Phase II control charts for monitoring dispersion when parameters are estimated

dc.contributor.authorDiko, M. D.
dc.contributor.authorGoedhart, R.
dc.contributor.authorChakraborti, S.
dc.contributor.authorDoes, R. J. M. M.
dc.contributor.authorEpprecht, E. K.
dc.contributor.otherUniversity of Amsterdam
dc.contributor.otherUniversity of Alabama Tuscaloosa
dc.contributor.otherPontificia Universidade Catolica do Rio de Janeiro
dc.date.accessioned2021-07-28T18:23:27Z
dc.date.available2021-07-28T18:23:27Z
dc.date.issued2017
dc.description.abstractShewhart control charts are among the most popular control charts used to monitor process dispersion. To base these control charts on the assumption of known in-control process parameters is often unrealistic. In practice, estimates are used to construct the control charts and this has substantial consequences for the in-control and out-of-control chart performance. The effects are especially severe when the number of Phase I subgroups used to estimate the unknown process dispersion is small. Typically, recommendations are to use around 30 subgroups of size 5 each.We derive and tabulate new corrected charting constants that should be used to construct the estimated probability limits of the Phase II Shewhart dispersion (e.g., range and standard deviation) control charts for a given number of Phase I subgroups, subgroup size and nominal in-control average run-length (ICARL). These control limits account for the effects of parameter estimation. Two approaches are used to find the new charting constants, a numerical and an analytic approach, which give similar results. It is seen that the corrected probability limits based charts achieve the desired nominal ICARL performance, but the out-of-control average run-length performance deteriorate when both the size of the shift and the number of Phase I subgroups are small. This is the price one must pay while accounting for the effects of parameter estimation so that the in-control performance is as advertised. An illustration using real-life data is provided along with a summary and recommendations.en_US
dc.format.mimetypeapplication/pdf
dc.identifier.citationDiko, M., Goedhart, R., Chakraborti, S., Does, R., Epprecht, E. (2017): Phase II Control Charts for Monitoring Dispersion when Parameters are Estimated. Quality Engineering. 29(4).
dc.identifier.doi10.1080/08982112.2017.1288915
dc.identifier.orcidhttps://orcid.org/0000-0003-3452-6441
dc.identifier.orcidhttps://orcid.org/0000-0001-9966-0284
dc.identifier.urihttp://ir.ua.edu/handle/123456789/8005
dc.languageEnglish
dc.language.isoen_US
dc.publisherTaylor & Francis
dc.rights.urihttps://creativecommons.org/licenses/by/4.0/
dc.subjectaverage run length (ARL)
dc.subjectcontrol charts
dc.subjectcontrol limits
dc.subjectPhase II analysis
dc.subjectprocess dispersion
dc.subjectstatistical process control
dc.subjectSHEWHART X
dc.subjectRUN-LENGTH
dc.subjectEngineering, Industrial
dc.subjectStatistics & Probability
dc.subjectEngineering
dc.subjectMathematics
dc.titlePhase II control charts for monitoring dispersion when parameters are estimateden_US
dc.typetext
dc.typeArticle
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