Integrating Mean and Median Charts for Monitoring an Outlier-Existing Process

An effective control scheme can be instrumental in increasing productivity and reducing cost. While facing an outlier-existing process, using the mean ( X ) control chart and the range (R) control chart for monitoring the process mean and variance will lead to high level false alarms. Recently, some median ( X~ ) control charts, such as the X~ Shewhart control chart, the exponentially weighted moving average (EWMA) X~ control chart, and the generally weighted moving average (GWMA)X~ median control chart have been developed in succession for monitoring the process mean/median. Although those mentioned X~ control charts are demonstrated much more robust than the X control charts with outliers, the shift-detecting ability is worse than that of X control charts without respect to outliers. Davis and Adams proposed a synthesized control scheme (called SS synthesized control scheme for short) which using the ShewhartX and R (denoted as R X / Shewhart ) charts and the Shewhart trimmed mean and trimmed range (denoted as * * / Shewhart R X ) charts for monitoring the process mean and variance with outliers. This study proposes a modified synthesized control scheme which integrating the EWMAX /R control charts and the EWMAX~ /R control charts (called EE synthesized control scheme for short) for monitoring an outlier-existing process. A diagnostic statistic technique is adopted herein to be a bridge between the X /R charts and the X~ (or * X )/R charts). With various shifts of the process sample mean, the average time to work stoppage (ATWS) is evaluated under some contaminated normal distributions. We conclude that the EE synthesized control scheme outperforms the SS synthesized control scheme for monitoring the small shift of the process mean or variance. This result provides a valuable recommendation while facing an outlier-existing process.