# Improve final GR&R value by taking average of more measurements?

G

#### garbagex

Hi All,

Someone mentioned to me before that if a gage has already been iteratively improved to the point that the Total Gage R&R is still not within acceptable 30% range, the gage can be 'improved' by taking more readings.

Eg Gage R&R is 50%, if you take average of 3 readings during actual measurement the Gage R&R drops to 50/ sqrt(3) = 29%

I have searched the web and forums but could not find any relevant supporting info. Does anyone know if the above is true, what is the name of the 'method' and where I can find more literature on this topic?

#### Miner

##### Forum Moderator
What you are referring to is the relationship between the variation of averages to the variation of individual values.

The formula is StDev(averages) = StDev(individuals) / SQRT.

Therefore, if you take the average of 4 measurements, you will reduce the measurement variation by half.

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#### Ninja

##### Looking for Reality
Trusted Information Resource
Note that taking an average of readings may help you to pass GRR, but consider the main purpose as well...meeting your customer's needs/requirements.

Passing GRR is not the point, determining if your data is good enough so you can tell "good" from "bad" is the point.

If you average your way into passing GRR, your future use of the gage should also use this averaging method as well since that is the test method you are "proving in".

...and consider strongly what your customer's outlook would be if that is what they found you doing. Sometimes it is mutually agreeable. Sometimes you lose the customer. Go in with your eyes open and keep meeting the customer's needs as the purpose, not a number less than 10 on a piece of paper in a file somewhere.

#### Miner

##### Forum Moderator
If you average your way into passing GRR, your future use of the gage should also use this averaging method as well since that is the test method you are "proving in".
Ninja is 100% on track here. If you use this approach to pass the MSA, you must continue using it. If it is a short term need such as performing a statistical study (which I have done myself) thats one thing, but to do it day after day is usually another unless it is infrequently done.

G

#### garbagex

Miner: I was searching for some complicated theorems, turns out it was just simple stats. Thanks!

Ninja: I absolutely agree with your observations. In fact I made it clear to persons conducting the gage study that this is a last resort since the gage itself has not been really improved. They are to perform iterative Xbar-R/operator/interactions/etc analysis and improvements first, and even consider alternative gages before going down this route.

And yes as a tradeoff the multiple n measurements will become default for the tool as such, with the process times increased n times as well. If this is acceptable, then by all means proceed.

Thanks again for chipping in!

#### Bev D

##### Heretical Statistician
Super Moderator
I woudl also add the caveat that if your gage error is actually due to TRUE product error (such as within piece or within lot for destruct tests) you could be fooling yourself and harming the Customer.

I've told the story here many times of an early project I was on where non-conforming product escaped our factory that posed a serious public safety issue and was costing the company millions of dollars. It turns out that a CMM programmer blindly took a poor gage R&R result to be due to a poor fixture and to get a 'good' result he averaged 3 measurements across the part. The 'error' was real product variation across the part.

G

#### garbagex

Thanks Bev, I will be sure to check on the implications before allowing them to use such a method.

#### Ninja

##### Looking for Reality
Trusted Information Resource
Out of curiosity, what are trying to measure?

Not the product...the attribute...
Is it Length? Thickness? Viscosity? Tensile strength?

There are a lot of folks here with a lot of knowledge about gages that work well for various attributes.

S

#### statdoug

With the other contributions in mind, let me say, first, that I have found this a very useful method for situations like vision system measurements where repeated measurements were cheap and easily averaged, but one additional warning is that the gage must have sufficient resolution. If a traditional repeatability study yeilds more than 4 or 5 zero ranges, you may find that your averaging is not helping to improve your error at all.

#### Miner

##### Forum Moderator
With the other contributions in mind, let me say, first, that I have found this a very useful method for situations like vision system measurements where repeated measurements were cheap and easily averaged, but one additional warning is that the gage must have sufficient resolution. If a traditional repeatability study yeilds more than 4 or 5 zero ranges, you may find that your averaging is not helping to improve your error at all.
Excellent point. One should always verify that the resolution is adequate before evaluating metrics such as %SV or ndc. If the resolution is inadequate, the metrics are unreliable, and as you said averaging may not help.

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