# Derivation of Gage R&R Formula and Calculations

M

#### marklee

derivation of gage R&R calculations

Does anyone have a book or journal reference that shows how the formulas for gage R&R are developed? Specifically, where do the tables and other constants come from that are used in the Range and Average method of gage R&R. Anyone have worked examples comparing ANOVA method with Range and Average method?
Thanks,
Mark

D

#### Don Winton

If you go to:

--> Obsolete Link Removed 2003-09-24 by Marc <--

Regards,

Don

M

#### marklee

Don,
Thanks for pointing me to your good tutorial. I have some more questions and comments after reading this through:
1. You refer to "Duncans's text", and it looks like it is described in a footnote which I can't see on my screen (pdf file bug?). Can you give me the name of this text by Duncan that you cite?
2. Repeatability is defined by 5.15*sigma_ev. I have assumed that gage R&R was using 6 sigma (99.7% compared to 99.0%)which would use 6.00*sigma_ev instead of 5.15. Thanks for clearing this up.
3. I can see that standand deviation and range would be related by a constant, but I still don't see where they come from. What are behind the estimations of the "d2" parameter in the equation sigma_ev = R_bar_bar / d2? Is there a For/Next loop that generates these?
Thanks,
Mark

#### Marc

##### Fully vaccinated are you?
Don Winton said:
If you go to:

--> Obsolete Link Removed 2003-09-24 by Marc <--

If anyone has a copy of this document, please let me know or attach to a post.

Thanks!

#### Wes Bucey

##### Prophet of Profit
For "stuff" about Gage R & R (MSA), a good start place is

Some interesting free tools and stuff at
https://www.issixsigma.com
I think it's worthwhile to check out.

S

#### Sam

Marc said:
If anyone has a copy of this document, please let me know or attach to a post.

Thanks!

Marc,
This may be similar to what you are looking for. It was downloaded from this site in 2000.

#### Attachments

• Re & Rep.pdf
108 KB · Views: 825
D

#### Darius

I have a file, may be to elemental, but it take other aproach to the explanation of the calculations.

And also the Anova aproach

I hope this may help to clarify R&R

#### Attachments

• MSA2.pdf
651.4 KB · Views: 1,059
• msa_rr.pdf
60.2 KB · Views: 855
A

#### Atul Khandekar

Sam said:
Marc,
This may be similar to what you are looking for. It was downloaded from this site in 2000.

Sam, Thanks a lot for that file. (.. and how I miss d'Wizard's lair!)

For derivation of Repeatability & Reproducibility formulae and the K factors, I was about to suggest Larry Barrentine's book "Concepts for R&R studies" ( referenced in the file above - available from ASQ for \$25. I just received my copy about 10 days ago.)

For more information on the d2* factors, try the attached PDF document from AIAG.

Crossed and Nested ANOVA calculations can be found in any standard statistical text book on DOE. The one I used was Design of Experiments by Douglas Montgomery.

#### Attachments

• StatExpose_d2.pdf
39.4 KB · Views: 643