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

TLDR

Conventional multivariate control charts assume normality, which is often unrealistic, motivating the need for monitoring techniques that remain effective when the quality characteristics deviate from a multivariate normal distribution. The authors propose a monitoring approach grounded in statistical learning theory to address this limitation. They develop a kernel‑distance‑based multivariate control chart that uses support‑vector‑machine–derived distances from a kernel centre and information from in‑control preliminary samples. A case study shows the chart outperforms conventional charts when the underlying distribution is non‑normal.

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.