SPM Methods Based on PLS

Large amounts of process data, such as temperatures and flow rates, are collected at high frequency by process data collection systems. Information on product quality variables is collected less frequently since these measurements are expensive. Although it is possible to measure some quality variables on-line by means of sophisticated devices, measurements are generally made off-line in the quality control laboratory and often involve time lags between data collection and receiving analysis results. Process data 

Cross correlations and colinearity among process variables severely limit the use of traditional linear regression techniques. PLS, as a projection method, offers a suitable solution for modeling such data. 

Since PLS technique is sensitive to outliers and scaling, outliers should be removed and data should be scaled prior to modeling. After data pretreatment, the number of latent variables (PLS dimensions) to be retained in the model is determined. Cumulative prediction sum of squares (CUM-PRESS) versus the number of latent variables or prediction sum of squares (PRESS) versus the number of latent variables plots are used for this purpose. It is usually enough to consider the first few PLS dimensions for monitoring activities, while more PLS dimensions are needed for prediction in order to improve the accuracy of predictions. 

The squared prediction error (SPE) can be calculated for the X and the Y block models 

Multivariate monitoring charts based on Hotelling s statistic (T ) and squared prediction errors SPEx and SPEy) are constructed using the PLS models. Hotelling s statistic for a new independent t vector is [298] 

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