Origins of 5.15 as the 'Magic Number' in Gage R&R Calculations

I

ivan99

#1
Origins of 5.15 in Gage R&R Calculations

Can someone please remind me where I can find a good text explanation why 5.15 is the "magical" number to multiply the sigma with to account for 99% of the data??? I need to "convince" someone with no statistical knowledge that this is the "right" number!! This person is calculating stuff from a normal distribution curve and is confused!!! Please enlighten us. Thank u all. :)
 
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A

Atul Khandekar

#2
I'm not aware of any specific reason for using 99% spread (5.15 multiplying factor). I believe it's the legacy from what is known as the "General Motors Long Form". The new MSA manual (3rd edition) gives you the freedom to use 99% (6*Sigma). On page vi, the manual says:

Historically, by convention, a 99% spread has been used to represent the "full" spread of measurement error,....
.... Awareness of which multiplying factor is used is critical to the integrity of the equations and resultant calculations. This is especially important if a comparison is to be made between measurement system variability and the tolerance."


According to Larry Barrentine:.. This approach commonly defines R&R in terms of an interval that contains 99% (5.15 Sigma) of the theoretical distribution. Some use a 99.7% (6 Sigma) interval; others use a 95% (4 Sigma) interval for defining intervals of R&R. To avoid confusion, clearly note which interval is used..

Finally, here's some good advice:
http://elsmar.com/Forums/showthread.php?p=63634#post63634
Rob Nix said:
Pick a measure of dispersion and use it consistently.
 
D

Dave Strouse

#3
It's bilateral around the mean

Ivan -

Your friend probably has a cumulative table. so it's harder to pick out.

The assumption is that the spread is around the mean and symmetric.
So we have half on each side or 2.575 sigma.

Looking up 2.575 in a one sided table gives 0.005 85 % to the right of 2.57 sigma (in the tail area) and 0.00494 to the right of 2.58 sigma. Simple interpolation (curve is NOT linear , but over this small range, the error is miniscule) gives 0.0050125 as the % area to the right of 2.575 sigma. Now, the curve IS symmetric so we do the same thing for -2.575 sigma (substuituting "to the left" for "to the right" above) and get the same numerical value to the left, i.e. 0.0050125. Adding these together, we see that 0.010025 or 1.0025% is outside of -2.575 and positive 2.575 sigma or 98.9975 % between. That is "close enough for government work"! :D
 
D

dfirka

#4
I would also agree that 5.15 is the spread of a 99% confidence interval for the measurements of the same mensurand, assuming the frequency distribution is gaussian.

What I cannot understand is the explanation of the paper "A review of methods for Measurement System Analysis" (Burdick, Borror and Montgomery, Journal of Quality Technology, Vol.35 No4, october 03). They say at page 343 :

"The value 5.15 corresponds to the limiting value of the number of standard deviations between bounds of a 95% tolerance interval that contains at least 99% of a normal population"

I dont get where the 95% tolerance interval is coming from.

Any ideas? comments?
 

Courier

another day closer
#5
5.15

The 5.15 has now been update to 6.0. The spread of sigma is 3, but most dont find they have a full +/_ 1.5. Some places are even looking to reduce this to +/_ 1. Its Used in Z tables, IF you look up 6 sigma in a Z chart for PPM you find its not 3.4ppm. The 3.4 comes from 4.5 Sigma. So when they say it has a 6 sigma process its is really looking up 4.5 standard deveations for the ppm due to using the standard of +/_ 1.5 sigma drift for a natural process. so taking 6 sigma - 1.5 for drift gives 4.5, looking this up gives 3.4 ppm defects so the 6 sigma process is 3.4 ppm. The way i understand it.
 
Last edited:

The Taz!

Quite Involved in Discussions
#6
As a statastician friend of mine (Developer of ANOVA method) once explained that to me about 10 years ago, you can be "sloppy" on one side of the equation or the other. . . 5.15s = 99%. . . 6s = 99.73%

Simple as that. . .
 
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