On the design of control charts with guaranteed conditional performance under estimated parameters

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dc.contributor.authorDoes, Ronald J. M. M.en
dc.contributor.authorGoedhart, Roben
dc.contributor.authorWoodall, William H.en
dc.contributor.departmentStatisticsen
dc.date.accessioned2021-01-05T14:13:20Zen
dc.date.available2021-01-05T14:13:20Zen
dc.date.issued2020-04-28en
dc.description.abstractWhen designing control charts the in-control parameters are unknown, so the control limits have to be estimated using a Phase I reference sample. To evaluate the in-control performance of control charts in the monitoring phase (Phase II), two performance indicators are most commonly used: the average run length (ARL) or the false alarm rate (FAR). However, these quantities will vary across practitioners due to the use of different reference samples in Phase I. This variation is small only for very large amounts of Phase I data, even when the actual distribution of the data is known. In practice, we do not know the distribution of the data, and it has to be estimated, along with its parameters. This means that we have to deal with model error when parametric models are used and stochastic error because we have to estimate the parameters. With these issues in mind, choices have to be made in order to control the performance of control charts. In this paper, we discuss some results with respect to the in-control guaranteed conditional performance of control charts with estimated parameters for parametric and nonparametric methods. We focus on Shewhart, exponentially weighted moving average (EWMA), and cumulative sum (CUSUM) control charts for monitoring the mean when parameters are estimated.en
dc.format.mimetypeapplication/pdfen
dc.identifier.doihttps://doi.org/10.1002/qre.2658en
dc.identifier.eissn1099-1638en
dc.identifier.issn0748-8017en
dc.identifier.issue8en
dc.identifier.urihttp://hdl.handle.net/10919/101737en
dc.identifier.volume36en
dc.language.isoenen
dc.rightsCreative Commons Attribution 4.0 Internationalen
dc.rights.urihttp://creativecommons.org/licenses/by/4.0/en
dc.subjectcumulative sumen
dc.subjectCUSUM control charten
dc.subjectEWMA control charten
dc.subjectexponentially weighted moving averageen
dc.subjectnonparametricen
dc.subjectparameter estimationen
dc.subjectPhase Ien
dc.subjectPhase IIen
dc.subjectShewhart control charten
dc.titleOn the design of control charts with guaranteed conditional performance under estimated parametersen
dc.title.serialQuality and Reliability Engineering Internationalen
dc.typeArticle - Refereeden
dc.type.dcmitypeTexten
dc.type.dcmitypeStillImageen
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