A Control Chart for the Multivariate Coefficient of Variation
Existing charts in the literature usually monitor either the mean or the variance of the process. However, in certain scenarios, the practitioner is not interested in the changes in the mean or the variance but is instead interested in monitoring the relative variability compared with the mean. This...
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| Autor*in: |
Yeong, Wai Chung [verfasserIn] |
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| Format: |
Artikel |
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| Sprache: |
Englisch |
| Erschienen: |
2016 |
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| Rechteinformationen: |
Nutzungsrecht: Copyright © 2015 John Wiley & Sons, Ltd. |
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| Schlagwörter: |
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| Übergeordnetes Werk: |
Enthalten in: Quality and reliability engineering international - Chichester [u.a.] : Wiley, 1985, 32(2016), 3, Seite 1213-1225 |
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| Übergeordnetes Werk: |
volume:32 ; year:2016 ; number:3 ; pages:1213-1225 |
| Links: |
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| DOI / URN: |
10.1002/qre.1828 |
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OLC1974010341 |
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| 520 | |a Existing charts in the literature usually monitor either the mean or the variance of the process. However, in certain scenarios, the practitioner is not interested in the changes in the mean or the variance but is instead interested in monitoring the relative variability compared with the mean. This relative variability is called the coefficient of variation (CV). In the existing literature, none of the control charts that monitor the CV are applied for multivariate data. To fill this gap in research, this paper proposes a CV chart that monitors the CV for multivariate data. To the best of the authors' knowledge, this proposed chart is the first control chart for this purpose. The distributional properties of the sample CV for multivariate data and the procedures to implement the chart are presented in this paper. Formulae to compute the control limits, the average run length, the standard deviation of the run length, and the expected average run length for the case of unknown shift size are derived. From the numerical examples provided, the effects of the number of variables, the sample size, the shift size and the in‐control value of the CV are studied. Finally, we demonstrate the usefulness and applicability of the proposed chart on real data. Copyright © 2015 John Wiley & Sons, Ltd. | ||
| 540 | |a Nutzungsrecht: Copyright © 2015 John Wiley & Sons, Ltd. | ||
| 650 | 4 | |a average run length | |
| 650 | 4 | |a unknown shift size | |
| 650 | 4 | |a multivariate coefficient of variation | |
| 650 | 4 | |a relative variability | |
| 650 | 4 | |a expected average run length | |
| 700 | 1 | |a Khoo, Michael Boon Chong |4 oth | |
| 700 | 1 | |a Teoh, Wei Lin |4 oth | |
| 700 | 1 | |a Castagliola, Philippe |4 oth | |
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10.1002/qre.1828 doi PQ20160610 (DE-627)OLC1974010341 (DE-599)GBVOLC1974010341 (PRQ)p1554-910ea50633c6a9ebae6962978db3c3a5f1287cc35a5f41df40d9aba7e12e1fb23 (KEY)0136540120160000032000301213controlchartforthemultivariatecoefficientofvariati DE-627 ger DE-627 rakwb eng 650 690 DNB 50.16 bkl 85.38 bkl Yeong, Wai Chung verfasserin aut A Control Chart for the Multivariate Coefficient of Variation 2016 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier Existing charts in the literature usually monitor either the mean or the variance of the process. However, in certain scenarios, the practitioner is not interested in the changes in the mean or the variance but is instead interested in monitoring the relative variability compared with the mean. This relative variability is called the coefficient of variation (CV). In the existing literature, none of the control charts that monitor the CV are applied for multivariate data. To fill this gap in research, this paper proposes a CV chart that monitors the CV for multivariate data. To the best of the authors' knowledge, this proposed chart is the first control chart for this purpose. The distributional properties of the sample CV for multivariate data and the procedures to implement the chart are presented in this paper. Formulae to compute the control limits, the average run length, the standard deviation of the run length, and the expected average run length for the case of unknown shift size are derived. From the numerical examples provided, the effects of the number of variables, the sample size, the shift size and the in‐control value of the CV are studied. Finally, we demonstrate the usefulness and applicability of the proposed chart on real data. Copyright © 2015 John Wiley & Sons, Ltd. Nutzungsrecht: Copyright © 2015 John Wiley & Sons, Ltd. average run length unknown shift size multivariate coefficient of variation relative variability expected average run length Khoo, Michael Boon Chong oth Teoh, Wei Lin oth Castagliola, Philippe oth Enthalten in Quality and reliability engineering international Chichester [u.a.] : Wiley, 1985 32(2016), 3, Seite 1213-1225 (DE-627)129167614 (DE-600)50641-2 (DE-576)028403312 0748-8017 nnns volume:32 year:2016 number:3 pages:1213-1225 http://dx.doi.org/10.1002/qre.1828 Volltext http://onlinelibrary.wiley.com/doi/10.1002/qre.1828/abstract http://search.proquest.com/docview/1774428921 GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-UMW SSG-OLC-ARC SSG-OLC-TEC SSG-OLC-WIW GBV_ILN_70 50.16 AVZ 85.38 AVZ AR 32 2016 3 1213-1225 |
