Simulation Study And Analysis Of The SPC Technique For Multivariate Autocorrelated Processes

Statistical process control, which uses control chart as the main tool, is of great importance to the on-line statistical process quality control. With the improvement of quality requirements, the focus on the characteristics of products has been turned from single to multiple. Meanwhile, with the development of measurement as well as data collecting technology, the phenomenon of high-frequency data collecting has been becoming increasingly universal, often making the data of processes auto-correlated. Therefore, how to achieve the on-line quality control of multivariate autocorrelated processes is a problem which needs to be resolved by both enterprises and researchers.In this thesis, the SPC technique for multivariate autocorrelated processes is discussed. Basing on the residual-controlling theory, conventional multivariate exponentially weighted moving average (MEWMA) and MEWMA-type control chart are applied to monitor the residual vector. Firstly, statistics of residual control charts are deduced theoretically. Then average-run-length analysis of residual control charts are presented by Monte-Carlo simulation method.By simulation analysis, it can be concluded that an excellent performance in detecting shifts in the mean vector and covariance matrix with different degrees in different directions can be obtained by the MEWMA and MEWMA-type control chart built on the residual vector respectively. Also, compared with the Hotelling residual control chart, the MEWMA residual control chart achieves a better performance in detecting shifts in the process mean vector, especially in small mean vector shifts. Finally, the value of the optimal process coefficient of residual control charts calculated from different degrees of shifts happening in different directions is analyzed. A value range of the optimal process coefficient which achieves the best performance in detecting shifts with different degrees in the mean vector using the MEWMA residual control chart in practical applications is given. In this study, to some extent, the application range of the SPC technique in the field of multivariate autocorrelated processes is expanded in theory; furthermore, references of certain degrees are given to enterprises in selecting effective control charts in practical situations.