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Article: A two-stage cumulative quantity control chart for monitoring poisson processes
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TitleA two-stage cumulative quantity control chart for monitoring poisson processes
 
AuthorsChan, LY1
Ouyang, J1
Lau, HYK1
 
KeywordsAverage quantity inspected
Average run length
CQC chart
Economic design
Gamma random variable
Statistical process control
Two-stage control chart
 
Issue Date2007
 
PublisherAmerican Society for Quality. The Journal's web site is located at http://www.asq.org/pub/jqt/
 
CitationJournal Of Quality Technology, 2007, v. 39 n. 3, p. 203-223 [How to Cite?]
 
AbstractThis paper is concerned with the cumulative quantity control chart (CQC chart) defined based on the gamma random variable that is the quantity of product inspected in order to observe r (= 1) nonconformities. A CQC chart with a small value of r has a smaller average run length (ARL), but has lower discriminating power for detecting shifts in the nonconforming rate ? than a CQC chart with a large r. In the present paper, inspired by the concepts of double sampling procedures in acceptance sampling as well as reduced inspection in MIL-STD-105E and the procedures for CSP plans in MIL-STD-1235C, a two-stage CQC chart is proposed aiming at gaining both the advantages of the 1-stage CQC charts with r = 1 and r = 2. The authors apply a rigorous analytic approach to perform sensitivity analysis to compare the discriminating power of CQC charts in detecting change in ?, rather than using the less rigorous approach of numerical verification based on an ac hoc choice of values of parameters. The authors also obtain and compare the analytic expressions for the ARLs of these CQC charts. Economic analysis of the CQC charts is performed. Numerical examples will be given to compare the performance of these control charts in terms of discriminating power (in detecting shift of ?), ARL, and average total cost, and to show that each of these charts could be the best choice in each specific situation. It is also shown that, when the penalty cost due to nonconformities is relatively low, it is optimal not to apply statistical process control at all. [From EbscoHost]
[This abstract is based on the authors' abstract.] The cumulative quantity control chart (CQC) is an effective alternative to traditional control charts for high yield processes with low nonconforming rates. Inspired by the concepts of double sampling procedures in acceptance sampling and reduced inspection, a two-stage CQC chart is proposed to gain both the advantages of the one-stage CQC charts with r=1 and r=2. An analytical approach is used to perform sensitivity analysis to compare the discriminating power of CQC charts. In addition, the analytic expressions for the average run length of these CQC charts are obtained and compared. Numerical examples show that each of these charts could be the best choice in a specific situation, and when the penalty cost due to nonconformities is relatively low, it is optimal not to apply statistical process control at all.
 
ISSN0022-4065
2013 Impact Factor: 1.271
2013 SCImago Journal Rankings: 1.743
 
ReferencesReferences in Scopus
 
DC FieldValue
dc.contributor.authorChan, LY
 
dc.contributor.authorOuyang, J
 
dc.contributor.authorLau, HYK
 
dc.date.accessioned2010-09-06T07:02:40Z
 
dc.date.available2010-09-06T07:02:40Z
 
dc.date.issued2007
 
dc.description.abstractThis paper is concerned with the cumulative quantity control chart (CQC chart) defined based on the gamma random variable that is the quantity of product inspected in order to observe r (= 1) nonconformities. A CQC chart with a small value of r has a smaller average run length (ARL), but has lower discriminating power for detecting shifts in the nonconforming rate ? than a CQC chart with a large r. In the present paper, inspired by the concepts of double sampling procedures in acceptance sampling as well as reduced inspection in MIL-STD-105E and the procedures for CSP plans in MIL-STD-1235C, a two-stage CQC chart is proposed aiming at gaining both the advantages of the 1-stage CQC charts with r = 1 and r = 2. The authors apply a rigorous analytic approach to perform sensitivity analysis to compare the discriminating power of CQC charts in detecting change in ?, rather than using the less rigorous approach of numerical verification based on an ac hoc choice of values of parameters. The authors also obtain and compare the analytic expressions for the ARLs of these CQC charts. Economic analysis of the CQC charts is performed. Numerical examples will be given to compare the performance of these control charts in terms of discriminating power (in detecting shift of ?), ARL, and average total cost, and to show that each of these charts could be the best choice in each specific situation. It is also shown that, when the penalty cost due to nonconformities is relatively low, it is optimal not to apply statistical process control at all. [From EbscoHost]
 
dc.description.abstract[This abstract is based on the authors' abstract.] The cumulative quantity control chart (CQC) is an effective alternative to traditional control charts for high yield processes with low nonconforming rates. Inspired by the concepts of double sampling procedures in acceptance sampling and reduced inspection, a two-stage CQC chart is proposed to gain both the advantages of the one-stage CQC charts with r=1 and r=2. An analytical approach is used to perform sensitivity analysis to compare the discriminating power of CQC charts. In addition, the analytic expressions for the average run length of these CQC charts are obtained and compared. Numerical examples show that each of these charts could be the best choice in a specific situation, and when the penalty cost due to nonconformities is relatively low, it is optimal not to apply statistical process control at all.
 
dc.description.natureLink_to_subscribed_fulltext
 
dc.identifier.citationJournal Of Quality Technology, 2007, v. 39 n. 3, p. 203-223 [How to Cite?]
 
dc.identifier.epage223
 
dc.identifier.hkuros160510
 
dc.identifier.hkuros122881
 
dc.identifier.issn0022-4065
2013 Impact Factor: 1.271
2013 SCImago Journal Rankings: 1.743
 
dc.identifier.issue3
 
dc.identifier.openurl
 
dc.identifier.scopuseid_2-s2.0-34547313588
 
dc.identifier.spage203
 
dc.identifier.urihttp://hdl.handle.net/10722/74574
 
dc.identifier.volume39
 
dc.languageeng
 
dc.publisherAmerican Society for Quality. The Journal's web site is located at http://www.asq.org/pub/jqt/
 
dc.publisher.placeUnited States
 
dc.relation.ispartofJournal of Quality Technology
 
dc.relation.referencesReferences in Scopus
 
dc.subjectAverage quantity inspected
 
dc.subjectAverage run length
 
dc.subjectCQC chart
 
dc.subjectEconomic design
 
dc.subjectGamma random variable
 
dc.subjectStatistical process control
 
dc.subjectTwo-stage control chart
 
dc.titleA two-stage cumulative quantity control chart for monitoring poisson processes
 
dc.typeArticle
 
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The cumulative quantity control chart (CQC) is an effective alternative to traditional control charts for high yield processes with low nonconforming rates. Inspired by the concepts of double sampling procedures in acceptance sampling and reduced inspection, a two-stage CQC chart is proposed to gain both the advantages of the one-stage CQC charts with r=1 and r=2. An analytical approach is used to perform sensitivity analysis to compare the discriminating power of CQC charts. In addition, the analytic expressions for the average run length of these CQC charts are obtained and compared. Numerical examples show that each of these charts could be the best choice in a specific situation, and when the penalty cost due to nonconformities is relatively low, it is optimal not to apply statistical process control at all.</description.abstract>
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Author Affiliations
  1. The University of Hong Kong