A Robust Hotelling-Type T2 Control Chart Combining the Minimum Covariance Determinant Estimator with Multiple Factor Analysis Weighting
- 1Departamento de Estadística, Universidad de Salamanca (USAL), 37008 Salamanca, Spain
- 2Centro de Estudios e Investigaciones Estadísticas (CEIE), Escuela Superior Politécnica del Litoral (ESPOL), Campus Gustavo Galindo, Km. 30.5 Vía Perimetral, Guayaquil 090902, Ecuador
- 3Departamento de Estadística, Universidad Estatal de Milagro (UNEMI), Milagro 091050, Ecuador
Abstract
The Hotelling T2 chart relies on Phase 1 parameters estimated from in-control data. When the calibration sample contains outlying observations or anomalous batches, the classical covariance is inflated, and this masking effect hides later mean shifts. We propose MFA-MCD, a robust T2 chart for batch processes. It estimates the covariance of each batch with the minimum covariance determinant (MCD), weights each batch by the inverse of its first eigenvalue, as in multiple factor analysis (MFA), and obtains the reference center with a second MCD on the batch centers. The control limit is a heuristic F-type approximation, not an exact distributional result, based on the size of the MCD subset. With six of thirty Phase 1 batches contaminated and a one-standard-deviation shift in all variables, it detects 88.5% of the shifted batches, against 27.0% for the classical chart and 73.0% for the MCD alone; its advantage stays above 0.49 across nine configurations. With a clean Phase 1 and shifts that do not move all variables together, it detects between 5.3 and 5.8 points less than the classical chart. On the Tennessee Eastman process it detects all twenty faulty batches without false alarms; the classical chart detects two. The method targets mean shifts and is implemented in the R package robustT2AFM.
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BibTeX
@article{frutosgalarza2026robust,
title = {{A Robust Hotelling-Type T2 Control Chart Combining the Minimum Covariance Determinant Estimator with Multiple Factor Analysis Weighting}},
author = {Sergio Daniel Frutos-Galarza and Omar Ruiz-Barzola and John Ramirez-Figueroa and Purificación Galindo-Villardón},
journal = {Mathematics},
year = {2026},
month = oct,
doi = {10.3390/math14203697},
url = {https://www.mdpi.com/2227-7390/14/20/3697},
note = {CC BY 4.0},
}
RIS
TY - JOUR
TI - A Robust Hotelling-Type T2 Control Chart Combining the Minimum Covariance Determinant Estimator with Multiple Factor Analysis Weighting
AU - Sergio Daniel Frutos-Galarza
AU - Omar Ruiz-Barzola
AU - John Ramirez-Figueroa
AU - Purificación Galindo-Villardón
PY - 2026
DA - 2026/10/12
JO - Mathematics
DO - 10.3390/math14203697
UR - https://www.mdpi.com/2227-7390/14/20/3697
AB - The Hotelling T2 chart relies on Phase 1 parameters estimated from in-control data. When the calibration sample contains outlying observations or anomalous batches, the classical covariance is inflated, and this masking effect hides later mean shifts. We propose MFA-MCD, a robust T2 chart for batch processes. It estimates the covariance of each batch with the minimum covariance determinant (MCD), weights each batch by the inverse of its first eigenvalue, as in multiple factor analysis (MFA), and obtains the reference center with a second MCD on the batch centers. The control limit is a heuristic F-type approximation, not an exact distributional result, based on the size of the MCD subset. With six of thirty Phase 1 batches contaminated and a one-standard-deviation shift in all variables, it detects 88.5% of the shifted batches, against 27.0% for the classical chart and 73.0% for the MCD alone; its advantage stays above 0.49 across nine configurations. With a clean Phase 1 and shifts that do not move all variables together, it detects between 5.3 and 5.8 points less than the classical chart. On the Tennessee Eastman process it detects all twenty faulty batches without false alarms; the classical chart detects two. The method targets mean shifts and is implemented in the R package robustT2AFM.
SN - 2227-7390
ER -