A generally weighted moving average t control chart for monitoring shifts in the process mean

Abstract

Control charts based on the sample mean $\overline{X}$ are used for monitoring shifts in the process mean under the assumption that the process standard deviation is stable or well estimated. However, in many applications, this assumption is violated. In this case, t control charts are preferred as they are robust to changes in the process standard deviation. In this article, a generally weighted moving average chart based on the t statistic (referred as GWMA t chart) is proposed for monitoring shifts in the process mean. Its performance is studied using Monte Carlo simulation. It is shown that the proposed chart is more effective than the Shewhart t and EWMA t charts. Moreover, it is found more robust than the GWMA $\overline{X}$ chart to changes in the process standard deviation. Finally, two illustrative examples are given to display the application of the proposed chart.

KEYWORDS:

• Average run-length
• control chart
• EWMA
• GWMA
• t statistic

Acknowledgements

The authors would like to thank the Editor and the referees for their useful comments which resulted in improving the quality of this article.