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) over bar) 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) over tilde) control charts, such as the Shewhart-(X) over tilde control chart, the exponentially weighted moving average (EWAM) -(X) over tilde control chart, and the generally weighted moving average (GWMA)-(X) over tilde median control chart have been developed in succession for monitoring the process mean/median. Although those mentioned (X) over tilde control charts are demonstrated much more robust than the (X) over tilde control charts with outliers, the shift-detecting ability is worse than that of (X) over tilde control charts without respect to outliers. Davis and Adams proposed a synthesized control scheme (called SS synthesized control scheme for short) which using the Shewhart-(X) over bar and R (denoted as Shewhart-(X) over bar /R) charts and the Shewhart trimmed mean and trimmed range (denoted as Shewhart -(X) over bar* / R*) charts for monitoring the process mean and variance with outliers. This study proposes a modified synthesized control scheme which integrating the EWMA- (X) over bar /R control charts and the EWMA- (X) over tilde /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) over bar /R charts and the (X) over tilde (or (X) over bar)*/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.