Detecting a downward shift in a proportion using a geometric CUSUM chart

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dc.contributor.authorBourke, Patrick D.
dc.date.accessioned2020-03-16T14:52:39Z
dc.date.available2020-03-16T14:52:39Z
dc.date.issued2019-12-19
dc.description.abstractIn monitoring an ordered stream of discrete items from a repetitive process, the geometric CUSUM chart may be used to detect sudden shifts from an acceptable level for a process-proportion (p) such as fraction nonconforming. Much of the investigative effort for this CUSUM scheme has been concentrated on the detection of upward shifts, and a recent paper has provided guidance to quality engineers in choosing the parameters (k, h) of such a scheme. In this article, the corresponding task of aiding the choice of parameters for detecting a downward shift is addressed. It is shown, using extensive numerical investigations, that the use of a value for the parameter k based on the Sequential Probability Ratio is not optimal when one is using steady-state evaluation of the detection performance of the CUSUM scheme. Tables are presented listing recommended values of parameters for detection of five sizes of downward shift, for each of 27 in-control levels for p in the range 0.20 to 0.001. Interpolation and extrapolation to find parameter values for other in-control levels of p are also considered, and a range of examples presented. There is an equivalence between a geometric CUSUM scheme and a Bernoulli CUSUM scheme, so that the results of this investigation may also be used in choosing parameter values for a Bernoulli CUSUM chart.en
dc.description.statusPeer revieweden
dc.description.versionAccepted Versionen
dc.format.mimetypeapplication/pdfen
dc.identifier.citationBourke, P. D. (2020) 'Detecting a downward shift in a proportion using a geometric CUSUM chart, Quality Engineering, 32:1, pp. 75-90, doi: 10.1080/08982112.2019.1664750en
dc.identifier.doi10.1080/08982112.2019.1664750en
dc.identifier.eissn1532-4222
dc.identifier.endpage90en
dc.identifier.issn0898-2112
dc.identifier.issued1en
dc.identifier.journaltitleQuality Engineeringen
dc.identifier.startpage75en
dc.identifier.urihttps://hdl.handle.net/10468/9765
dc.identifier.volume32en
dc.language.isoenen
dc.publisherTaylor & Francisen
dc.relation.urihttps://www.tandfonline.com/doi/citedby/10.1080/08982112.2019.1664750
dc.rights© 2018 Informa UK Limited. This is an Accepted Manuscript of an article published by Taylor & Francis in Quality Engineering on 19 December 2019, available online: http://www.tandfonline.com/ 10.1080/08982112.2019.1664750en
dc.subjectBernoulli CUSUMen
dc.subjectCumulative sum schemeen
dc.subjectCurtailed CUSUMen
dc.subjectExponential CUSUMen
dc.subjectProcess monitoringen
dc.subjectStatistical process controlen
dc.titleDetecting a downward shift in a proportion using a geometric CUSUM charten
dc.typeArticle (peer-reviewed)en
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