# Question-Barrentine book: Concepts for GR&R Studies

K

#### KMAAA

I'm somewhat new to GR&R studies though the statisitcs involved are very familiar.

Barrentine suggests in his book "Concepts for Gage R&R Studies" that doing the GRR & subsequently the Measurement Capability Index vs the process variation rather than the product tolerance(specs) is a better approach. Seems like a reasonable approach to me. However, there is something in his "sample procedure" on page 7 that doesn't make sense.

For those that don't happen to have a copy of the book in front of them:

>(In a sample R&R study calculation) He states his "Process Sigma" as = 50

>In the sample R&R study calculation he determines a sigma(R&R) of 11.4.

>Next he determines his Measurement Capability Index(MCI) as the sigma(R&R)/Process Sigma or [ 11.4/50 ] * 100 = 22.8%

This is where it doesn't make sense:

>If one were to use the traditional GRR approach of determining the MCI vs the tolerance(specs) then the MCI above would be MCI = [ 11.4/ (USL - LSL) ] * 100

>If one were to use the newer GRR approach of using the process variation then, it seems to me, that one would use an MCI calculation of {[ 11.4/ (UCL-LCL) ] * 100} not the "Process Sigma" he's stated as 50 or MCI = [ 11.4/50 ] * 100.

>If you've transitioned from the older traditional [GRR vs the tolerance] to the [GRR vs the Process Sigma(as Barrentine states)] NOT [GRR vs UCL-LCL] then I would think a successful GRR result would become MUCH more difficult & have less meaning in the long run.

What am I missing here? Is Barrentine's "Process Sigma" of 50 actually (6*sigma)?

#### Atul Khandekar

##### Quite Involved in Discussions
KMAAA said:
This is where it doesn't make sense:

>If one were to use the traditional GRR approach of determining the MCI vs the tolerance(specs) then the MCI above would be MCI = [ 11.4/ (USL - LSL) ] * 100

>If one were to use the newer GRR approach of using the process variation then, it seems to me, that one would use an MCI calculation of {[ 11.4/ (UCL-LCL) ] * 100} not the "Process Sigma" he's stated as 50 or MCI = [ 11.4/50 ] * 100.

>If you've transitioned from the older traditional [GRR vs the tolerance] to the [GRR vs the Process Sigma(as Barrentine states)] NOT [GRR vs UCL-LCL] then I would think a successful GRR result would become MUCH more difficult & have less meaning in the long run.

What am I missing here? Is Barrentine's "Process Sigma" of 50 actually (6*sigma)?
KMAAA,

Welcome to the Cove Forums.

Measurement Capability Index MCI_1 based on Process Variation is defined as:
MCI_1 = 100 (Sigma_GRR/Sigma_process)

The other index, based on tolerance is:
MCI_2=100(5.15 * Sigma_GRR/(USL-LSL) )
On place of 5.15 you can also use 6 to cover 99.73% spread).

Barrentine's calculations:
- K factor used are from MSA edition 2, ie. they are already multiplied by 5.15.
- To calculate GRR variation, he divides by 5.15 , ie. resulting value is 1 Sigma_GRR =11.4
- So MCI_1 is calculated using 1 Sigma values for GRR and Process Variation.
The value of 50 is 1*Sigma value.

If we were to use the 'traditional' approach,
MCI_2 = [ 5.15* 11.4/ (USL - LSL) ] * 100

Hope this helps.

- Atul.

K

#### KMAAA

aah..

...And that was exactly what I was missing. Your remarks clear everything up...the world has regained order.

Thanks for having this forum available. I just became aware of it as I was searching for the answer to my question(confusion). I'll try to add as much as I ask...if possible.

thanks, & take care,
Kevin

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