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10.1002/qre.1828 doi PQ20160610 (DE-627)OLC1974010341 (DE-599)GBVOLC1974010341 (PRQ)p1554-910ea50633c6a9ebae6962978db3c3a5f1287cc35a5f41df40d9aba7e12e1fb23 (KEY)0136540120160000032000301213controlchartforthemultivariatecoefficientofvariati DE-627 ger DE-627 rakwb eng 650 690 DNB 50.16 bkl 85.38 bkl Yeong, Wai Chung verfasserin aut A Control Chart for the Multivariate Coefficient of Variation 2016 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier Existing charts in the literature usually monitor either the mean or the variance of the process. However, in certain scenarios, the practitioner is not interested in the changes in the mean or the variance but is instead interested in monitoring the relative variability compared with the mean. This relative variability is called the coefficient of variation (CV). In the existing literature, none of the control charts that monitor the CV are applied for multivariate data. To fill this gap in research, this paper proposes a CV chart that monitors the CV for multivariate data. To the best of the authors' knowledge, this proposed chart is the first control chart for this purpose. The distributional properties of the sample CV for multivariate data and the procedures to implement the chart are presented in this paper. Formulae to compute the control limits, the average run length, the standard deviation of the run length, and the expected average run length for the case of unknown shift size are derived. From the numerical examples provided, the effects of the number of variables, the sample size, the shift size and the in‐control value of the CV are studied. Finally, we demonstrate the usefulness and applicability of the proposed chart on real data. Copyright © 2015 John Wiley & Sons, Ltd. Nutzungsrecht: Copyright © 2015 John Wiley & Sons, Ltd. average run length unknown shift size multivariate coefficient of variation relative variability expected average run length Khoo, Michael Boon Chong oth Teoh, Wei Lin oth Castagliola, Philippe oth Enthalten in Quality and reliability engineering international Chichester [u.a.] : Wiley, 1985 32(2016), 3, Seite 1213-1225 (DE-627)129167614 (DE-600)50641-2 (DE-576)028403312 0748-8017 nnns volume:32 year:2016 number:3 pages:1213-1225 http://dx.doi.org/10.1002/qre.1828 Volltext http://onlinelibrary.wiley.com/doi/10.1002/qre.1828/abstract http://search.proquest.com/docview/1774428921 GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-UMW SSG-OLC-ARC SSG-OLC-TEC SSG-OLC-WIW GBV_ILN_70 50.16 AVZ 85.38 AVZ AR 32 2016 3 1213-1225 |
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10.1002/qre.1828 doi PQ20160610 (DE-627)OLC1974010341 (DE-599)GBVOLC1974010341 (PRQ)p1554-910ea50633c6a9ebae6962978db3c3a5f1287cc35a5f41df40d9aba7e12e1fb23 (KEY)0136540120160000032000301213controlchartforthemultivariatecoefficientofvariati DE-627 ger DE-627 rakwb eng 650 690 DNB 50.16 bkl 85.38 bkl Yeong, Wai Chung verfasserin aut A Control Chart for the Multivariate Coefficient of Variation 2016 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier Existing charts in the literature usually monitor either the mean or the variance of the process. However, in certain scenarios, the practitioner is not interested in the changes in the mean or the variance but is instead interested in monitoring the relative variability compared with the mean. This relative variability is called the coefficient of variation (CV). In the existing literature, none of the control charts that monitor the CV are applied for multivariate data. To fill this gap in research, this paper proposes a CV chart that monitors the CV for multivariate data. To the best of the authors' knowledge, this proposed chart is the first control chart for this purpose. The distributional properties of the sample CV for multivariate data and the procedures to implement the chart are presented in this paper. Formulae to compute the control limits, the average run length, the standard deviation of the run length, and the expected average run length for the case of unknown shift size are derived. From the numerical examples provided, the effects of the number of variables, the sample size, the shift size and the in‐control value of the CV are studied. Finally, we demonstrate the usefulness and applicability of the proposed chart on real data. Copyright © 2015 John Wiley & Sons, Ltd. Nutzungsrecht: Copyright © 2015 John Wiley & Sons, Ltd. average run length unknown shift size multivariate coefficient of variation relative variability expected average run length Khoo, Michael Boon Chong oth Teoh, Wei Lin oth Castagliola, Philippe oth Enthalten in Quality and reliability engineering international Chichester [u.a.] : Wiley, 1985 32(2016), 3, Seite 1213-1225 (DE-627)129167614 (DE-600)50641-2 (DE-576)028403312 0748-8017 nnns volume:32 year:2016 number:3 pages:1213-1225 http://dx.doi.org/10.1002/qre.1828 Volltext http://onlinelibrary.wiley.com/doi/10.1002/qre.1828/abstract http://search.proquest.com/docview/1774428921 GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-UMW SSG-OLC-ARC SSG-OLC-TEC SSG-OLC-WIW GBV_ILN_70 50.16 AVZ 85.38 AVZ AR 32 2016 3 1213-1225 |
