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Designing Phase I Shewhart X ¯ charts: Extended tables and software
Author(s) -
Yao Y.,
Hilton C.W.,
Chakraborti S.
Publication year - 2017
Publication title -
quality and reliability engineering international
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 62
eISSN - 1099-1638
pISSN - 0748-8017
DOI - 10.1002/qre.2225
Subject(s) - control chart , computer science , software , shewhart individuals control chart , statistics , chart , phase (matter) , statistical process control , constant (computer programming) , process (computing) , extension (predicate logic) , constant false alarm rate , control (management) , reliability engineering , mathematics , data mining , algorithm , engineering , programming language , artificial intelligence , ewma chart , chemistry , organic chemistry
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 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.