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Gage R&R (Ranges Method) - Reproducibility standard deviation

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  Post Number #1  
Old 17th October 2003, 01:25 PM
Martin Kies

 
 
Total Posts: 1
Question Gage R&R (Ranges Method) - Reproducibility standard deviation

I have an XL spreadsheet that someone forwarded me with the following details:

3 Operators
10 samples
3 trials

Operator A average (30 measurements) is 5.481
Operator B average (30 measurements) is 5.471
Operator C average (30 measurements) is 5.507

To get the reproducibility standard deviation, the following is used:

= (5.507 - 5.471) * 0.524

Question: where does the 0.524 come from? Actually, the full formula in the cell is a nested IF statement (if the operator sample averages were only 2 instead of 3, the constant would be 0.709), but I have shortened this for simplicity.

I have checked the usual SPC table of constants (A2, D4, d2, etc), but could not find where this one came from. I even tried some reciprocals of these constants to no avail.

Any help in where these came from would help, along with a table of this constant.

Thanks to anyone in advance who replies.

Martin

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  Post Number #2  
Old 17th October 2003, 01:49 PM
ben sortin

 
 
Total Posts: 59
"Spreadsheet that someone forwarded me" is the root cause of your problem. I wouldn't let Euclid forward me a spreadsheet without the algorithm(s).
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  Post Number #3  
Old 25th October 2003, 04:52 AM
Atul Khandekar's Avatar
Atul Khandekar

 
 
Total Posts: 1,383
Quote:
In Reply to Parent Post by Martin Kies

To get the reproducibility standard deviation, the following is used:

= (5.507 - 5.471) * 0.524

Question: where does the 0.524 come from?
I have checked the usual SPC table of constants (A2, D4, d2, etc), but could not find where this one came from. I even tried some reciprocals of these constants to no avail.

Any help in where these came from would help, along with a table of this constant.
Martin,
First off, Welcome to the Cove!

I would suggest you get hold of the AIAG MSA Manual - third edition, where R&R procedures, formulas and constants are explained. ( http://www.aiag.org )

Appraiser Variation (AV) or reproducibility is calculated by dividing the range of appraiser averages by a constant d2*. K2 is the inverse of d2*. The manual gives the complete table for d2*.

AV = XBar_Diff *K2
K2 = 1 / d2*

For 2 operators: d2*= 1.41421; K2= 0.7071
For 3 operators: d2*= 1.91155; K2= 0.5231

The formula you have given appears incomplete. The reproducibility value obtained as above has to be adjusted to remove the 'contamination' by Equipment Variation (EV), because taking the appraiser averages does not completely isolate AV & EV. The complete formula is:

AV = Sqrt( (XBar_Diff *K2)^2 - (EV^2/nr) ), where
n = No of Samples
r = No of Trials

Hope this helps..

-Atul.
  Post Number #4  
Old 28th October 2003, 04:53 AM
candy_hy

 
 
Total Posts: n/a
Question

Sometimes I've use 1 operator in GR&R, But it's difficut to find these factor for 1 operator, m Samples and n Trials.

Please tell me how to get these factors?

Thank you.
  Post Number #5  
Old 28th October 2003, 06:54 AM
Atul Khandekar's Avatar
Atul Khandekar

 
 
Total Posts: 1,383
Quote:
In Reply to Parent Post by candy_hy

Sometimes I've use 1 operator in GR&R, But it's difficut to find these factor for 1 operator, m Samples and n Trials.

Please tell me how to get these factors?
candy_hy,

Welcome to the Cove Forums.

Reproducibility can be calculated only when you have more than one operator in a GRR study. For one operator, AV=0. So there should be no need to find out the value of K2 factor - its not given in the AIAG manual.

Also see: R&R study with one appraiser

Hope this helps.

- Atul.
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