First problem: In your initial question, you mention %GRR. Is this % Tolerance or % Study Variation?

Second problem: There's a lot of people who make this interpretation of the result:

You are saying your %GRR is 15,66 (we will assume this is % Tol) and that your specification is +/-,20 or 0,40 in total. So.....

you then take 0,1566 * 0,40 and get 0,0626. Which means the tolerance should be reduced to run limits by guard bands of 0,0626 / 2 = 0,0312 per side. So your "run limits" are then 10 +/- 0,17. THIS IS THE WRONG INTERPRETATION OF % Tol.

It IS correct to reduce your run limits due to gage noise, BUT ... what you are after is the gage uncertainty.

From the MSA 3rd Edition p. 61 ...

"U is the term for “expanded uncertainty” of the measurand and measurement result. Expanded uncertainty is the combined standard error (uc), or standard deviation of the combined errors (random and systematic), in the measurement process multiplied by a coverage factor (k) that represents the area of the normal curve for a desired level of confidence. Remember, a normal distribution is often applied as a principle assumption for measurement systems. The ISO/IEC Guide to the Uncertainty in Measurement establishes the coverage factor as sufficient to report uncertainty at 95% of a normal distribution. This is often interpreted as k = 2."

What you do is use an alpha of 5% and calculate your statistical uncertainty. (I've been in arguments where people wanted me to use alpha of 1%, thinking that affects the pass fail rate with some gobbledy gook explanation. 5% is just fine.)

How do you do this? (Because it's not standard Minitab output ....)

Method 1:

Your Gage R&R should have a standard, tabular output. With rows like Repeatability, Total Variation, Reproducability and Total Gage R&R. You are interested in the Total Gage R&R row.

It should also have standardized columns such as: Variance Component, % Contribution, Std Dev, Study Variation. You are interested in the Standard Deviation or SD column.

The intersection is the Standard Deviation of your Total Gage R&R. (This is a k =1, or zscore of 1 from the MSA paragraph above).

Your uncertainty is 2 times this number, which corresponds to k=2. Let's say your standard deviation on Total Gage R&R is 0.00129. Double this to get 0.00258. You may want to round up to 0.003. Your gages uncertainty is then +/- 0.003. That's what you reduce your tolerance by, per side so in your example you would be running to 10 +/- 0,197

Pause here and consider the logic ... why would you use % Tol to determine this? The value of % Tol depends on the tolerance. The tolerance is some arbitrary number on a print that has NOTHING to do with the gage's accuracy. If your NEXT part, had the same nominal radius, but the tolerance was tighter or looser, why would your guard bands change size? Because they would if you use % Tol to figure them. The gage is the gage and it has noise/uncertainty that is not affected by ink on a blueprint.

Method 2: (Less accepted, give comparable results ...)

Back to your standard output table... still looking in our Std Dev Column, you should ALSO have a row called "Total Variation". In Method 1, we were interested in Total Gage R&R which is the noise of the gage (gage itself + operator). In this method, we want Total Variation. This is Total Gage R&R PLUS the noise of the parts. (Total Gage R&R seeks to isolate gage noise from total noise, gage noise is bad, part noise (differences) is good).

So find this Total Variation Standard Deviation, remembering that this is the total noise of the study. Divide this by your Number of Distinct Categories. This is the number of groups you can separate the parts you measured into consistently. THEN divide this by 2 to get it into +/- format. Boom. Also a measure of your uncertainty. Example: If your SD for Total Variation is 0.00446 and your NDC is 4, you have 0.00446 / (2 * 4) = 0.003, so your uncertainty is +/- 0.003 and that's what you guard band to.

Also consider - SD for Total Variation and NDC have NOTHING to do with the tolerance on the print - that's how it should be.

Also also consider - BOTH of these methods DO depend on the differences between your parts. What I mean is ... if your parts in your study are very close together, these numbers won't be as good. This makes sense. Think about trying to determine the accuracy of your gage with ONE part. That doesn't make sense at all, you need to check DIFFERENT parts. If you weigh 180 lbs, you could verify your bathroom scale by repeatedly getting on and off it and seeing it measures 180 lbs. But it would be better to get several people, right? If your parts are VERY close together, they may as well be the same part, and your R&R will consequently suffer. As will your uncertainties. Again - NOTHING to do with what the tolerance is.