Monitoring the Process Mean When Standards Are Unknown: A Classic Problem Revisited
One of the most common applications in statistical process monitoring is the use of control charts to monitor a process mean. In practice, this is often performed with a Shewhart chart along with a Shewhart R (or an S ) chart. Thus, two charts are typically used together, as a scheme, each using the...
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| Autor*in: |
Diko, M. D [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), 2, Seite 609-622 |
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| Übergeordnetes Werk: |
volume:32 ; year:2016 ; number:2 ; pages:609-622 |
| Links: |
|---|
| DOI / URN: |
10.1002/qre.1776 |
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OLC1973068249 |
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| 520 | |a One of the most common applications in statistical process monitoring is the use of control charts to monitor a process mean. In practice, this is often performed with a Shewhart chart along with a Shewhart R (or an S ) chart. Thus, two charts are typically used together, as a scheme, each using the 3‐sigma limits. Moreover, the process mean and standard deviation are often unknown and need to be estimated before monitoring can begin. We show that there are three major issues with this monitoring scheme described in most textbooks. The first issue is not accounting for the effects of parameter estimation, which is known to degrade chart performance. The second issue is the implicit assumption that the charting statistics are both normally distributed and, accordingly, using the 3‐sigma limits. The third issue is multiple charting, because two charts are used, in this scheme, at the same time. We illustrate the deleterious effects of these issues on the in‐control properties of the charting scheme and present a method for finding the correct charting constants taking proper account of these issues. Tables of the new charting constants are provided for some commonly used nominal in‐control average run length values and different sample sizes. This will aid in implementing the charting scheme correctly in practice. Examples are given along with a summary and some conclusions. Copyright © 2015 John Wiley & Sons, Ltd. | ||
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10.1002/qre.1776 doi PQ20160430 (DE-627)OLC1973068249 (DE-599)GBVOLC1973068249 (PRQ)c2248-8262c6ecd63aae00bcf52051a8637969f035bde698848c0cfc584d6f76ad2b383 (KEY)0136540120160000032000200609monitoringtheprocessmeanwhenstandardsareunknownacl DE-627 ger DE-627 rakwb eng 650 690 DNB 50.16 bkl 85.38 bkl Diko, M. D verfasserin aut Monitoring the Process Mean When Standards Are Unknown: A Classic Problem Revisited 2016 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier One of the most common applications in statistical process monitoring is the use of control charts to monitor a process mean. In practice, this is often performed with a Shewhart chart along with a Shewhart R (or an S ) chart. Thus, two charts are typically used together, as a scheme, each using the 3‐sigma limits. Moreover, the process mean and standard deviation are often unknown and need to be estimated before monitoring can begin. We show that there are three major issues with this monitoring scheme described in most textbooks. The first issue is not accounting for the effects of parameter estimation, which is known to degrade chart performance. The second issue is the implicit assumption that the charting statistics are both normally distributed and, accordingly, using the 3‐sigma limits. The third issue is multiple charting, because two charts are used, in this scheme, at the same time. We illustrate the deleterious effects of these issues on the in‐control properties of the charting scheme and present a method for finding the correct charting constants taking proper account of these issues. Tables of the new charting constants are provided for some commonly used nominal in‐control average run length values and different sample sizes. This will aid in implementing the charting scheme correctly in practice. Examples are given along with a summary and some conclusions. Copyright © 2015 John Wiley & Sons, Ltd. Nutzungsrecht: Copyright © 2015 John Wiley & Sons, Ltd. monitoring mean and variance parameter estimation false alarm rate Shewhart multiple charting average run length Shewhart chart chart 3‐sigma limits Chakraborti, S oth Graham, M. A oth Enthalten in Quality and reliability engineering international Chichester [u.a.] : Wiley, 1985 32(2016), 2, Seite 609-622 (DE-627)129167614 (DE-600)50641-2 (DE-576)028403312 0748-8017 nnns volume:32 year:2016 number:2 pages:609-622 http://dx.doi.org/10.1002/qre.1776 Volltext http://onlinelibrary.wiley.com/doi/10.1002/qre.1776/abstract http://search.proquest.com/docview/1764092081 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 2 609-622 |
