Identifying Variables Contributing to Outliers in Phase I

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 ...