Robust multivariate control chart based on shrinkage for individual observations

Abstract

A robust multivariate quality control technique for individual observations is proposed, based on the robust reweighted shrinkage estimators. A simulation study is done to check the performance and compare the method with the classical Hotelling approach, and the robust alternative based on the reweighted minimum covariance determinant estimator. The results show the appropriateness of the method even when the dimension or the Phase I contamination are high, with both independent and correlated variables, showing additional advantages about computational efficiency. The approach is illustrated with two real data-set examples from production processes.

Keywords:

• Hotelling T2
• multivariate process control
• reweighted MCD
• reweighted shrinkage estimator

Acknowledgments

The authors are grateful to the editor and the referees for their constructive and valuable comments that led to considerable improvement in this paper.

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This research was partially supported by research grants and Project PID2019-104901RB-I00 from Ministerio de Ciencia e Innovacion.

Notes on contributors

Elisa Cabana

Elisa Cabana is a postdoc researcher at IMDEA Networks Institute in Madrid, Spain. Prior to joining IMDEA she got her PhD in Mathematical Engineering at the University Carlos III of Madrid. She also collaborates in the uc3m-Santander Big Data Institute. Her areas of interest include robust methods for data analysis, outlier detection, Machine Learning and Artificial Intelligence.

Rosa E. Lillo

Rosa E. Lillo is a Full Professor at the University Carlos III of Madrid and director of the uc3m-Santander Big Data Institute in Madrid, Spain. Her areas of research are stochastic processes and their applications, stochastic ordering, reliability, Bayesian inference, robust methods for data analysis and functional data.