Monitoring the process mean when standards are unknown : a classic problem revisited

dc.contributor.authorDiko, Mandla D.
dc.contributor.authorChakraborti, Subhabrata
dc.contributor.authorGraham, Marien Alet
dc.contributor.emailmarien.graham@up.ac.zaen_ZA
dc.date.accessioned2016-09-27T05:05:23Z
dc.date.issued2016-03
dc.description.abstractOne of the most common applications in statistical process monitoring is the use of control charts to monitor a process mean. In practice, this is often done with a Shewhart X chart along with a Shewhart R (or an S) chart. Thus two charts are typically used together, as a scheme, each using the 3-sigma limits. Moreover, the process mean and standard deviation are often unknown and need to be estimated before monitoring can begin. We show that there are three major issues with this monitoring scheme described in most textbooks. The first issue is not accounting for the effects of parameter estimation, which is known to degrade chart performance. The second issue is the implicit assumption that the charting statistics are both normally distributed and, accordingly, using the 3-sigma limits. The third issue is multiple testing, since two charts are used, in this scheme, at the same time. We illustrate the deleterious effects of these issues on the in-control properties of the (X,R) charting scheme and present a method for finding the correct charting constants taking proper account of these issues. Tables of the new charting constants are provided for some commonly used nominal in-control average run-length (ICARL0) values and different sample sizes. This will aid in implementing the (X,R) charting scheme correctly in practice. Examples are given along with a summary and some conclusions.en_ZA
dc.description.departmentStatisticsen_ZA
dc.description.embargo2017-03-31
dc.description.librarianhb2016en_ZA
dc.description.urihttp://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1099-1638en_ZA
dc.identifier.citationDiko, MD, Chakraborti, S & Graham, MA 2016, 'Monitoring the process mean when standards are unknown : a classic problem revisited', Quality and Reliability Engineering International, vol. 32, no. 2, pp. 609-622.en_ZA
dc.identifier.issn0748-8017 (print)
dc.identifier.issn1099-1638 (online)
dc.identifier.other10.1002/qre.1776
dc.identifier.urihttp://hdl.handle.net/2263/57023
dc.language.isoenen_ZA
dc.publisherWileyen_ZA
dc.rights© 2015 John Wiley & Sons, Ltd. This is the pre-peer reviewed version of the following article: Monitoring the process mean when standards are unknown : a classic problem revisited, Quality and Reliability Engineering International, vol. 32, no. 2, pp. 609-622, 2016. doi : 10.1002/qre.1776. The definite version is available at http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1099-1638.en_ZA
dc.subjectFalse alarm rateen_ZA
dc.subjectMonitoring mean and varianceen_ZA
dc.subjectMultiple testingen_ZA
dc.subjectParameter estimationen_ZA
dc.subject3-Sigma limitsen_ZA
dc.subjectShewhart X charten_ZA
dc.subjectShewhart R charten_ZA
dc.titleMonitoring the process mean when standards are unknown : a classic problem revisiteden_ZA
dc.typePostprint Articleen_ZA

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