A Multivariate Chart is a control chart for variables data. Multivariate Charts are used to detect shifts in the mean or the relationship (covariance) between several related parameters.
Several charts are available for Multivariate analysis:
The T2 control chart, based upon the Hotelling T2 statistic, is used to detect shifts in the process. Instead of using the raw Process Variables, the T2 statistic is calculated for the Principal Components of the process, which are linear combinations of the Process Variables. While the Process Variables may be correlated with one another, the Principal Components are defined such that they are orthogonal, or independent, of one another, which is necessary for the analysis.
The Squared Prediction Error (SPE) chart may also be used to detect shifts. The SPE is based on the error between the raw data and a fitted PCA (Principal Component Analysis) model (a prediction) to that data.
Contribution Charts are available for determining the contributions of the Process Variables to either the Principal Component (Score Contributions) or the SPE (Error Contributions) for a given sample. This is particularly useful for determining the Process Variable that is responsible for process shifts.
Loading Charts provide an indication of the relative contribution of each Process Variable towards a given Principal Component for all groups in the analysis.
Some restrictions apply to these analyses:
The process variables are restricted to a subgroups of size one.
No provision is made for missing data. If a sample row has an empty cell, an error message is provided, requiring that either the affected variable or the affected sample be dropped from the analysis.
This implementation specifically excludes PLS (Partial Least Squares) analyses, where the samples for the process variables are associated with quality parameters.
For technical reference, see also
1. Martens, H. and Næs, T., Multivariate Calibration, , J. Wiley and Sons, 1989.
2. MacGregor, J.F. and Kourti, T., Statistical Process Control of Multivariate Processes, Control Eng. Practice, Vol.3, No. 3, pp.403-414, 1995.
3. Miller, P., Swanson, R.E. and Heckler, C.E., Contribution Plots: A Missing Link in Multivariate Quality Control, Multivariate Statistical Process Control and Plant Performance Monitoring Industrial Representatives Meeting, December 19, 1995.
4. Jackson, J.E., A User Guide to Principal Components, J. Wiley and Sons, 1991.
Interpretation & Calculations