence has a dynamic shift pattern, e.g., residuals from a time series. In these cases, the conventional control charts may perform poorly, as they do not consider the information due to what is known as "forecast recovery" contained in the patterned mean shift. This paper proposes a new weighted cumulative sum (WCUSUM) procedure for monitoring a sequence with a patterned mean shift. This method first estimates the dynamic mean of the sequence, then uses the estimates for weighting the incremental in the conventional CUSU M chart. Guidelines for designing the WCUSUM chart are proposed, and the performance is compared with that of the conventional CUSU M chart and other alternatives for detecting patterned mean shifts. It is found that the WCUSUM chart performs far superior to other charts for detecting small to moderate shifts when forecast recovery is present and performs competitively otherwise.