Monitoring the mean vector with Mahalanobis kernels

Abstract

Statistical process control (SPC) applies the science of statistics to various process controls in order to provide higher-quality products and better services. Multivariate control charts are essential tools in multivariate SPC. Hotelling’s charts based on rational subgroups of sample sizes larger than one are very sensitive for detecting relatively large shifts in the process mean vectors. However, it makes some very restrictive assumptions (multivariate normal distribution) that are usually difficult to be satisfied in real applications. Modern processes do not satisfy classical methods assumptions, such as normality or linearity. To overcome this issue, introduction of new techniques from statistical machine learning theory has been applied. Control charts based on Support Vector Data Description (SVDD), a popular data classifier method inspired by Support Vector Machines, benefit from a wide variety of choices of kernels, which determine the effectiveness of the whole model. Among the most popular choices of kernels is the Euclidean distance-based Gaussian kernel, which enables SVDD to obtain a flexible data description, thus enhances its overall predictive capability. This paper explores an even more robust approach by incorporating the Mahalanobis distance-based kernel (hereinafter referred to as Mahalanobis kernel) to SVDD and compares it with SVDD using the traditional Gaussian kernel.

KEYWORDS:

• Mercer kernel
• statistical process control
• average run length (ARL)
• support vectors
• machine learning

Acknowledgements

We would like to express our thanks to the unknown referees and the editor for their insightful comments and suggestions on improving this manuscript to its present form.

Notes

No potential conflict of interest was reported by the authors.