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Why multiply the median by 3.14??
Message posted by Marie on March 6, 2000 at 12:00 AM (ET)
In a book by Brian Joiner called "Fourth Generation Management" he shows how to calculate control limits on process charts using a formula that multiplies the median of the data by 3.14. I don't get it - why does this work? Or does it? He is a Deming disciple and seems to know what he is talking about! Help! Thanks!
READERS RESPOND:
(In chronological order. Most recent at the bottom.)
Re: Why multiply the median by 3.14??
Message posted by Vern Myers on March 6, 2000 at 12:00 AM (ET)
I haven't read Joiner's book, but I would be very skeptical of a control limit calculation based solely on a measurement of central tendency times a constant, with no regard to measurement of dispersion. I have read Deming extensively, and find that Deming's approach is very faithful to that of Walter Shewhart's, i.e., control limits at +/- 3 standard deviations.
Re: Why multiply the median by 3.14??
Message posted by Phil Rosenkrantz on March 7, 2000 at 12:00 AM (ET)
Joiner is not messing with the traditional Shewhart Control Charts. If you look on page 267 of Joiner's book he explains the formula in more detail. He is referring specifically to "individuals" charts here. Multiplying the median R by 3.14 gives more appropriate limits than +/- 3 sigma control limits. This applies to individiuals charts only. He gives the traditional x-bar & R-chart formulas just below on the same page.With individuals charts you don't have the central limit theorem working for you to make the data normal (when the process is stable). Joiner uses tighter limits on individuals charts so you don't "mask" assignable causes.
He doesn't explain "how" he got 3.14 or what the Type I error is, but when dealing with "order statistics" the mathematical statistics gets quite advanced.
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