Statistical and economic analyses of an EWMA-based synthesised control scheme for monitoring processes with outliers

Abstract

This work presents an exponentially weighted moving average (EWMA)-based synthesised control scheme for a process with outliers. Based on experience, some processes occasionally have outliers. The use of traditional mean ( X ) and range (R) control charts (denoted as X /R) for monitoring process mean and variance leads to high-level false alarms. In this study, the fast-detection technique (EWMA control chart) and robust control chart (median () control chart) are adopted. Via simulations, with various shifts in process sample mean and variance, the average time to work stoppage (ATWS) and average quality cost (AQC) for the synthesised control schemes are evaluated under some contaminated normal distributions and cost parameter settings. We conclude that, from a statistical perspective, the EWMA-based synthesised control scheme detects process shifts faster than the Shewhart-based (SB) synthesised control scheme with or without contaminated data. From an economic perspective, when the percentage of contaminated data is small or none, the EWMA-based synthesised control scheme again outperforms the SB synthesised control scheme. When the percentage of contaminated data is large, the SB synthesised control scheme performs better than the EWMA-based synthesised control scheme. This analytical result is a valuable reference for practitioners facing a process with outliers.

Keywords:

• control chart
• EWMA
• synthesised
• median
• outliers
• quality cost

Acknowledgement

This work was supported in part by the National Science Council, Taiwan, ROC, under Contract nos. NSC 97-2221-E-129-013 and NSC 98-2221-E-129-007.