Designing Phase I Shewhart
X¯charts: Extended tables and software |
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| Authors: | Y. Yao C.W. Hilton S. Chakraborti |
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| Affiliation: | Department of Information Systems, Statistics, and Management Science, The University of Alabama, Tuscaloosa, AL, USA |
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| Abstract: | 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 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. |
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| Keywords: | multivariate t distribution, R program normal distribution parameter estimation Phase II statistical process control false alarm probability (FAP) |
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