Multivariate Statistical Process Capability Analysis And Control

The research of the multivariate statistical process control has been carried out for a long time and there are a lot of methods such as principal component analysis (PCA), stepwise regression, multiple regression, test of additional information and multivariate process control charts and so on. But the research of the multivariate process capability analysis(MPCA) has not been carried out for a long time. In contrast to the system of univariate process capability analysis(UPCA), the system of the MPCA theories has not been set up. So we should study MPCA further to make it apply well in practice.Firstly, the T~2 statistic method is introduced to provide the foundation for the whole thesis. In this part, there are three aspects: the concept of the statistical distance, the hypothesis of the T~2 statistic and distributional properties of the T~2 statistic. Then is the research of the collection and construction of the history data set. Data is the foundation of the MPCA. The chapter is focused on how to solve the problems that existing in the practice. Thirdly, we discussed how to decide whether the process is in control and if not, what shall we do to remove the signals. In this part, there are two aspects: T~2 statistic with unknown parameters and T~2 statistic with known parameters. After the process is under control, we can evaluate the capability of the process with the multivariate process capability index. If the multivariate process capability index has reached the criterion, then we can go to the next control stage. Finally, we make use of the system of MPCA to evaluate the process capability of a practical system and get a very good result.