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10.1002/qre.1828 doi PQ20160610 (DE-627)OLC1974010341 (DE-599)GBVOLC1974010341 (PRQ)p1554-910ea50633c6a9ebae6962978db3c3a5f1287cc35a5f41df40d9aba7e12e1fb23 (KEY)0136540120160000032000301213controlchartforthemultivariatecoefficientofvariati DE-627 ger DE-627 rakwb eng 650 690 DNB 50.16 bkl 85.38 bkl Yeong, Wai Chung verfasserin aut A Control Chart for the Multivariate Coefficient of Variation 2016 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier Existing charts in the literature usually monitor either the mean or the variance of the process. However, in certain scenarios, the practitioner is not interested in the changes in the mean or the variance but is instead interested in monitoring the relative variability compared with the mean. This relative variability is called the coefficient of variation (CV). In the existing literature, none of the control charts that monitor the CV are applied for multivariate data. To fill this gap in research, this paper proposes a CV chart that monitors the CV for multivariate data. To the best of the authors' knowledge, this proposed chart is the first control chart for this purpose. The distributional properties of the sample CV for multivariate data and the procedures to implement the chart are presented in this paper. Formulae to compute the control limits, the average run length, the standard deviation of the run length, and the expected average run length for the case of unknown shift size are derived. From the numerical examples provided, the effects of the number of variables, the sample size, the shift size and the in‐control value of the CV are studied. Finally, we demonstrate the usefulness and applicability of the proposed chart on real data. Copyright © 2015 John Wiley & Sons, Ltd. Nutzungsrecht: Copyright © 2015 John Wiley & Sons, Ltd. average run length unknown shift size multivariate coefficient of variation relative variability expected average run length Khoo, Michael Boon Chong oth Teoh, Wei Lin oth Castagliola, Philippe oth Enthalten in Quality and reliability engineering international Chichester [u.a.] : Wiley, 1985 32(2016), 3, Seite 1213-1225 (DE-627)129167614 (DE-600)50641-2 (DE-576)028403312 0748-8017 nnns volume:32 year:2016 number:3 pages:1213-1225 http://dx.doi.org/10.1002/qre.1828 Volltext http://onlinelibrary.wiley.com/doi/10.1002/qre.1828/abstract http://search.proquest.com/docview/1774428921 GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-UMW SSG-OLC-ARC SSG-OLC-TEC SSG-OLC-WIW GBV_ILN_70 50.16 AVZ 85.38 AVZ AR 32 2016 3 1213-1225 |
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10.1002/qre.1828 doi PQ20160610 (DE-627)OLC1974010341 (DE-599)GBVOLC1974010341 (PRQ)p1554-910ea50633c6a9ebae6962978db3c3a5f1287cc35a5f41df40d9aba7e12e1fb23 (KEY)0136540120160000032000301213controlchartforthemultivariatecoefficientofvariati DE-627 ger DE-627 rakwb eng 650 690 DNB 50.16 bkl 85.38 bkl Yeong, Wai Chung verfasserin aut A Control Chart for the Multivariate Coefficient of Variation 2016 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier Existing charts in the literature usually monitor either the mean or the variance of the process. However, in certain scenarios, the practitioner is not interested in the changes in the mean or the variance but is instead interested in monitoring the relative variability compared with the mean. This relative variability is called the coefficient of variation (CV). In the existing literature, none of the control charts that monitor the CV are applied for multivariate data. To fill this gap in research, this paper proposes a CV chart that monitors the CV for multivariate data. To the best of the authors' knowledge, this proposed chart is the first control chart for this purpose. The distributional properties of the sample CV for multivariate data and the procedures to implement the chart are presented in this paper. Formulae to compute the control limits, the average run length, the standard deviation of the run length, and the expected average run length for the case of unknown shift size are derived. From the numerical examples provided, the effects of the number of variables, the sample size, the shift size and the in‐control value of the CV are studied. Finally, we demonstrate the usefulness and applicability of the proposed chart on real data. Copyright © 2015 John Wiley & Sons, Ltd. Nutzungsrecht: Copyright © 2015 John Wiley & Sons, Ltd. average run length unknown shift size multivariate coefficient of variation relative variability expected average run length Khoo, Michael Boon Chong oth Teoh, Wei Lin oth Castagliola, Philippe oth Enthalten in Quality and reliability engineering international Chichester [u.a.] : Wiley, 1985 32(2016), 3, Seite 1213-1225 (DE-627)129167614 (DE-600)50641-2 (DE-576)028403312 0748-8017 nnns volume:32 year:2016 number:3 pages:1213-1225 http://dx.doi.org/10.1002/qre.1828 Volltext http://onlinelibrary.wiley.com/doi/10.1002/qre.1828/abstract http://search.proquest.com/docview/1774428921 GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-UMW SSG-OLC-ARC SSG-OLC-TEC SSG-OLC-WIW GBV_ILN_70 50.16 AVZ 85.38 AVZ AR 32 2016 3 1213-1225 |
