Robust Multivariate Dispersion Charts for Quality Control: Application to Sulfur Dioxide Monitoring

Abstract

This study introduces two robust multivariate Shewhart-type control charts based on grouped observations to detect changes in the covariance matrix, with a focus on monitoring sulfur dioxide levels during quality control processes. We compute the covariance matrix of observations, and apply the least absolute shrinkage and selection operator to penalize it in the in-control process. Logarithms are then applied to eigenvalues derived through singular value decomposition (SVD) of the shrunken covariance matrix, ensuring robustness to non-normality in the multivariate data. The proposed methods offer significant advantages, particularly in their ability to maintain robustness to non-normality without relying on strict distributional assumptions. Performance comparisons using the average run length demonstrate that the proposed charts exhibit superior robustness to normality assumptions compared with existing methods. However, potential limitations include the computational complexity of the shrinkage and SVD processes, which may affect the scalability of large datasets. An application to the white wine production process illustrates the effectiveness of the proposed methods for analyzing complex multivariate chemical data. These findings indicate that the introduced charts enhance the detection of shifts in the covariance matrix of physicochemical properties, thereby improving the reliability of quality control processes in non-normal environments. This study provides valuable tools for quality engineers and practitioners in industries dealing with multivariate analytical data, contributing to improved process monitoring and control, ensuring higher quality standards, and ensuring consistent product outcomes in fields such as food science and industrial chemistry.