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10.1002/qre.1776 doi PQ20160430 (DE-627)OLC1973068249 (DE-599)GBVOLC1973068249 (PRQ)c2248-8262c6ecd63aae00bcf52051a8637969f035bde698848c0cfc584d6f76ad2b383 (KEY)0136540120160000032000200609monitoringtheprocessmeanwhenstandardsareunknownacl DE-627 ger DE-627 rakwb eng 650 690 DNB 50.16 bkl 85.38 bkl Diko, M. D verfasserin aut Monitoring the Process Mean When Standards Are Unknown: A Classic Problem Revisited 2016 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier One of the most common applications in statistical process monitoring is the use of control charts to monitor a process mean. In practice, this is often performed with a Shewhart chart along with a Shewhart R (or an S ) chart. Thus, two charts are typically used together, as a scheme, each using the 3‐sigma limits. Moreover, the process mean and standard deviation are often unknown and need to be estimated before monitoring can begin. We show that there are three major issues with this monitoring scheme described in most textbooks. The first issue is not accounting for the effects of parameter estimation, which is known to degrade chart performance. The second issue is the implicit assumption that the charting statistics are both normally distributed and, accordingly, using the 3‐sigma limits. The third issue is multiple charting, because two charts are used, in this scheme, at the same time. We illustrate the deleterious effects of these issues on the in‐control properties of the charting scheme and present a method for finding the correct charting constants taking proper account of these issues. Tables of the new charting constants are provided for some commonly used nominal in‐control average run length values and different sample sizes. This will aid in implementing the charting scheme correctly in practice. Examples are given along with a summary and some conclusions. Copyright © 2015 John Wiley & Sons, Ltd. Nutzungsrecht: Copyright © 2015 John Wiley & Sons, Ltd. monitoring mean and variance parameter estimation false alarm rate Shewhart multiple charting average run length Shewhart chart chart 3‐sigma limits Chakraborti, S oth Graham, M. A oth Enthalten in Quality and reliability engineering international Chichester [u.a.] : Wiley, 1985 32(2016), 2, Seite 609-622 (DE-627)129167614 (DE-600)50641-2 (DE-576)028403312 0748-8017 nnns volume:32 year:2016 number:2 pages:609-622 http://dx.doi.org/10.1002/qre.1776 Volltext http://onlinelibrary.wiley.com/doi/10.1002/qre.1776/abstract http://search.proquest.com/docview/1764092081 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 2 609-622 |
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10.1002/qre.1776 doi PQ20160430 (DE-627)OLC1973068249 (DE-599)GBVOLC1973068249 (PRQ)c2248-8262c6ecd63aae00bcf52051a8637969f035bde698848c0cfc584d6f76ad2b383 (KEY)0136540120160000032000200609monitoringtheprocessmeanwhenstandardsareunknownacl DE-627 ger DE-627 rakwb eng 650 690 DNB 50.16 bkl 85.38 bkl Diko, M. D verfasserin aut Monitoring the Process Mean When Standards Are Unknown: A Classic Problem Revisited 2016 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier One of the most common applications in statistical process monitoring is the use of control charts to monitor a process mean. In practice, this is often performed with a Shewhart chart along with a Shewhart R (or an S ) chart. Thus, two charts are typically used together, as a scheme, each using the 3‐sigma limits. Moreover, the process mean and standard deviation are often unknown and need to be estimated before monitoring can begin. We show that there are three major issues with this monitoring scheme described in most textbooks. The first issue is not accounting for the effects of parameter estimation, which is known to degrade chart performance. The second issue is the implicit assumption that the charting statistics are both normally distributed and, accordingly, using the 3‐sigma limits. The third issue is multiple charting, because two charts are used, in this scheme, at the same time. We illustrate the deleterious effects of these issues on the in‐control properties of the charting scheme and present a method for finding the correct charting constants taking proper account of these issues. Tables of the new charting constants are provided for some commonly used nominal in‐control average run length values and different sample sizes. This will aid in implementing the charting scheme correctly in practice. Examples are given along with a summary and some conclusions. Copyright © 2015 John Wiley & Sons, Ltd. Nutzungsrecht: Copyright © 2015 John Wiley & Sons, Ltd. monitoring mean and variance parameter estimation false alarm rate Shewhart multiple charting average run length Shewhart chart chart 3‐sigma limits Chakraborti, S oth Graham, M. A oth Enthalten in Quality and reliability engineering international Chichester [u.a.] : Wiley, 1985 32(2016), 2, Seite 609-622 (DE-627)129167614 (DE-600)50641-2 (DE-576)028403312 0748-8017 nnns volume:32 year:2016 number:2 pages:609-622 http://dx.doi.org/10.1002/qre.1776 Volltext http://onlinelibrary.wiley.com/doi/10.1002/qre.1776/abstract http://search.proquest.com/docview/1764092081 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 2 609-622 |
