Robust Multivariate Shewhart Control Chart Based on the Stahel-Donoho Robust Estimator and Mahalanobis Distance for Multivariate Outlier Detection

Abstract

While researchers and practitioners may seamlessly develop methods of detecting outliers in control charts under a univariate setup, detecting and screening outliers in multivariate control charts pose serious challenges. In this study, we propose a robust multivariate control chart based on the Stahel-Donoho robust estimator (SDRE), whilst the process parameters are estimated from phase-I. Through intensive Monte-Carlo simulation, the study presents how the estimation of parameters and presence of outliers affect the efficacy of the Hotelling T2 chart, and then how the proposed outlier detector brings the chart back to normalcy by restoring its efficacy and sensitivity. Run-length properties are used as the performance measures. The run length properties establish the superiority of the proposed scheme over the default multivariate Shewhart control charting scheme. The applicability of the study includes but is not limited to manufacturing and health industries. The study concludes with a real-life application of the proposed chart on a dataset extracted from the manufacturing process of carbon fiber tubes.

Keywords

• multivariate control charts
• Mahalanobis distance
• control chart
• Hotelling <i>T</i>²
• Stahel-Donoho robust estimators
• outlier detection