An enhanced EWMA-t control chart for monitoring the process mean

ABSTRACT

The exponentially weighted moving average (EWMA) control chart with the sample mean $\bar{X}$ (EWMA-$\bar{X}$) is widely recognized as a competent tool to detect small and moderate shifts in the mean of a normally distributed process. One shortcoming of the EWMA-$\bar{X}$ chart is that it triggers an out-of-control signal when the process standard deviation is not stable. An alternative to the EWMA-$\bar{X}$ chart is the EWMA-t chart. Unlike the EWMA-$\bar{X}$ chart, the EWMA-t chart is robust to the changes in the process standard deviation. In this paper, we propose an auxiliary information-based (AIB) EWMA-t chart for monitoring the process mean, which requires information on the quality characteristic under study and any correlated auxiliary characteristic, named the AIB-EWMA-t chart. The Monte Carlo simulation method is used to compute the run length profiles of the proposed control chart. It is shown that the AIB-EWMA-t chart is uniformly and substantially better than the existing EWMA-t chart. Moreover, the AIB-EWMA-t chart could be used as an efficient alternative to the existing AIB-EWMA mean chart when the process standard deviation is unstable. An example is also used to demonstrate the implementation of the proposed and existing control charts.

KEYWORDS:

• Auxiliary information
• Average run length
• Control chart
• EWMA
• Regression estimator
• Statistical Process Control.

MATHEMATICS SUBJECT CLASSIFICATION:

• 62N10
• 62P30
• 62F03