ABSTRACT
Multivariate SPM (MSPM) methods are gaining acceptance in monitoring continuous processes because multivariate monitoring charts provide more accurate information about the process, give warnings earlier than the signals of univariate charts, and are easy to compute and interpret. MSPM relies on the statistical distance concept which is a generalization of the Student t statistic. First discussed in [226] and later proposed independently in [112] and [179], it provides a useful statistic for representing the deviation of the process from its desired state. If the process has a few variables, the statistical distance statistic T 2 can be computed by using all variables and its charts can be plotted for MSPM [190]. If the number of variables is large and there is significant colinearity among some of them, the PCA or PLS can be used. If the data used for chart development are process variables, MSPM charts are based on principal components (PC). When both process and quality variables are used, and the two blocks of data need to be related as well, the MSPM charts are based on the latent variables (LV) of PLS. Both sets of charts summarize the information about the status of the process by using two statistics, the Hotelling’s T 2 and the squared prediction error (SPE). The details are discussed in Sections 5.1 and 5.2. The charts are simply the plots of T 2 or SPE values computed by using the information collected at each sampling time on the time axis. The T 2 chart indicates the distance of the current operation from the desired operation as captured by the PCs or LVs included in the development of the PCA or the PLS model of the process. Since only the first few PCs or LVs that capture most of the variation in the data are used to build the model, the model is a somewhat accurate but incomplete description of the process. The SPE chart captures the magnitude of the error caused by deviations resulting from events that are not described by the model. The T 2 chart indicates a deviation based on process behavior that can be explained by
the model while the SPE chart indicates a significant deviation that can not be explained by the model (the prediction error is inflated). The T 2
and SPE charts must be used as a pair and if either chart indicates a significant deviation from expected operation, the presence of an abnormal process operation must be declared.
