Multivariate Statistics Process Control Chart

Statistical process control(SPC) is the way to realize the quality control of the products in modern-day industries. The traditional statistical process control adopts univariate statistical process control method which monitoring several important indexes individually. However, it can't provide the interactive information on many quality characteristics.Multivariate statistical process control bases on the theory of multivariate statistic analysis, especially multivariate t distribution theory. It can discover the main causes for the decline of the products quality from the multivariate statistic analysis of quality characteristics in the products process,at the same time, it can alarm us the process is out of control. Operators can take measures to improve the quality according to the useful information and keep the products process in control.when the quality indexes of the product be a p-variate normal distribution, we can analyze the product process whether out of control or not with using T~2 chart and A chart. The relationships between the T~2 statistics and F statistics, A statistics and F statistics are discussed in this paper. And then,we obtain two kind of F Statistical Process Control(SPC) Chart and give an example.All calculations are carried out by R software and the main procedures are given in the end of the paper.