Support Vector Data Description Based Multivariate Cumulative Sum Control Chart

As the development of the international economy and keen competition of market, the quality of products and service is one of the most important factors in the success of enterprise. It is important to monitor manufacturing processes in order to improve product quality and reduce production cost. Statistical Process Control (SPC) is the most commonly used method for process monitoring and making a significant contribution to continuous quality improvement. Control chart is one of the primary techniques in SPC. In face of ever more complex manufacturing processes, it is needed to control two or more quality characteristics simultaneously. As the quality characteristics are correlated with each other, using the univariate control chart to control the process may lead to incorrect conclusion. The techniques of Multivariate Statistical Process Control (MSPC) are developed. MSPC based on the underlying assumption that the distribution of process data is the multivariate normal distribution. However, the distributional assumption of MSPC restricts their applicability to the nonnormal data, which can be found in many modern industries. Support Vector Data Description (SVDD) is a one-class classification method that developed from the statistic learning theory and support vector machine. Because of the advantages of well robustness, rapid calculation and the ability of dealing with small samples, SVDD has the potential to address the limitation of distributional assumptions in MSPC. In this paper, a SVDD based MCUSUM (Multivariate Cumulative Sum) control chart is proposed and referred as S-MCUSUM chart. The most advantage of the S-MCUSUM chart is that it is distribution free. Numerical experiments using Monte Carlo simulation methods are presented and the performance of the S-MCUSUM chart is compared to the COT (Cumulative of T) chart. The results show that the COT chart is somewhat better than the S-MCUSUM chart for multivariate normally distributed data. However, the S-MCUSUM chart is better than the COT chart for banana-shaped distributed data which is a typical non-normal distribution.