Multivariate control charts are used to monitor two or more interrelated process variables. Where univariate control charts are used to monitor a single independent process characteristic, multivariate control charts are necessary when process variables are correlated. A Hotelling T2 chart, or just T2 chart for short, is one type of multivariate control chart. A T2 chart can detect shifts in the mean or the relationship between several interrelated variables. The observations can either be individual observations of the process variables or they can be grouped into rational subgroups.
You can construct a multivariate control chart using current or historical data. The control chart is said to be a Phase I chart if it is constructed using current data; the control chart is said to be a Phase II chart if it is constructed using target statistics from a historical data set. In Phase I, you check that the process is stable and establish a historical data set from which to calculate target statistics for the process. In Phase II, the multivariate control chart uses the target statistics from Phase I in order to monitor new process observations.
To construct a Phase II multivariate control chart, first identify a period of time during which the process is stable and capable.
1. Develop a Phase I control chart to verify that the process is stable over this period.
The data used in Phase I provides a historical data set.
2. Save the target statistics for this historical data set.
3. Monitor the on-going process using a Phase II control chart based on the target statistics that were saved in step 2.