Principal component analysis-based control charts using support vector machines for multivariate non-normal distributions

Abstract

The growing demand for statistical process monitoring has led to the vast utilization of multivariate control charts. Complicated structure of the measured variables associated with highly correlated characteristics, has given rise to daily increasing urge for reliable substitutes of conventional methods. In this regard, projection methods have been developed to address the issue of high correlation among characteristics by transforming them to an uncorrelated set of variables. Principal component analysis (PCA)-based control charts are widely used to overcome the issue of correlation among measured variables by defining linear transformations of the existing variables to a new uncorrelated space. Newly transformed variables explain different amount of variations in the measured variables with the first PC explaining the highest amount, the second PC explains the second highest one, and so on. PCA, also gives the opportunity of dimension reduction to the researcher, in cost of losing a part of information extracted from observed variation, yet using all the original measured variables. In spite of the mentioned strength of the PCA based methods, the underlying assumption of observations to be normally distributed, has limited the applicability of PCA-based schemes, as the normality assumption is widely violated in real practices. With this in regard, a distribution-free method to establish the limits of PCA-based control charts can be a good modification to keep the scheme reliable when the normality assumption is not met. The proposed method presented in this article is based on support vector machines (SVM) as a substitute for conventional methods to construct control limits for PCA-based control charts. As SVM uses real-world observations of the process, no distributional assumption is required to construct control limits. Extensive simulation experiments are conducted using normal and non-normal datasets to compare the performance of the proposed method with those of the conventional and some non-parametric methods existing in the literature. The results show a relatively good performance of the proposed method compared to others in terms of the average and the standard deviation of run lengths.

Keywords:

• Bootstrap
• Multivariate control charts; Principal component analysis; Support vector machine

Acknowledgment

The authors are thankful for constructive comments of the respected anonymous reviewers. Taking care of the comments improved the presentation, significantly.