# Gage R&R derivation with respect to ndc - Lessons Learned

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#### Geese

For the record, you might wanna double check my calculations, but I think these are right.

I wanted to derive a relation between Rp (Average Part Variation) and R (Average Range of Appraisers) with respect to an ndc of 5 which is the minimum requiremnt.

I was having trouble with some of our GRR's because the measurements were so close between parts and on the same part. Seems odd that you wouldn't meet criteria for ndc when everyones measurements are 1/1000th off from each other across the board and between parts. Oh well, what do I know about quality when statistics must be satisfied

So, I used the GRR form calculations below to derive this final result and found that Xdiff (difference between the average measurements of the appraisers) also was needed in the derivation. You might say I have too much time on my hands, but it was bugging me that we had such close measurements with little variation and yet we weren't meeting the ndc criteria of 5 or more categories.

This is for a run of 10 parts with 3 appraisers when determining K constants.
The form used is on page 114 of the MSA 3rd edition manual.

Rp > (29.6R^2 + 34.8Xdiff^2) ^ 1/2

I got this by starting with the ndc calculation, putting 5 in its place and adding a greater than sign.

Having derived it, I then needed to interpret it. As best as I can figure, this says that for a good ndc number, your sample of parts needs to be very diverse in size while your appraisers measurements are very precise between each appraiser and their own measurements of the same part.

This sounds like a great concept, but its almost comical that if your part variation is small and your appraisers measurements are only 1/1000th off on a part with a 1/100th tolerance, that your ndc would fall below 5. But this seems to be the case.

Lesson learned: Make sure you pick a batch of parts that have some good variation on them (still falling within tolerance). Otherwise you wont be able to show how good your measurement techniques are between appraisers and get that high ndc.

Please refute me if I'm wrong. I know this analysis is somewhat hard to follow, but if you take the GRR data form and focus on Rp, R, and Xdiff, you'll see where they come from and how they fit into the equations for analysis with respect to ndc.

#### Marc

##### Fully vaccinated are you?
Good points! Thanks for the Lesson Learned!

G

#### Geese

I think I missed a square somewhere in there, but the basic relationship is there. If one thing goes up, the other will go down and so on so you can get a grasp of how the variables affect each other.

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