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10.1002/qre.1776 doi PQ20160430 (DE-627)OLC1973068249 (DE-599)GBVOLC1973068249 (PRQ)c2248-8262c6ecd63aae00bcf52051a8637969f035bde698848c0cfc584d6f76ad2b383 (KEY)0136540120160000032000200609monitoringtheprocessmeanwhenstandardsareunknownacl DE-627 ger DE-627 rakwb eng 650 690 DNB 50.16 bkl 85.38 bkl Diko, M. D verfasserin aut Monitoring the Process Mean When Standards Are Unknown: A Classic Problem Revisited 2016 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier One of the most common applications in statistical process monitoring is the use of control charts to monitor a process mean. In practice, this is often performed with a Shewhart chart along with a Shewhart R (or an S ) chart. Thus, two charts are typically used together, as a scheme, each using the 3‐sigma limits. Moreover, the process mean and standard deviation are often unknown and need to be estimated before monitoring can begin. We show that there are three major issues with this monitoring scheme described in most textbooks. The first issue is not accounting for the effects of parameter estimation, which is known to degrade chart performance. The second issue is the implicit assumption that the charting statistics are both normally distributed and, accordingly, using the 3‐sigma limits. The third issue is multiple charting, because two charts are used, in this scheme, at the same time. We illustrate the deleterious effects of these issues on the in‐control properties of the charting scheme and present a method for finding the correct charting constants taking proper account of these issues. Tables of the new charting constants are provided for some commonly used nominal in‐control average run length values and different sample sizes. This will aid in implementing the charting scheme correctly in practice. Examples are given along with a summary and some conclusions. Copyright © 2015 John Wiley & Sons, Ltd. Nutzungsrecht: Copyright © 2015 John Wiley & Sons, Ltd. monitoring mean and variance parameter estimation false alarm rate Shewhart multiple charting average run length Shewhart chart chart 3‐sigma limits Chakraborti, S oth Graham, M. A oth Enthalten in Quality and reliability engineering international Chichester [u.a.] : Wiley, 1985 32(2016), 2, Seite 609-622 (DE-627)129167614 (DE-600)50641-2 (DE-576)028403312 0748-8017 nnns volume:32 year:2016 number:2 pages:609-622 http://dx.doi.org/10.1002/qre.1776 Volltext http://onlinelibrary.wiley.com/doi/10.1002/qre.1776/abstract http://search.proquest.com/docview/1764092081 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 2 609-622 |
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10.1002/qre.1776 doi PQ20160430 (DE-627)OLC1973068249 (DE-599)GBVOLC1973068249 (PRQ)c2248-8262c6ecd63aae00bcf52051a8637969f035bde698848c0cfc584d6f76ad2b383 (KEY)0136540120160000032000200609monitoringtheprocessmeanwhenstandardsareunknownacl DE-627 ger DE-627 rakwb eng 650 690 DNB 50.16 bkl 85.38 bkl Diko, M. D verfasserin aut Monitoring the Process Mean When Standards Are Unknown: A Classic Problem Revisited 2016 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier One of the most common applications in statistical process monitoring is the use of control charts to monitor a process mean. In practice, this is often performed with a Shewhart chart along with a Shewhart R (or an S ) chart. Thus, two charts are typically used together, as a scheme, each using the 3‐sigma limits. Moreover, the process mean and standard deviation are often unknown and need to be estimated before monitoring can begin. We show that there are three major issues with this monitoring scheme described in most textbooks. The first issue is not accounting for the effects of parameter estimation, which is known to degrade chart performance. The second issue is the implicit assumption that the charting statistics are both normally distributed and, accordingly, using the 3‐sigma limits. The third issue is multiple charting, because two charts are used, in this scheme, at the same time. We illustrate the deleterious effects of these issues on the in‐control properties of the charting scheme and present a method for finding the correct charting constants taking proper account of these issues. Tables of the new charting constants are provided for some commonly used nominal in‐control average run length values and different sample sizes. This will aid in implementing the charting scheme correctly in practice. Examples are given along with a summary and some conclusions. Copyright © 2015 John Wiley & Sons, Ltd. Nutzungsrecht: Copyright © 2015 John Wiley & Sons, Ltd. monitoring mean and variance parameter estimation false alarm rate Shewhart multiple charting average run length Shewhart chart chart 3‐sigma limits Chakraborti, S oth Graham, M. A oth Enthalten in Quality and reliability engineering international Chichester [u.a.] : Wiley, 1985 32(2016), 2, Seite 609-622 (DE-627)129167614 (DE-600)50641-2 (DE-576)028403312 0748-8017 nnns volume:32 year:2016 number:2 pages:609-622 http://dx.doi.org/10.1002/qre.1776 Volltext http://onlinelibrary.wiley.com/doi/10.1002/qre.1776/abstract http://search.proquest.com/docview/1764092081 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 2 609-622 |
