Yi c Xi Si y y E

with the columns of matrix © being the principal directions (loadings) and E being the PCA residuals matrix.

Several monitoring charts can be developed to detect abnormal batch-to-batch behavior. T2 and Q charts of principal components would be one alternative. But T2 charts of states X, and prediction errors £_ t offer better alternatives. The use of a small window CUSUM chart of prediction error T2 has also been proposed [134], It filters out high frequency variation in £_ i over i, and enhances the trends by accumulating the deviation over a number of batches. A window size of 5 batches provides a good compromise between capturing trends and delay in indicating big increases in the prediction error of one batch run.

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