Kernel distance-based robust support vector methods and its application in developing a robust K-chart

Abstract

Traditional statistical process control (SPC) techniques are not applicable in many process industries due to autocorrelation among data. In addition, most conventional charts are based on the assumption that quality characteristics follow a multivariate normality assumption. Therefore, the reduction in process variability obtained through the use of SPC techniques has not been realized in the industries. However, this may not be reasonable in many real-world problems and its extension poses serious limitations. Hence, it is not only desirable, but also inevitable to have some techniques that can serve the same purpose as SPC control charts used for correlated parameters. In this paper, a robust support vector method drawn from statistical learning theory was applied to develop a multivariate control chart based on kernel distance, which is a measure of the distance between the centre of a class and the sample to be monitored. The proposed robust chart takes advantage of information extracted from in-control preliminary samples. A robust support vector method-based chart aims to solve the over fitting problems when outliers exist in the training data set. The robust support vector method makes the decision function less sensitive towards the noise and outliers. The performance of the robust chart is tested on the problem taken from the literature and the results verify the effectiveness of the chart and validate that the robust chart is better than the conventional charts when the distribution of the quality characteristics is not multivariate normal. Experiments for the problem undertaken confirm the reduction in the number of support vectors and there is significant improvement in performance when compared with the standard support vector methods.