A comparative study of phase II robust multivariate control charts for individual observations

Shojaeddin Chenouri · Asokan Mulayath Variyath

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Advanced Statistical Process Monitoring Fault Detection and Control Systems Advanced Statistical Methods and Models

Abstract

Abstract Use of Hotelling's T2 charts with high breakdown robust estimates to monitor multivariate individual observations are the recent trend in the control chart methodology. Vargas (J. Qual. Tech. 2003; 35: 367‐376) introduced Hotelling's T2 charts based on the minimum volume ellipsoid (MVE) and the minimum covariance determinant (MCD) estimates to identify outliers in Phase I data. Studies carried out by Jensen et al. (Qual. Rel. Eng. Int. 2007; 23: 615‐629) indicated that the performance of these charts heavily depends on the sample size, amount of outliers and the dimensionality of the Phase I data. Chenouri et al. (J. Qual. Tech. 2009; 41: 259‐271) recently proposed robust Hotelling's T2 control charts for monitoring Phase II data based on the reweighted MCD (RMCD) estimates of the mean vector and covariance matrix from Phase I. They showed that Phase II RMCD charts have better performance compared with Phase II standard Hotelling's T2 charts based on outlier free Phase I data, where the outlier free Phase I data were obtained by applying MCD and MVE T2 charts to historical data. Reweighted MVE (RMVE) and S‐estimators are two competitors of the RMCD estimators and it is a natural question whether the performance of Phase II Hotelling's T2 charts with RMCD and RMVE estimates exhibits similar pattern observed by Jensen et al. (Qual. Rel. Eng. Int. 2007; 23: 615‐629) in the case of MCD and MVE‐based Phase I Hotelling's T2 charts. In this paper, we conduct a comparative study to assess the performance of Hotelling's T2 charts with RMCD, RMVE and S‐estimators using large number of Monte Carlo simulations by considering different data scenarios. Our results are generally in favor of the RMCD‐based charts irrespective of sample size, outliers and dimensionality of Phase I data. Copyright © 2010 John Wiley & Sons, Ltd.

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References

2003Robust Estimation in Multivariate Control Charts for Individual Observations 2006High breakdown estimation methods for Phase I multivariate control charts 2009A Multivariate Robust Control Chart for Individual Observations 1983A Festschrift for Erich L. Lehmann in honor of his sixty-fifth birthday

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2012A Robust Bivariate Control Chart Alternative to the Hotelling's T2 Control Chart 2013Robust Control Charts for Monitoring Process Variability in Phase I Multivariate Individual Observations 2020Robust T2 control chart using median‐based estimators 2012Alternative Hotelling's T2 Charts using Winsorized Modified One‐Step M‐estimator 2014Application of hotelling’s T² control chart for a machining process of the inside diameter of a steel cylinder 2015A Control Chart Based on Cluster-Regression Adjustment for Retrospective Monitoring of Individual Characteristics

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