A kernel-distance-based multivariate control chart using support vector methods

Abstract

This paper focuses on the monitoring techniques applied in multivariate processes when the underlying distribution of the quality characteristics departs from normality. For most conventional control charts, such as Hotelling's T 2 charts, the design of the control limits is commonly based on the assumption that the quality characteristics follow a multivariate normal distribution. However, this may not be reasonable in many real-world problems. This paper addresses this issue and proposes a monitoring approach motivated by statistical learning theory, which has been applied successfully in the field of pattern recognition. The developed multivariate control chart is based on the kernel distance, which is a measure of the distance between the 'kernel centre' and the incoming new sample to be monitored. The kernel distance can be calculated using support vector methods. This chart makes use of information extracted from in-control preliminary samples. A case study demonstrates that the kernel-distance-based chart can perform better than conventional charts when the underlying distribution of the quality characteristics is not multivariate normal.