Gauging Gage Part 1: Is 10 Parts Enough?"You take 10 parts and have 3 operators measure each 2 times." This standard approach to a Gage R&R experiment is so common, so accepted, so ubiquitous that few people ever ques tion whether it is effective. Obviously one could loo k at whether 3 is an adequate number of operators or 2 an adequate number of replicates, but in this first of a series of pos ts about "Gauging Gage," I want to look at 10. Just 10 parts. How accurately can you asses your measurement system with 10 parts? Assessing a Measurement System with 10 Parts I'm going to use a simple scenario as an example. I'm going to simulate the results of 1,000 Gage R&R Studies with the following underlying characteristics: 1.There are no operator-to-operator differences, and no operator*par t interaction. 2.The measurement system variance and part-to-part variance used would result in a %Contribution of 5.88%, between the popular guidelines of <1% is excellent and >9% is poor. So—no looking ahead here—based on my 1,000 simulated Gage studies, what do you think the distribution of %Con tribution looks like acros s all studies? Specifically, do yo u think it is centered near the true value (5.88%), or do you think the distribution is skewed, and if so, how much do you think the estimates vary? Go ahead and think about it...I'll just wait here for a minute. Okay, ready? Here is the distribution, with the guidelines and true value indicated:
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"You take 10 parts and have 3 operators measure each 2 times."
This standard approach to a Gage R&R experiment is so common, so accepted, so ubiquitous
that few people ever question whether it is effective. Obviously one could look at whether 3 is
an adequate number of operators or 2 an adequate number of replicates, but in this first of a
series of posts about "Gauging Gage," I want to look at 10. Just 10 parts. How accurately can
you asses your measurement system with 10 parts?
Assessing a Measurement System with 10 Parts
I'm going to use a simple scenario as an example. I'm going to simulate the results of 1,000Gage R&R Studies with the following underlying characteristics:
1. There are no operator-to-operator differences, and no operator*part interaction.
2. The measurement system variance and part-to-part variance used would result in a
%Contribution of 5.88%, between the popular guidelines of <1% is excellent and
>9% is poor.
So —no looking ahead here —based on my 1,000 simulated Gage studies, what do you think the
distribution of %Contribution looks like across all studies? Specifically, do you think it is
centered near the true value (5.88%), or do you think the distribution is skewed, and if so, how
much do you think the estimates vary?
Go ahead and think about it...I'll just wait here for a minute.
Okay, ready?
Here is the distribution, with the guidelines and true value indicated:
Gauging Gage Part 2: Are 3 Operatorsor 2 Replicates Enough?
In Part 1 of Gauging Gage, I looked at how adequate a sampling of 10 parts is for a GageR&R Study and providing some advice based on the results.
Now I want to turn my attention to the other two factors in the standard Gage experiment: 3
operators and 2 replicates. Specifically, what if instead of increasing the number of parts in the
experiment (my previous post demonstrated you would need an unfeasible increase in parts),
you increased the number of operators or number of replicates?
In this study, we are only interested in the effect on our estimate of overall Gage variation.
Obviously, increasing operators would give you a better estimate of of the operator term and
reproducibility, and increasing replicates would get you a better estimate of repeatability. But Iwant to look at the overall impact on your assessment of the measurement system.
Operators
First we will look at operators. Using the same simulation engine I described in Part 1, this time
I did two different simulations. In one, I increased the number of operators to 4 and continued
using 10 parts and 2 replicates (for a total of 80 runs); in the other, I increased to 4 operators
and still used 2 replicates, but decreased the number of parts to 8 to get back close to the
original experiment size (64 runs compared to the original 60).
Here is a comparison of the standard experiment and each scenario laid out here:
In Parts 1 and 2 of Gauging Gage we looked at the numbers of parts, operators, andreplicates used in a Gage R&R Study and how accurately we could estimate %Contribution based
on the choice for each. In doing so, I hoped to provide you with valuable and interesting
information, but mostly I hoped to make you like me. I mean like me so much that if I told you
that you were doing something flat-out wrong and had been for years and probably screwed
somethings up, you would hear me out and hopefully just revert back to being indifferent
towards me.
