Identifying Variables Contributing to Outliers in Phase I

Abstract

When a process is monitored with a T ² control chart in a Phase II setting, the MYT decomposition is a valuable diagnostic tool for interpreting signals in terms of the process variables. The decomposition splits a signaling T ² statistic into independent components that can be associated with either individual variables or groups of variables. Since these components are T ² statistics with known distributions, they can be used to determine which of the process variable(s) contribute to the signal. However, this procedure cannot be applied directly to Phase I since the distributions of the individual components are unknown. In this article, we develop the MYT decomposition procedure for a Phase I operation, when monitoring a random sample of individual observations and identifying outliers. We use a relationship between the T ² statistic in Phase I with the corresponding T ² statistic resulting when an observation is omitted from this sample to derive the distributions of these components and demonstrate the Phase I application of the MYT decomposition.

Keywords:

• Beta distribution
• Multivariate statistical process control
• MYT decomposition
• T ² statistic

Mathematics Subject Classification:

• Primary 62P30
• Secondary 62E15

Acknowledgments

The authors would like to thank the referee and the editor for their useful comments which helped improve this manuscript.

Notes

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∗p < 0.01