The effectiveness of robust mixed EWMA-CUSUM control chart on G-and-H distribution

Cumulative sum (CUSUM) chart and exponentially weighted moving average (EWMA) chart are popularly used in statistical process control (SPC) as they can quickly detect small shifts in the process mean. Recently, a Mixed EWMA-CUSUM (MEC) control chart was introduced for better detection of small shifts. Like the EWMA and CUSUM control charts, the MEC chart relies on the normality assumption for optimal performances. In the case that the underlying distribution of the data is non-normal, the chart may no longer be effective in signaling a true out-of-control process. Therefore, this paper proposed the use of a median estimator for Phase II monitoring of location via the MEC chart. The performance of this robust MEC control chart was tested on various g-and-h distributions in terms of the average run length (ARL). It has been found to perform well regardless of the distributional shapes compared to the standard MEC chart which uses the mean as the estimator.