CUSUM design for detection of event-rate increases for a Poisson process

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dc.contributor.authorBourke, Patrick D.
dc.date.accessioned2022-11-23T15:46:37Z
dc.date.available2022-11-23T15:46:37Z
dc.date.issued2021-12-03
dc.description.abstractIn quantifying the performance of a CUSUM chart for detecting upward shifts in event rate, it has been recommended that steady-state evaluation of performance measures such as ARL be used. In this article, the methodology for making such evaluations using the Markov-chain approach is presented, for the case of an exponential CUSUM. This is much more efficient than the alternative of simulation, which is still in use. It is also shown that if one is using steady-state ARL as a measure of detection performance, one can find better choices for the CUSUM parameter k than that provided by the SPRT-based formula. Two types of shift in event rate are considered, and corresponding tables of recommended choices of CUSUM parameters (k, h) are presented for ten levels of in-control ARL, and for nine sizes of shift. These tables can assist quality engineers in the design of CUSUMs for monitoring inter-event times in steady-state operation. It is also shown that these exponential CUSUM tables may be used to find values for the parameters of a geometric CUSUM or a Bernoulli CUSUM chart for monitoring a proportion, provided the in-control value of the proportion is no more than approximately 0.5%en
dc.description.statusPeer revieweden
dc.description.versionAccepted Versionen
dc.format.mimetypeapplication/pdfen
dc.identifier.citationBourke, P. D. (2021) 'CUSUM design for detection of event-rate increases for a Poisson process', Quality Engineering, 34(1), pp. 36-51. doi: 10.1080/08982112.2021.1978489en
dc.identifier.doi10.1080/08982112.2021.1978489en
dc.identifier.eissn1532-4222
dc.identifier.endpage51en
dc.identifier.issn0898-2112
dc.identifier.issued1en
dc.identifier.journaltitleQuality Engineeringen
dc.identifier.startpage36en
dc.identifier.urihttps://hdl.handle.net/10468/13876
dc.identifier.volume34en
dc.language.isoenen
dc.publisherTaylor & Francisen
dc.rights© 2021, Taylor & Francis Group. This is an Accepted Manuscript of an item published by Taylor & Francis in Quality Engineering on 3 December 2021, available online: https://doi.org/10.1080/08982112.2021.1978489en
dc.subjectStatistical process controlen
dc.subjectProcess monitoringen
dc.subjectCumulative sum charten
dc.subjectExponential CUSUMen
dc.subjectGeometric CUSUMen
dc.subjectSteady-state ARLen
dc.subjectMarkov chainen
dc.titleCUSUM design for detection of event-rate increases for a Poisson processen
dc.typeArticle (peer-reviewed)en
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