# Gage R&R Acceptable (10-30%), deduct Total Variation from Tolerance

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#### bibo_auto

Dear all,

I recently submitted an R&R for the following dimension: Radius 10+/-0,20.
The result was: %GRR = 15,66.
so, folowing the company rules, based on AIAGs manual (automotive product), we considered this acceptable.

The customer replied stating that also for them the result is acceptable, but we'd have to measure the dimension considering the "nominal tolerance - Total Variation".
to sum up:
- Dimension Nominal Vaue and Nominal Tolerance: 10 +/- 0,20;
- Total Variation is 0,05 (not real value).

So, the questions are:
- What the customer is suggestiong is correct? I think yes, but why? where can I find this rule?
- If it is not a rule, is it a "best practice" commonly agreed?
- Considering the values above, what is the actual dimension/tolerance I should use? 10 +/- 0,10?

Thanks a lot!

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#### rbriggs5145

I believe the tolerance you should use is the +/-0.2- 15.66% of 0.2. This calculates into +/-0.168. I do not remember ever seeing any rule about having to measure nominal tolerance - total variation. It normally is nominal tolerance - GR&R %.

#### UncleFester

##### Involved In Discussions
Using the total variation helps you compare the results in the variation of the parts you used.

Sorry, I have more questions rather than answers:
How did you select the parts for the study? Were they from a process with a high CpK or low Cpk? Were the parts using the entire tolerance range or did you have to doctor some of the parts to ensure that your measurement process could detect them?
What number of distinct categories did your study give you?
Importantly, what gauging method were you using to measure radii?
If you're happy with the %GRR, balancing cost and application against the possibility of missing rejects then that's the discussion needed with the customer.
As your range falls within 10-30%, then the measurement system may be acceptable - but to who?

Why are you asking if you can change the tolerance of the part? Are you the design authority, meaning you are free to change the tolerance if your manufacturing process can maintain a high enough CpK? If the required tolerance is 10± 0.2 then that's the tolerance you should aim for.

#### Miner

##### Forum Moderator
This practice is called guardbanding, but is typically used only for critical CTQs, not for everything.

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#### ncwalker

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.

#### Bev D

##### Heretical Statistician
Super Moderator
"find this Total Variation Standard Deviation, remembering that this is the total noise of the study. Divide this by your Number of Distinct Categories" yes! this is the most effective path to guardbanding.

Do NOT EVER use %R&R to Tolerance. Not only is the tolerance not related to the system noise the formula for that percentage is not mathematically correct. Donald Wheeler has a couple of great articles on this topic. I strongly recommend them. There are several more than I listed... He can repeat himself from article to article but that's not always a bad thing as lately too many people only look at recent history. Research has become a lost art unfortunately.... you might also find the attached article useful to your understanding.

Where do Manufacturing Specifications Come From
Is the Part In Spec?
How Measurement Error Affects the Four Ways We Use Data

#### Attachments

• The Statistical Cracks in the Foundation of the Popular Gauge R and R.pdf
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#### John Predmore

Trusted Information Resource
Bibo_auto is asking if his customer’s instructions are correct and wants to understand the rationale. I envision measurement variation as a cloud or fog which diminishes our ability to see clearly the underlying reality. Variation always works against us and our ability to hit the target.

The Red X people have a tool called Tolerance Parallelogram, used to generate meaningful tolerances after process variation is understood. In this case, measurement is a process which generates data, given uncertainty or imprecision of measurement, which is the source of variation.

As is characteristic of most of Dorian Shainin’s original methods, variation in the Tolerance Parallelogram is depicted graphically. The separation of two lines, parallel and equidistant from the regression line Y=f(X) on axes of X=true dimension vs Y=output value, represents variation (in this example, measurement uncertainty).

The recommended X tolerance is derived starting from the desired limits on the output side of the regression (Y-axis). A horizontal line is drawn from the USL on the Y-value to the TOP line, and from that intersection, a vertical line is drawn to the X-axis, which determines the upper X-value limit. Similarly, a horizontal line from the lower Y-limit to the LOWER line, dropped to the X-axis determines the lower X-value limit. The graphic illustrates how variation always works against you in quality assurance (don't try to reverse engineer the particular X,Y values, I found a stock graphic unrelated to the measurement scenario).

The width of the sloped lines (which represents uncertainty or imprecision) will reduce the width of the X-value tolerance, and also a steeper slope of the regression line (which represents the relative influence of X on Y) will reduce the width of the X tolerance. If the slope is too steep, the lower X-limit falls to the right of the upper X-limit, an impossibility which means the process is incapable of hitting the target with any assurance.

Graphic source: (broken link removed) page 9

In this manner, as long as the process is stable and predictable, the diminished tolerance of X will produce a functional response within limits. Mathematically, variation adds as the square of standard deviation, and with a multitude of factors ANOVA is a better analysis tool, but this graphical method is a simple illustration of the impact of variation.

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#### ncwalker

Can someone explain why we keep bringing the process into this?

bibo_auto is asking how to evaluate a gage. That has nothing to do with the process at all, why would we want to introduce process noise in the discussion of gage performance?

I'm not saying we don't consider process noise. That's definitely step 2 (step 1 being, understand how well you control device works). But I'm not seeing where process should be involved in the discussion at all. I could be wrong - which is why I am asking ....

#### Bev D

##### Heretical Statistician
Super Moderator
This "Tolerance parrelllogram" (this phrase is service marked to Shainin LLC, it is a simple regression plot) is a great way to set input tolerances given the process variation which includes measurement error of course. This approach does provide a from of guardbanding that protects against measurement error. It addresses what your input tolerances must be...it doesn't address the effect of measurement error when inspecting to the output tolerance however. TheShainin approach ("isoplot" is also serviced mark to Shainin) teaches exactly what Wheeler teaches (Youden plot, intraclass correlation etc.) to understand measurement error and the relative usefullness of a measurement.

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#### bibo_auto

Thank you all!
I think I got the hang of it, we'll propose the
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.

it is actually what the customer asked but with no real explanation.

So, just one last question, is there any literature on the topic?
So that if another customer asks I can mention the source.

Thanks a lot again!