Modified Multivariate $T^2$-Chart based on Robust Estimation

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Journal of Korean Society for Quality Management > Volume 29(1); 2001 > Article

Journal of Korean Society for Quality Management 2001;29(1): 1-.

로버스트 추정에 근거한 수정된 다변량 $T^2$- 관리도

성웅현, 박동련

한신대학교 정보통계학과

Modified Multivariate $T^2$-Chart based on Robust Estimation

ABSTRACT

We consider the problem of detecting special variations in multivariate $T^2$-control chart when two or more multivariate outliers are present. Since a multivariate outlier may reflect slippage in mean, variance, or correlation, it can distort the sample mean vector and sample covariance matrix. Damaged sample mean vector and sample covariance matrix have difficulty in examining special variations clearly, An alternative to detection outliers or special variations is to use robust estimators of mean vector and covariance matrix that are less sensitive to extreme observations than are the standard estimators $ar{x}$ and $ extbf{S}$. We applied popular minimum volume ellipsoid(MVE) and minimum covariance determinant(MCD) method to estimate mean vector and covariance matrix and compared its results with standard $T^2$-control chart using simulated multivariate data with outliers. We found that the modified $T^2$-control chart based on the above robust methods were more effective in detecting special variations clearly than the standard $T^2$-control chart.