For the third (and maybe final) installment, I want to talk about something that drives me
crazy. It really gets under my skin. I see it all of the time, maybe more often than not. You
might even do it. If you do, I'm going to try to convince you that you are very, very wrong. If
you're an instructor, you may even have to contact past students with groveling apologies and
admit you steered them wrong. And that's the best-case scenario. Maybe instead of admitting
error, you will post scathing comments on this post insisting I am wrong and maybe even
insulting me despite the evidence I provide here that I am, in fact, right.
Let me ask you a question:
When you choose parts to use in a Gage R&R Study, how do youchoose them?
If your answer to that question required anymore than a few words - and it can be done in oneword —then I'm afraid you may have been making a very popular but very bad decision. If
you're in that group, I bet you're already reciting your rebuttal in your head now, without even
hearing what I have to say. You've had this argument before, haven't you? Consider whether
your response was some variation on the following popular schemes:
1. Sample parts at regular intervals across the range of measurements typically seen
2. Sample parts at regular intervals across the process tolerance (lower spec to upper
spec)
3. Sample randomly but pull a part from outside of either spec
#1 is wrong. #2 is wrong. #3 is wrong.
You see, the statistics you use to qualify your measurement system are all reported relative to
the part-to-part variation and all of the schemes I just listed do not accurately estimate your
true part-to-part variation. The answer to the question that would have provided the most
But enough with the small talk —this is a statistics blog, so let's see what the statistics say.
In Part 1 I described a simulated Gage R&R experiment, which I will repeat here using the
standard design of 10 parts, 3 operators, and 2 replicates. The difference is that in only one setof 1,000 simulations will I randomly pull parts, and we'll consider that our baseline. The other
schemes I will simulate are as follows:
1. An "exact" sampling - while not practical in real life, this pulls parts corresponding
to the 5th, 15th, 25, ..., and 95th percentiles of the underlying normal distribution
and forms a (nearly) "exact" normal distribution as a means of seeing how much
the randomness of sampling affects our estimates.
2. Parts are selected uniformly (at equal intervals) across a typical range of parts seen
in production (from the 5th to the 95th percentile).
3. Parts are selected uniformly (at equal intervals) across the range of the specs, inthis case assuming the process is centered with a Ppk of 1.
4. 8 of the 10 parts are selected randomly, and then one part each is used that lies
one-half of a standard deviation outside of the specs.
Keep in mind that we know with absolute certainty that the underlying %Contribution is
5.88325%.
Random Sampling for Gage
Let's use "random" as the default to compare to, which, as you recall from Parts 1 and 2,
already does not provide a particularly accurate estimate:
On several occasions I've had people tell me that you can't just sample randomly because you
might get parts that don't really match the underlying distribution.
Sample 10 Parts that Match the Distribution
So let's compare the results of random sampling from above with our results if we couldmagically pull 10 parts that follow the underlying part distribution almost perfectly, thereby
To really assess a measurement system, I advise performing both a Bias and Linearity Study as
well as a Gage R&R.
Which Sampling Scheme to Use?
In the beginning I suggested that a random scheme be used but then clearly illustrated that the"exact" method provides even better results. Using an exact method requires you to know the
underlying distribution from having enough previous data (somewhat reasonable although
existing data include measurement error) as well as to be able to measure those parts
accurately enough to ensure you're pulling the right parts (not too feasible...if you know you can
measure accurately, why are you doing a Gage R&R?). In other words, it isn't very realistic.
So for the majority of cases, the best we can do is to sample randomly. But we can do a reality
check after the fact by looking at the average measurement for each of the parts chosen and
verifying that the distribution seems reasonable. If you have a process that typically shows
normality and your sample shows unusually high skewness, there's a chance you pulled anunusual sample and may want to pull some additional parts and supplement the original