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MULTIVARIATE
CONTROL CHARTS
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 Hotelling's T2 statistic, is used to detect shifts in the
process. Instead of using the raw Process Variables, the T2 statistic
is calculated for the process' Principal Components, 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 Process Variables' contributions 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.
.
See also:
When
to Use a Multivariate Chart
Interpreting
a Multivariate Chart
For technical reference,
see also
- Martens, H. and Nęs,
T., Multivariate Calibration, , J. Wiley and Sons, 1989.
- MacGregor, J.F. and
Kourti, T., Statistical Process Control of Multivariate Processes,
Control Eng. Practice, Vol.3, No. 3, pp.403-414, 1995.
- 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.
- Jackson, J.E., A
User's Guide to Principal Components, J. Wiley and Sons, 1991.
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