Shewhart-type control charts for variation in phase I data analysis
Control charts for variation play a key role in the overall statistical process control (SPC) regime. We study the popular Shewhart-type S 2 , S and R control charts when the mean and the variance of a normally distributed process are both unknown and are estimated from m independent samples (subgro...
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| Veröffentlicht in: | Computational statistics & data analysis 2010-04, Vol.54 (4), p.863-874 |
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| creator | Human, S.W. Chakraborti, S. Smit, C.F. |
| description | Control charts for variation play a key role in the overall statistical process control (SPC) regime. We study the popular Shewhart-type
S
2
,
S
and
R
control charts when the mean and the variance of a normally distributed process are both unknown and are estimated from
m
independent samples (subgroups) each of size
n
. This is the Phase I setting. Current uses of these charts do not recognize that in this setting the signalling events are statistically dependent and that
m
comparisons are made with the same control limits simultaneously. These are important issues because they affect the design and the performance of the control charts. The proposed methodology addresses these issues (which leads to working with the joint distribution of a set of dependent random variables) by calculating the correct control limits, so that the false alarm probability (
FAP), defined as the probability of at least one false alarm, is at most equal to some given nominal value
F
A
P
0
. To aid practical implementation, tables are provided for the charting constants for each Phase I chart, for an
F
A
P
0
of 0.01 and 0.05, respectively. An illustrative example is given. |
| doi_str_mv | 10.1016/j.csda.2009.09.026 |
| format | Article |
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S
2
,
S
and
R
control charts when the mean and the variance of a normally distributed process are both unknown and are estimated from
m
independent samples (subgroups) each of size
n
. This is the Phase I setting. Current uses of these charts do not recognize that in this setting the signalling events are statistically dependent and that
m
comparisons are made with the same control limits simultaneously. These are important issues because they affect the design and the performance of the control charts. The proposed methodology addresses these issues (which leads to working with the joint distribution of a set of dependent random variables) by calculating the correct control limits, so that the false alarm probability (
FAP), defined as the probability of at least one false alarm, is at most equal to some given nominal value
F
A
P
0
. To aid practical implementation, tables are provided for the charting constants for each Phase I chart, for an
F
A
P
0
of 0.01 and 0.05, respectively. An illustrative example is given.</description><identifier>ISSN: 0167-9473</identifier><identifier>EISSN: 1872-7352</identifier><identifier>DOI: 10.1016/j.csda.2009.09.026</identifier><language>eng</language><publisher>Amsterdam: Elsevier B.V</publisher><subject>Applications ; Exact sciences and technology ; General topics ; Mathematics ; Multivariate analysis ; Numerical analysis ; Numerical analysis. Scientific computation ; Numerical methods in probability and statistics ; Probability and statistics ; Reliability, life testing, quality control ; Sciences and techniques of general use ; Statistics</subject><ispartof>Computational statistics & data analysis, 2010-04, Vol.54 (4), p.863-874</ispartof><rights>2009 Elsevier B.V.</rights><rights>2015 INIST-CNRS</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c429t-13d966695b6970671543bee725417b88770487d575ac9ee8a1619e8d27b4627d3</citedby><cites>FETCH-LOGICAL-c429t-13d966695b6970671543bee725417b88770487d575ac9ee8a1619e8d27b4627d3</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktohtml>$$Uhttps://dx.doi.org/10.1016/j.csda.2009.09.026$$EHTML$$P50$$Gelsevier$$H</linktohtml><link.rule.ids>314,777,781,3537,3994,27905,27906,45976</link.rule.ids><backlink>$$Uhttp://pascal-francis.inist.fr/vibad/index.php?action=getRecordDetail&idt=22598288$$DView record in Pascal Francis$$Hfree_for_read</backlink><backlink>$$Uhttp://econpapers.repec.org/article/eeecsdana/v_3a54_3ay_3a2010_3ai_3a4_3ap_3a863-874.htm$$DView record in RePEc$$Hfree_for_read</backlink></links><search><creatorcontrib>Human, S.W.</creatorcontrib><creatorcontrib>Chakraborti, S.</creatorcontrib><creatorcontrib>Smit, C.F.</creatorcontrib><title>Shewhart-type control charts for variation in phase I data analysis</title><title>Computational statistics & data analysis</title><description>Control charts for variation play a key role in the overall statistical process control (SPC) regime. We study the popular Shewhart-type
S
2
,
S
and
R
control charts when the mean and the variance of a normally distributed process are both unknown and are estimated from
m
independent samples (subgroups) each of size
n
. This is the Phase I setting. Current uses of these charts do not recognize that in this setting the signalling events are statistically dependent and that
m
comparisons are made with the same control limits simultaneously. These are important issues because they affect the design and the performance of the control charts. The proposed methodology addresses these issues (which leads to working with the joint distribution of a set of dependent random variables) by calculating the correct control limits, so that the false alarm probability (
FAP), defined as the probability of at least one false alarm, is at most equal to some given nominal value
F
A
P
0
. To aid practical implementation, tables are provided for the charting constants for each Phase I chart, for an
F
A
P
0
