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Statistical Monitoring of Complex Multivariate Processes: With Applications in Industrial Process Control by Lei Xie, Uwe Kruger

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Chapter 3

Process monitoring charts

The aim of this chapter is:

  • to design monitoring charts on the basis of the extracted LV sets and the residuals;
  • to show how to utilize these charts for evaluating the performance of the process and for assessing product quality on-line; and
  • to outline how to diagnose behavior that is identified as abnormal by these monitoring charts.

For monitoring a complex process on-line, the set of score and residual variables give rise to the construction of a statistical fingerprint of the process. This fingerprint serves as a benchmark for assessing whether the process is in-statistical control or out-of-statistical-control. Based on Chapters 3 and Chapters 2, the construction of this fingerprint relies on the following assumptions for identifying PCA/PLS data models:

  • the error vectors associated with the PCA/PLS data models follow a zero mean Gaussian distribution that is described by full rank covariance matrices;
  • the score variables, describing common cause variation of the process, follow a zero mean Gaussian distribution that is described by a full rank covariance matrix;
  • for any recorded process variable, the variance contribution of the source signals (common cause variation) is significantly larger than the variance contribution of the corresponding error signal;
  • the number of source variables is smaller than the number of recorded process (PCA) or input variables (PLS);
  • recorded variable sets have constant mean and covariance matrices over time; ...

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