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However, in certain scenarios, the practitioner is not interested in the changes in the mean or the variance but is instead interested in monitoring the relative variability compared with the mean. This relative variability is called the coefficient of variation (CV). In the existing literature, none of the control charts that monitor the CV are applied for multivariate data. To fill this gap in research, this paper proposes a CV chart that monitors the CV for multivariate data. To the best of the authors' knowledge, this proposed chart is the first control chart for this purpose. The distributional properties of the sample CV for multivariate data and the procedures to implement the chart are presented in this paper. Formulae to compute the control limits, the average run length, the standard deviation of the run length, and the expected average run length for the case of unknown shift size are derived. From the numerical examples provided, the effects of the number of variables, the sample size, the shift size and the in‐control value of the CV are studied. Finally, we demonstrate the usefulness and applicability of the proposed chart on real data. 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Existing charts in the literature usually monitor either the mean or the variance of the process. However, in certain scenarios, the practitioner is not interested in the changes in the mean or the variance but is instead interested in monitoring the relative variability compared with the mean. This relative variability is called the coefficient of variation (CV). In the existing literature, none of the control charts that monitor the CV are applied for multivariate data. To fill this gap in research, this paper proposes a CV chart that monitors the CV for multivariate data. To the best of the authors' knowledge, this proposed chart is the first control chart for this purpose. The distributional properties of the sample CV for multivariate data and the procedures to implement the chart are presented in this paper. Formulae to compute the control limits, the average run length, the standard deviation of the run length, and the expected average run length for the case of unknown shift size are derived. From the numerical examples provided, the effects of the number of variables, the sample size, the shift size and the in‐control value of the CV are studied. Finally, we demonstrate the usefulness and applicability of the proposed chart on real data. Copyright © 2015 John Wiley & Sons, Ltd. |
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Existing charts in the literature usually monitor either the mean or the variance of the process. However, in certain scenarios, the practitioner is not interested in the changes in the mean or the variance but is instead interested in monitoring the relative variability compared with the mean. This relative variability is called the coefficient of variation (CV). In the existing literature, none of the control charts that monitor the CV are applied for multivariate data. To fill this gap in research, this paper proposes a CV chart that monitors the CV for multivariate data. To the best of the authors' knowledge, this proposed chart is the first control chart for this purpose. The distributional properties of the sample CV for multivariate data and the procedures to implement the chart are presented in this paper. Formulae to compute the control limits, the average run length, the standard deviation of the run length, and the expected average run length for the case of unknown shift size are derived. From the numerical examples provided, the effects of the number of variables, the sample size, the shift size and the in‐control value of the CV are studied. Finally, we demonstrate the usefulness and applicability of the proposed chart on real data. Copyright © 2015 John Wiley & Sons, Ltd. |
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Existing charts in the literature usually monitor either the mean or the variance of the process. However, in certain scenarios, the practitioner is not interested in the changes in the mean or the variance but is instead interested in monitoring the relative variability compared with the mean. This relative variability is called the coefficient of variation (CV). In the existing literature, none of the control charts that monitor the CV are applied for multivariate data. To fill this gap in research, this paper proposes a CV chart that monitors the CV for multivariate data. To the best of the authors' knowledge, this proposed chart is the first control chart for this purpose. The distributional properties of the sample CV for multivariate data and the procedures to implement the chart are presented in this paper. Formulae to compute the control limits, the average run length, the standard deviation of the run length, and the expected average run length for the case of unknown shift size are derived. From the numerical examples provided, the effects of the number of variables, the sample size, the shift size and the in‐control value of the CV are studied. Finally, we demonstrate the usefulness and applicability of the proposed chart on real data. Copyright © 2015 John Wiley & Sons, Ltd. |
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