Designing Phase I Shewhart X¯charts: Extended tables and software

Control charts play an important role in Phase I studies, which are conducted to establish process control and generate reference data for parameter estimation and calculation of prospective (Phase II) control limits. Researchers have tabulated the necessary charting constants for the normal theory–...

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Bibliographic Details
Published inQuality and reliability engineering international Vol. 33; no. 8; pp. 2667 - 2672
Main Authors Yao, Y., Hilton, C.W., Chakraborti, S.
Format Journal Article
LanguageEnglish
Published Bognor Regis Wiley Subscription Services, Inc 01.12.2017
Subjects
Alarm systems
Control charts
Control limits
false alarm probability (FAP)
False alarms
Mathematical analysis
multivariate t distribution, R program
normal distribution
Parameter estimation
Phase II
Process controls
statistical process control
Subgroups
Tables
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Summary:Control charts play an important role in Phase I studies, which are conducted to establish process control and generate reference data for parameter estimation and calculation of prospective (Phase II) control limits. Researchers have tabulated the necessary charting constants for the normal theory–based Phase I Shewhart X¯ chart for the process mean to achieve a desired nominal false alarm probability given the number of Phase I subgroups, m, up to 15. However, in practice, when parameters are estimated, the currently recommended number of Phase I subgroups is much larger than covered by their tables. Recognizing the need and taking advantage of some recently available software and computing resources, an extension to these tables is provided for m = 3(1)10 , 15(5)30 , 50(25)300 and n = 3 , 5 , 7 , 10. In addition to the tables, an R program is provided to calculate the charting constant, on demand, for user‐given values of nominal false alarm probability, m, and n. An appendix shows the details of how the program should be used.
ISSN:0748-8017
1099-1638
DOI:10.1002/qre.2225