Tr(R2) control charts based on kernel density estimation for monitoring multivariate variability process

The multivariate control charts are not only used to monitor the mean vector but also can be used to monitor the covariance matrix. The multivariate variability charts are used to guarantee the consistency of products in the subgroup. Many researchers have been studied the multivariate control chart...

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Autores principales:	Muhammad Mashuri, Haryono Haryono, Diaz Fitra Aksioma, Wibawati Wibawati, Muhammad Ahsan, Hidayatul Khusna
Formato:	article
Lenguaje:	EN
Publicado:	Taylor & Francis Group 2019
Materias:	multivariate variability process trace squared correlation matrix control chart kernel density estimation average run length Engineering (General). Civil engineering (General) TA1-2040
Acceso en línea:	https://doaj.org/article/04653da05c1e4aa3953e5624d4c14dd4
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spelling	oai:doaj.org-article:04653da05c1e4aa3953e5624d4c14dd42021-11-04T15:51:56ZTr(R2) control charts based on kernel density estimation for monitoring multivariate variability process2331-191610.1080/23311916.2019.1665949https://doaj.org/article/04653da05c1e4aa3953e5624d4c14dd42019-01-01T00:00:00Zhttp://dx.doi.org/10.1080/23311916.2019.1665949https://doaj.org/toc/2331-1916The multivariate control charts are not only used to monitor the mean vector but also can be used to monitor the covariance matrix. The multivariate variability charts are used to guarantee the consistency of products in the subgroup. Many researchers have been studied the multivariate control chart for variability. Nevertheless, those conventional methods have several drawbacks because it is developed based on the determinant of the covariance matrix and not free of the measurement unit. To overcome such issues, this paper proposes the multivariate control chart for variability based on trace of the squared correlation matrix. Kernel Density Estimation is used to improve estimated control limit. The kernel density estimation method is used to calculate the control limit. Through simulation studies, the performance of the proposed chart is evaluated using the average run length (ARL). The control limits of the proposed chart are produced in control ARL at about 370 for α = 0.00273. Meanwhile, the proposed chart demonstrated better performance to detect the shift for the large value of quality characteristics and sample size. The proposed chart also produces a better performance than the conventional generalized variance chart when used to monitor the real case data.Muhammad MashuriHaryono HaryonoDiaz Fitra AksiomaWibawati WibawatiMuhammad AhsanHidayatul KhusnaTaylor & Francis Grouparticlemultivariate variability processtrace squared correlation matrixcontrol chartkernel density estimationaverage run lengthEngineering (General). Civil engineering (General)TA1-2040ENCogent Engineering, Vol 6, Iss 1 (2019)
institution	DOAJ
collection	DOAJ
language	EN
topic	multivariate variability process trace squared correlation matrix control chart kernel density estimation average run length Engineering (General). Civil engineering (General) TA1-2040
spellingShingle	multivariate variability process trace squared correlation matrix control chart kernel density estimation average run length Engineering (General). Civil engineering (General) TA1-2040 Muhammad Mashuri Haryono Haryono Diaz Fitra Aksioma Wibawati Wibawati Muhammad Ahsan Hidayatul Khusna Tr(R2) control charts based on kernel density estimation for monitoring multivariate variability process
description	The multivariate control charts are not only used to monitor the mean vector but also can be used to monitor the covariance matrix. The multivariate variability charts are used to guarantee the consistency of products in the subgroup. Many researchers have been studied the multivariate control chart for variability. Nevertheless, those conventional methods have several drawbacks because it is developed based on the determinant of the covariance matrix and not free of the measurement unit. To overcome such issues, this paper proposes the multivariate control chart for variability based on trace of the squared correlation matrix. Kernel Density Estimation is used to improve estimated control limit. The kernel density estimation method is used to calculate the control limit. Through simulation studies, the performance of the proposed chart is evaluated using the average run length (ARL). The control limits of the proposed chart are produced in control ARL at about 370 for α = 0.00273. Meanwhile, the proposed chart demonstrated better performance to detect the shift for the large value of quality characteristics and sample size. The proposed chart also produces a better performance than the conventional generalized variance chart when used to monitor the real case data.
format	article
author	Muhammad Mashuri Haryono Haryono Diaz Fitra Aksioma Wibawati Wibawati Muhammad Ahsan Hidayatul Khusna
author_facet	Muhammad Mashuri Haryono Haryono Diaz Fitra Aksioma Wibawati Wibawati Muhammad Ahsan Hidayatul Khusna
author_sort	Muhammad Mashuri
title	Tr(R2) control charts based on kernel density estimation for monitoring multivariate variability process
title_short	Tr(R2) control charts based on kernel density estimation for monitoring multivariate variability process
title_full	Tr(R2) control charts based on kernel density estimation for monitoring multivariate variability process
title_fullStr	Tr(R2) control charts based on kernel density estimation for monitoring multivariate variability process
title_full_unstemmed	Tr(R2) control charts based on kernel density estimation for monitoring multivariate variability process
title_sort	tr(r2) control charts based on kernel density estimation for monitoring multivariate variability process
publisher	Taylor & Francis Group
publishDate	2019
url	https://doaj.org/article/04653da05c1e4aa3953e5624d4c14dd4
work_keys_str_mv	AT muhammadmashuri trr2controlchartsbasedonkerneldensityestimationformonitoringmultivariatevariabilityprocess AT haryonoharyono trr2controlchartsbasedonkerneldensityestimationformonitoringmultivariatevariabilityprocess AT diazfitraaksioma trr2controlchartsbasedonkerneldensityestimationformonitoringmultivariatevariabilityprocess AT wibawatiwibawati trr2controlchartsbasedonkerneldensityestimationformonitoringmultivariatevariabilityprocess AT muhammadahsan trr2controlchartsbasedonkerneldensityestimationformonitoringmultivariatevariabilityprocess AT hidayatulkhusna trr2controlchartsbasedonkerneldensityestimationformonitoringmultivariatevariabilityprocess
_version_	1718444691904528384

Tr(R2) control charts based on kernel density estimation for monitoring multivariate variability process

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