Efficient and Highly Robust Hotelling T² Control Charts Using Reweighted Mininum Vector Variance

Efficient and Highly Robust Hotelling T² Control Charts Using Reweighted Mininum Vector Variance

Hotelling T² control chart is an effective tool in statistical process control for multivariate environment. However, the performance of traditional Hotelling T² control chart using classical location and scatter estimators is usually marred by the masking and swamping effects. In order to alleviate...

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Main Author: Hazlina, Ali
Format: Thesis
Language:eng
eng
Published: 2013
Subjects:
QA273-280 Probabilities
Mathematical statistics
Online Access:https://etd.uum.edu.my/3870/1/s91512.pdf
https://etd.uum.edu.my/3870/7/s91512.pdf
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id my-uum-etd.3870
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institution Universiti Utara Malaysia
collection UUM ETD
language eng
eng
advisor Syed Yahaya, Sharipah Soaad
Omar, Zurni
topic QA273-280 Probabilities
Mathematical statistics
spellingShingle QA273-280 Probabilities
Mathematical statistics
Hazlina, Ali
Efficient and Highly Robust Hotelling T² Control Charts Using Reweighted Mininum Vector Variance
description Hotelling T² control chart is an effective tool in statistical process control for multivariate environment. However, the performance of traditional Hotelling T² control chart using classical location and scatter estimators is usually marred by the masking and swamping effects. In order to alleviate the problem, robust estimators are recommended. The most popular and widely used robust estimator in the Hotelling T² control chart is the minimum covariance determinant (MCD). Recently, a new robust estimator known as minimum vector variance (MVV) was introduced. This estimator possesses high breakdown point, affine equivariance and is superior in terms of computational efficiency. Due to these nice properties, this study proposed to replace the classical estimators with the MVV location and scatter estimators in the construction of Hotelling T² control chart for individual observations in Phase II analysis. Nevertheless, some drawbacks such as inconsistency under normal distribution, biased for small sample size and low efficiency under high breakdown point were discovered. To improve the MVV estimators in terms of consistency and unbiasedness, the MVV scatter estimator was multiplied by consistency and correction factors respectively. To maintain the high breakdown point while having high statistical efficiency, a reweighted version of MVV estimator (RMVV) was proposed. Subsequently, the RMVV estimators were applied in the construction of Hotelling T² control chart. The new robust Hotelling T² chart produced positive impact in detecting outliers while simultaneously controlling false alarm rates. Apart from analysis of simulated data, analysis of real data also found that the new robust Hotelling T² chart was able to detect out of control observations better than the other charts investigated in this study. Based on the good performance on both simulated and real data analysis, the new robust Hotelling T² chart is a good alternative to the existing Hotelling T² charts.
format Thesis
qualification_name Ph.D.
qualification_level Doctorate
author Hazlina, Ali
author_facet Hazlina, Ali
author_sort Hazlina, Ali
title Efficient and Highly Robust Hotelling T² Control Charts Using Reweighted Mininum Vector Variance
title_short Efficient and Highly Robust Hotelling T² Control Charts Using Reweighted Mininum Vector Variance
title_full Efficient and Highly Robust Hotelling T² Control Charts Using Reweighted Mininum Vector Variance
title_fullStr Efficient and Highly Robust Hotelling T² Control Charts Using Reweighted Mininum Vector Variance
title_full_unstemmed Efficient and Highly Robust Hotelling T² Control Charts Using Reweighted Mininum Vector Variance
title_sort efficient and highly robust hotelling t² control charts using reweighted mininum vector variance
granting_institution Universiti Utara Malaysia
granting_department Awang Had Salleh Graduate School of Arts & Sciences
publishDate 2013
url https://etd.uum.edu.my/3870/1/s91512.pdf
https://etd.uum.edu.my/3870/7/s91512.pdf
_version_ 1747827657951674368
spelling my-uum-etd.38702022-10-06T07:06:04Z Efficient and Highly Robust Hotelling T² Control Charts Using Reweighted Mininum Vector Variance 2013 Hazlina, Ali Syed Yahaya, Sharipah Soaad Omar, Zurni Awang Had Salleh Graduate School of Arts & Sciences Awang Had Salleh Graduate School of Arts and Sciences QA273-280 Probabilities. Mathematical statistics Hotelling T² control chart is an effective tool in statistical process control for multivariate environment. However, the performance of traditional Hotelling T² control chart using classical location and scatter estimators is usually marred by the masking and swamping effects. In order to alleviate the problem, robust estimators are recommended. The most popular and widely used robust estimator in the Hotelling T² control chart is the minimum covariance determinant (MCD). Recently, a new robust estimator known as minimum vector variance (MVV) was introduced. This estimator possesses high breakdown point, affine equivariance and is superior in terms of computational efficiency. Due to these nice properties, this study proposed to replace the classical estimators with the MVV location and scatter estimators in the construction of Hotelling T² control chart for individual observations in Phase II analysis. Nevertheless, some drawbacks such as inconsistency under normal distribution, biased for small sample size and low efficiency under high breakdown point were discovered. To improve the MVV estimators in terms of consistency and unbiasedness, the MVV scatter estimator was multiplied by consistency and correction factors respectively. To maintain the high breakdown point while having high statistical efficiency, a reweighted version of MVV estimator (RMVV) was proposed. Subsequently, the RMVV estimators were applied in the construction of Hotelling T² control chart. The new robust Hotelling T² chart produced positive impact in detecting outliers while simultaneously controlling false alarm rates. Apart from analysis of simulated data, analysis of real data also found that the new robust Hotelling T² chart was able to detect out of control observations better than the other charts investigated in this study. Based on the good performance on both simulated and real data analysis, the new robust Hotelling T² chart is a good alternative to the existing Hotelling T² charts. 2013 Thesis https://etd.uum.edu.my/3870/ https://etd.uum.edu.my/3870/1/s91512.pdf text eng public https://etd.uum.edu.my/3870/7/s91512.pdf text eng public Ph.D. doctoral Universiti Utara Malaysia Alfaro, J. L., & Ortega, J. F. (2009). A comparison of robust alternatives to Hotelling's T2 control chart. Journal of Applied Statistics, 36(12),1385-1396. Ali, H., Djauhari, M. A., & Syed-Yahaya, S. S. (2008). On the distribution of FMCD-based robust mahalanobis distance. 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