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

M

#### Martin Kies

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

B

#### ben sortin

"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).

#### Atul Khandekar

##### Quite Involved in Discussions
Martin Kies said:
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.

C

#### 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?

Thank you.

#### Atul Khandekar

##### Quite Involved in Discussions
candy_hy said:
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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