Accounting for phase I sampling variability in the performance of the MEWMA control chart with estimated parameters

ABSTRACT

In this article, we assess the performance of the multivariate exponentially weighted moving average (MEWMA) control chart with estimated parameters while considering the practitioner-to-practitioner variability. We evaluate the chart performance in terms of the in-control average run length (ARL) distributional properties; mainly the average (AARL), the standard deviation (SDARL), and some percentiles. We show through simulations that using estimates in place of the in-control parameters may result in an in-control ARL distribution that almost completely lies below the desired value. We also show that even with the use of larger amounts of historical data, there is still a problem with the excessive false alarm rates. We recommend the use of a recently proposed bootstrap-based design technique for adjusting the control limits. The technique is quite effective in controlling the percentage of short in-control ARLs resulting from the estimation error.

KEYWORDS:

• Bootstrap
• Estimation effect
• MEWMA control chart
• Phase I
• SPC
• Standard deviation of average run length
• Statistical process control

MATHEMATICS SUBJECT CLASSIFICATION:

• Primary 62
• Secondary 62P30
• 62HXX
• 62F40

Acknowledgment

The authors would like to thank the editor and the anonymous reviewer for their helpful comments.