Gage R&R (Repeatability and Reproducability) - Tolerance vs. Variation


Fully vaccinated are you?
Posted for Teguh Sujatno:

Subject: MSA and Calibration
Date: Thu, 21 Jan 1999 22:37:43 +0000

As you can see, in the MSA manual issued by the Big Three, calculation of gage R&R uses total variation instead of tolerance. Currently I have a problem in my client ( I am a consultant), since its gage R&R in several devices is more than 30%. Howeve, when I read a bool with the title "Concept for R&R studies" by Larry B Barrentine (In the book, he always mentioned the Big Three requirements as well), the calculation of gage R& R uses tolerance. And this makes more sense to me. Any body could make comments??.

Teguh (Mr)


We just passed our QS9000 audit yesterday. The difference between variation results and tolerance results are as follow;
1) variation: your process must vary enough to show up with your measuring equipment. It is not always possible to get equipment that will measure your variation if your process is extremly stable. Thus;
2) tolerance: If your process repeats and is very stable the the only way to show good results is with the tolerance version.

Every auditor may not agree with this, but ours was extremly pleased with my explanation. I hope this answers your question.


Roger Eastin

This explanation sounds interesting. So, if your process stability is so good that your measuring device can't measure it, you look at R&R with respect to the tolerance? And if your device is able to measure process variation, you can stop with that? If you can't measure process variation, how do you know when you've improved your process (you can't measure it)? Or does this assume that the Cpk of the process is very good, so process improvement for this process is not a priority? Or does this assume that you measure process improvement against the tolerance? I'm not sure that I completely follow your logic. Maybe you could explain your rules a little more...

Don Winton

As that I have neither the MSA manual or the book mentioned in my library, perhaps I am completely off the mark here, so if I am, please, someone let me know.

As you can see, in the MSA manual issued by the Big Three, calculation of gage R&R uses total variation instead of tolerance.

The R&R studies I have done include variation as:

SIGMA(ev) = Equipment Variation (Repeatability)
SIGMA(ov) = Operator Variation (Reproducibility)
SIGMA(r&r) = Total Variation (Repeatability & Reproducibility)

This is the variation within the study itself. From that, it should be determined how this variation affects measurement uncertainty, usually by Percent Tolerance Consumed, as follows:

Percent Tolerance Consumed by Repeatability (PTCR)
Percent Tolerance Consumed by Measurements (PTCM)
Percent Tolerance Consumed by inspection Capability (PTCC)

The criteria for PTCC is normally:

< 10% Acceptable
> 10% and < 25 % Marginal
> 25% Not Acceptable

Of course, the above is from using the range method. The ANOVA method is a bit more difficult. Somewhere, I have a paper I did in the past that explains these concepts in more detail. I will try to find, dust off and forward. Marc’s MSA presentation in the pdf zone also does a good job of presenting this information.



Sorry it took so long to get back to you. Our study is preformed using the AIAG method. We then have software that we plug the numbers into. The software we have is a replica of the AIAG methods. In the software there is a switch to compare results from both the variation and tolerance. The MSA manual also states that you can choose either method(chapterII-sec4pg.60). All I am stating is that depending on your process you may never get a good R&R from the variation method in this case compare it to the tolerance method. You must look at your part tolerance, measurment equipment and process. Determine if your equipment will detect enough variation or you will have to use the tolerance method. Example ; you are cutting a bore, your tol. is +/-.0005 and you measure with a bore gauge that measures to .0001. If your process runs at +/-.0001 you will not get an acceptable R&R from the variation method. You will however, providing you have repeatability get good results using the tol. method. We have checked this with our auditors and they agree. I hope this helps you understand my point.



The software package we use is from The Crosby Co. We run a calibration program called Gauge Boss and MSA called Magic Windows MSA. The MSA program features results from every chart referenced in the MSA manual. You can find them at

Roger Eastin

Yeah, Scott, your explanation helps. Obviously, your Cp is very, very good, so measuring process improvement is not a priority. I don't know your application beyond your description of measuring the bore of hole. I guess the only other question I have is about gauge resolution. Normally, the expectation is that the gauge resolution (its scaling) is 10% of either (the smaller of two)the process variation or the tolerance (rule 4, page 5 of the MSA manual). In your case, this sounds impractical. However, there are statistical methods that limit the impact of this resolution rule ("of thumb"). But with your Cp being what it is (as long as the resolution factor doesn't inflate it too much - it can do that), I doubt, for you, it is much of worry. It may be something that someone else, who has a Cp not as good as yours, needs to be careful of. Anyway, thanks for the explanation!


As posted in previous messages, the MSA manual does list the tolerance method as an acceptable method (pg. 60). However they also state (pg. 15) "The long-standing tradition of reporting measurement error only as a percent of tolerance spread is inadequate for the challenges of the market place of the future in which emphasis will be upon continual process improvement.”

I have found that most people are not familiar with the tolerance method. And if that is the preferred method, be prepared to argue and justify your approach.

Keep in mind rule 4 (pg. 39) when doing a R&R. “The sample parts must be selected from the process and represent its entire operating range.” In situations where my CP has been very tight, I have actually altered the process slightly to produce product at both ends of the spec to qualify the measurement system. As far as I can see it’s legal, the result is usually within a couple percent of the tolerance method and no argument or justification for the method selected.

Let me know what you think. I am still a young buck in the world of quality with a lot to learn.
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