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

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dc.contributor.author Bourke, Patrick D.
dc.date.accessioned 2020-03-16T14:52:39Z
dc.date.available 2020-03-16T14:52:39Z
dc.date.issued 2019-12-19
dc.identifier.citation Bourke, P. D. (2020) 'Detecting a downward shift in a proportion using a geometric CUSUM chart, Quality Engineering, 32:1, pp. 75-90, doi: 10.1080/08982112.2019.1664750 en
dc.identifier.volume 32 en
dc.identifier.issued 1 en
dc.identifier.startpage 75 en
dc.identifier.endpage 90 en
dc.identifier.issn 0898-2112
dc.identifier.uri http://hdl.handle.net/10468/9765
dc.identifier.doi 10.1080/08982112.2019.1664750 en
dc.description.abstract In 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.format.mimetype application/pdf en
dc.language.iso en en
dc.publisher Taylor & Francis en
dc.relation.uri https://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/ 10.1080/08982112.2019.1664750 en
dc.subject Bernoulli CUSUM en
dc.subject Cumulative sum scheme en
dc.subject Curtailed CUSUM en
dc.subject Exponential CUSUM en
dc.subject Process monitoring en
dc.subject Statistical process control en
dc.title Detecting a downward shift in a proportion using a geometric CUSUM chart en
dc.type Article (peer-reviewed) en
dc.internal.authorcontactother Patrick D. Bourke, Statistics, Mathematical Sciences, University College Cork, Cork, Ireland. +353-21-490-3000 Email: p.bourke@ucc.ie en
dc.internal.availability Full text available en
dc.check.info Access to this article is restricted until 12 months after publication by request of the publisher. en
dc.check.date 2020-12-19
dc.description.version Accepted Version en
dc.description.status Peer reviewed en
dc.identifier.journaltitle Quality Engineering en
dc.internal.IRISemailaddress p.bourke@ucc.ie en
dc.identifier.eissn 1532-4222


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