of 0.01 and 0.05, respectively. An illustrative example is given.</description><subject>Applications</subject><subject>Exact sciences and technology</subject><subject>General topics</subject><subject>Mathematics</subject><subject>Multivariate analysis</subject><subject>Numerical analysis</subject><subject>Numerical analysis. Scientific computation</subject><subject>Numerical methods in probability and statistics</subject><subject>Probability and statistics</subject><subject>Reliability, life testing, quality control</subject><subject>Sciences and techniques of general use</subject><subject>Statistics</subject><issn>0167-9473</issn><issn>1872-7352</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2010</creationdate><recordtype>article</recordtype><sourceid>X2L</sourceid><recordid>eNp9kEtrGzEUhUVpoW6aP9CVNqWrcfQaPSCbYvIk0EWTtbjWXGOZ8cxEUhz876PBIcvAPRJcvnO4HEJ-cbbkjOuL3TLkDpaCMbecR-gvZMGtEY2RrfhKFhUyjVNGfic_ct4xxoQydkFW_7f4uoVUmnKckIZxKGnsaZhXmW7GRA-QIpQ4DjQOdNpCRnpHOyhAYYD-mGP-Sb5toM94_v6fkafrq8fVbfPw7-Zu9fehCUq40nDZOa21a9faGaYNb5VcIxrRKm7W1hrDlDVda1oIDtEC19yh7YRZKy1MJ8_In1PulMbnF8zF72MO2Pcw4PiSvVFSOsm0rKQ4kSGNOSfc-CnFPaSj58zPhfmdnwvzc2F-HqGr6f5kSjhh-HAg4owO4A9eQqvqc6wSrEZJiFXzaqqyWnprlN-WfQ37_X4r5AD9JsEQYv4IFaJ1VlhbucsTh7W4Q8Tkc4g4BOxiwlB8N8bPbn4DG_mYdw</recordid><startdate>20100401</startdate><enddate>20100401</enddate><creator>Human, S.W.</creator><creator>Chakraborti, S.</creator><creator>Smit, C.F.</creator><general>Elsevier B.V</general><general>Elsevier</general><scope>IQODW</scope><scope>DKI</scope><scope>X2L</scope><scope>AAYXX</scope><scope>CITATION</scope><scope>7SC</scope><scope>8FD</scope><scope>JQ2</scope><scope>L7M</scope><scope>L~C</scope><scope>L~D</scope></search><sort><creationdate>20100401</creationdate><title>Shewhart-type control charts for variation in phase I data analysis</title><author>Human, S.W. ; Chakraborti, S. ; Smit, C.F.</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c429t-13d966695b6970671543bee725417b88770487d575ac9ee8a1619e8d27b4627d3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2010</creationdate><topic>Applications</topic><topic>Exact sciences and technology</topic><topic>General topics</topic><topic>Mathematics</topic><topic>Multivariate analysis</topic><topic>Numerical analysis</topic><topic>Numerical analysis. Scientific computation</topic><topic>Numerical methods in probability and statistics</topic><topic>Probability and statistics</topic><topic>Reliability, life testing, quality control</topic><topic>Sciences and techniques of general use</topic><topic>Statistics</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Human, S.W.</creatorcontrib><creatorcontrib>Chakraborti, S.</creatorcontrib><creatorcontrib>Smit, C.F.</creatorcontrib><collection>Pascal-Francis</collection><collection>RePEc IDEAS</collection><collection>RePEc</collection><collection>CrossRef</collection><collection>Computer and Information Systems Abstracts</collection><collection>Technology Research Database</collection><collection>ProQuest Computer Science Collection</collection><collection>Advanced Technologies Database with Aerospace</collection><collection>Computer and Information Systems Abstracts Academic</collection><collection>Computer and Information Systems Abstracts Professional</collection><jtitle>Computational statistics & data analysis</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Human, S.W.</au><au>Chakraborti, S.</au><au>Smit, C.F.</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Shewhart-type control charts for variation in phase I data analysis</atitle><jtitle>Computational statistics & data analysis</jtitle><date>2010-04-01</date><risdate>2010</risdate><volume>54</volume><issue>4</issue><spage>863</spage><epage>874</epage><pages>863-874</pages><issn>0167-9473</issn><eissn>1872-7352</eissn><abstract>Control charts for variation play a key role in the overall statistical process control (SPC) regime. We study the popular Shewhart-type
S
2
,
S
and
R
control charts when the mean and the variance of a normally distributed process are both unknown and are estimated from
m
independent samples (subgroups) each of size
n
. This is the Phase I setting. Current uses of these charts do not recognize that in this setting the signalling events are statistically dependent and that
m
comparisons are made with the same control limits simultaneously. These are important issues because they affect the design and the performance of the control charts. The proposed methodology addresses these issues (which leads to working with the joint distribution of a set of dependent random variables) by calculating the correct control limits, so that the false alarm probability (
FAP), defined as the probability of at least one false alarm, is at most equal to some given nominal value
F
A
P
0
. To aid practical implementation, tables are provided for the charting constants for each Phase I chart, for an
F
A
P
0
of 0.01 and 0.05, respectively. An illustrative example is given.</abstract><cop>Amsterdam</cop><pub>Elsevier B.V</pub><doi>10.1016/j.csda.2009.09.026</doi><tpages>12</tpages></addata></record> |
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| ispartof | Computational statistics & data analysis, 2010-04, Vol.54 (4), p.863-874 |
| issn | 0167-9473 1872-7352 |
| language | eng |
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| source | RePEc; Elsevier ScienceDirect Journals Complete |
| subjects | Applications Exact sciences and technology General topics Mathematics Multivariate analysis Numerical analysis Numerical analysis. Scientific computation Numerical methods in probability and statistics Probability and statistics Reliability, life testing, quality control Sciences and techniques of general use Statistics |
| title | Shewhart-type control charts for variation in phase I data analysis |
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