Detecting outliers in the multivariate control charts for dispersion monitoring

• Published in: Quality and reliability engineering international 2024-06, Vol.40 (4), p.1904-1917
• Main Authors: Ajadi, Jimoh Olawale, Raji, Ishaq Adeyanju, Abbas, Nasir, Riaz, Muhammad
• Format: Article
• Language: English
• Subjects: Control charts; Covariance matrix; Data analysis; minimum volume ellipsoid; Monitoring; Monte Carlo simulation; Multivariate analysis; multivariate control chart; outliers; Outliers (statistics); parameter estimation; Phase I; Statistical analysis
• ISSN: 0748-8017; 1099-1638
• DOI: 10.1002/qre.3500

Outlier detection is an important aspect of statistical process monitoring (SPM) because outliers affect the performance of control charts. SPM researchers study the negative impact of outliers on control charts for monitoring location parameters. However, there is little research on outlier detection in multivariate charts for monitoring process dispersion. This study aims to investigate the impact of outliers in multivariate control charts for monitoring covariance matrix of a process, and then to recommend techniques for detecting potential outliers present from Phase I samples. We propose a new multivariate dispersion chart that employs the determinant of logarithm of estimated covariance matrix as the monitoring statistic. Through Monte Carlo simulations, the results show how outliers from the first phase affect the overall performance of multivariate charts. The results also demonstrate that the minimum volume ellipsoid (MVE) estimator is effective in reducing the effect of outliers on the proposed control scheme than the other compared estimators.