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Monitoring the Process Mean When Standards Are Unknown: A Classic Problem Revisited |
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One of the most common applications in statistical process monitoring is the use of control charts to monitor a process mean. In practice, this is often performed with a Shewhart chart along with a Shewhart R (or an S ) chart. Thus, two charts are typically used together, as a scheme, each using the 3‐sigma limits. Moreover, the process mean and standard deviation are often unknown and need to be estimated before monitoring can begin. We show that there are three major issues with this monitoring scheme described in most textbooks. The first issue is not accounting for the effects of parameter estimation, which is known to degrade chart performance. The second issue is the implicit assumption that the charting statistics are both normally distributed and, accordingly, using the 3‐sigma limits. The third issue is multiple charting, because two charts are used, in this scheme, at the same time. We illustrate the deleterious effects of these issues on the in‐control properties of the charting scheme and present a method for finding the correct charting constants taking proper account of these issues. Tables of the new charting constants are provided for some commonly used nominal in‐control average run length values and different sample sizes. This will aid in implementing the charting scheme correctly in practice. Examples are given along with a summary and some conclusions. Copyright © 2015 John Wiley & Sons, Ltd. |
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One of the most common applications in statistical process monitoring is the use of control charts to monitor a process mean. In practice, this is often performed with a Shewhart chart along with a Shewhart R (or an S ) chart. Thus, two charts are typically used together, as a scheme, each using the 3‐sigma limits. Moreover, the process mean and standard deviation are often unknown and need to be estimated before monitoring can begin. We show that there are three major issues with this monitoring scheme described in most textbooks. The first issue is not accounting for the effects of parameter estimation, which is known to degrade chart performance. The second issue is the implicit assumption that the charting statistics are both normally distributed and, accordingly, using the 3‐sigma limits. The third issue is multiple charting, because two charts are used, in this scheme, at the same time. We illustrate the deleterious effects of these issues on the in‐control properties of the charting scheme and present a method for finding the correct charting constants taking proper account of these issues. Tables of the new charting constants are provided for some commonly used nominal in‐control average run length values and different sample sizes. This will aid in implementing the charting scheme correctly in practice. Examples are given along with a summary and some conclusions. Copyright © 2015 John Wiley & Sons, Ltd. |
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One of the most common applications in statistical process monitoring is the use of control charts to monitor a process mean. In practice, this is often performed with a Shewhart chart along with a Shewhart R (or an S ) chart. Thus, two charts are typically used together, as a scheme, each using the 3‐sigma limits. Moreover, the process mean and standard deviation are often unknown and need to be estimated before monitoring can begin. We show that there are three major issues with this monitoring scheme described in most textbooks. The first issue is not accounting for the effects of parameter estimation, which is known to degrade chart performance. The second issue is the implicit assumption that the charting statistics are both normally distributed and, accordingly, using the 3‐sigma limits. The third issue is multiple charting, because two charts are used, in this scheme, at the same time. We illustrate the deleterious effects of these issues on the in‐control properties of the charting scheme and present a method for finding the correct charting constants taking proper account of these issues. Tables of the new charting constants are provided for some commonly used nominal in‐control average run length values and different sample sizes. This will aid in implementing the charting scheme correctly in practice. Examples are given along with a summary and some conclusions. Copyright © 2015 John Wiley & Sons, Ltd. |
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