Multivariate statistical process monitoring charts

Tates AA, Louwerse DJ, Smilde AK, Koot GLM, Berndt H, Monitoring a PVC batch process with multivariate statistical process control charts, Industrial and Engineering Chemistry Research, 1999, 38, 4769 1776. 

Data generated from process analysis techniques are commonly displayed on control charts and the term statistical process control (SPC) is often used to describe the use of such data visualisation [5], As the amount of data available increases, due both to different measurements and greater frequency of measurements, then combinations of different data provide improved methods of monitoring the processes concerned. The procedures and concepts of multivariate SPC incorporating principal component analysis (PCA) and partial least squares (PLS) analysis then become important [6]. The different SPC approaches are all aimed at providing better process control and improved process understanding. 

If dependency exists. Hotelling 7 control chart is commonly used procedure for a multivariate process monitoring and controlling. For individual observations, suppose that there are m samples, each of size n=, and p is the number of quality characteristics observed in each sample. Let x be the sample mean vector and S be covariance matrix of these observations. The Hotelling 7 statistic is calculated as = x — (x — x). The phase I limits should be based on a beta distribution. 

---