Mixed Exponentially Weighted Moving Average–Cumulative Sum Charts for Process Monitoring

TLDR

Control charts are widely used in statistical process control to detect special‑cause variation, with Shewhart charts sensitive to large shifts and CUSUM/EWMA charts designed to identify small to moderate disturbances. This study proposes a mixed EWMA–CUSUM chart to detect shifts in the process mean and evaluates its average run lengths. The proposed chart’s performance was compared to classical CUSUM, classical EWMA, fast‑initial‑response variants, adaptive CUSUM with EWMA shift estimator, weighted CUSUM, and runs‑rules‑based CUSUM/EWMA. The mixed chart proved more sensitive to small mean shifts than all other evaluated schemes. © 2012 John Wiley & Sons, Ltd.

Abstract

The control chart is a very popular tool of statistical process control. It is used to determine the existence of special cause variation to remove it so that the process may be brought in statistical control. Shewhart‐type control charts are sensitive for large disturbances in the process, whereas cumulative sum (CUSUM)–type and exponentially weighted moving average (EWMA)–type control charts are intended to spot small and moderate disturbances. In this article, we proposed a mixed EWMA–CUSUM control chart for detecting a shift in the process mean and evaluated its average run lengths. Comparisons of the proposed control chart were made with some representative control charts including the classical CUSUM, classical EWMA, fast initial response CUSUM, fast initial response EWMA, adaptive CUSUM with EWMA‐based shift estimator, weighted CUSUM and runs rules–based CUSUM and EWMA. The comparisons revealed that mixing the two charts makes the proposed scheme even more sensitive to the small shifts in the process mean than the other schemes designed for detecting small shifts. Copyright © 2012 John Wiley & Sons, Ltd.