When to Use a Multivariate Chart
A Multivariate (Control Chart) Analysis (MVA) may be useful in SPC whenever there is more than one process variable. MVA usually becomes useful when the effect of multiple parameters is not independent or when some parameters are partial or complete measures of some other parameters (correlation). In some cases the true source of variation may not be recognized or may not be measurable. For example, Pressure and Volumetric Flow may be the process parameters being controlled, but Temperature at some point in the process may influence both; the common parameter affecting the process might be Mass Flow.
An essential point is that almost all processes are multivariate but MVA is often not necessary because there are only a few controlled variables acting sufficiently independently. With that proviso, those variables may usefully be controlled independently. However, even when the variables do act independently the use of a single control chart for each variable increases the chance of randomly finding a variable out of control; the more variables there are the more likely it is that one of those charts will contain an out of control condition even when the process has not shifted. Thus, the false alarm rate (or probability of Type 1 error) is increased if each variable is controlled separately.
Multivariate control charting provides a means to identify shifts in any q related characteristics by charting only one parameter, T2. The control region for two separately acting variables is a rectangle; an ellipse would be formed as the control region for two jointly-acting parameters.