Publication date: 07/30/2020

The value for each of the i observations is plotted on the T2 control chart. For historical and current data, the T2 values for a PCA or PLS model with k components are defined as:

where:

ti = the vector of k scores for the ith observation

Sk = the diagonal sample covariance matrix of the k scores for historical observations

For PCA models, is the diagonal eigenvalue matrix.

The mean of each of the k historical score vectors is 0 when the data is centered during the data preprocessing step. This step occurs in PCA on correlations or covariances and in PLS with centering. For preprocessing options where X is not centered, the mean of each of the k score vectors is 0 by assumption. For more information about Hotellingâ€™s T2, see Montgomery (2013).

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