# Gage R&R with ATE (Automatic Test Equipment)

A

#### Alys Madge

Can Gage R&R be useful when you are using Automatic Test Equipment to measure parts as there will be no operator to operator variation? Would you still get several operators to produce the data so that it fits into the normal analysis systems?

I am quite new to this so forgive me if my question appears strange!

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K

#### KenK - 2009

Yes, you can most certainly do a measurement system analysis. In automated test equipment you would not necessarily assess operator varation.

The first thing you need to do is sit down and consider ALL the possible sources of measurement variation. If you have multiple test bays, you might want to know the variation between test bays.

The only trick is that you may have to analyze your data using a General Linear Model tool that will let you identify random effects (as opposed to fixed effects).

MINITAB, for example, will not accept NO operators, so you need to use their GLM tool and do the simple tabular math yourself.

Any good GLM tool should output the variance components for each source of variation. In MINITAB you need to click on the Results button and check the box. These components are simply the variance estimate for each source of variation. The error term will be your Repeatability.

Since the components are variances, you can sum them up as needed. Total variation equals the sum of all of them. Measurement variation equals the sum of all sources related to measurement variation (including any interactions related to measurement).

You can then take the square root of the variances to get the respective standard deviations, divide them by the total to get percentages, and multiply them by 5.15 to get the usual metrics.

J

#### JStain - 2008

ATe Cpk and gage R&R

We have 18 seperate ATE's. All the same model. I need to perform a Gage R&R. because they are automted there will only need to be one operator. I have an unlimited source of parts to test.

using MSA 3rd edition, MINITAB 14.

my question is:
how many parts?
trials?
repeats?

What would be my best approach for testing variations from one ATE to the other?

Would it be possible to test for cpk?

R

#### Rob Nix

Jstain,

I have not used Minitab (except in demo form) but I imagine it does ANOVA. Do an ANOVA using:

5 parts (possibly 1 bad, 1 nearly bad, 1 in the middle, 1 just barely good, and 1 good)

All 18 Machines (as your "trials" instead of "operators")

and

10 repeats (more or less depending on the accuracy you need).

Cpk does not apply to testing!

Just my suggestion.

D

#### dfirka

Rob, Jstain

I would say that you can analyze the Cpk with MSA, but usually will be very difficult in practical terms:

If the following conditions apply:

- The process is stable (under statistic control)
- The underlying distribution of the parts is normal
- The parts used are a random sample of the process population.

Then, the total variance resulting from Anova could be used to obtain a value for Cp/Cpk.

But, having only 5 parts will give a very "uncertain" estimation of the variance. This variance itself is a random variable which has confidence intervals that decrease as the number of parts increase.

Therefore the amount of parts that should be taken to make a good estimation would make impractical the R&R study.

Daniel

J

#### JStain - 2008

Dazed and confused for so long, it's now OK!

Saginaw Michigan? I live for Shotts bread. My aunt and uncle are in saginaw of Shattuck. anyways;

I ran my study as you indicated, (kind of, 5 parts,2 trials, 3 ATe's) i'll do more once I know I'm on the right track) and want to make sure I understand what I just did.

part
number N Lower StDev Upper
1 6 0.0066168 0.0121106 0.0422025
2 6 0.0075311 0.0137840 0.0480341
3 6 0.0048868 0.0089443 0.0311686
4 6 0.0080423 0.0147196 0.0512942
5 6 0.0053718 0.0098319 0.0342619

Bartlett's Test (normal distribution)
Test statistic = 1.63, p-value = 0.804

Levene's Test (any continuous distribution)
Test statistic = 0.80, p-value = 0.535

Test for Equal Variances: data versus part number

Gage R&R Study - Nested ANOVA

Gage R&R (Nested) for data

Source DF SS MS F P
trial 1 0.0001633 0.0001633 0.33447 0.579
part number (trial) 8 0.0039067 0.0004883 2.98980 0.022
Repeatability 20 0.0032667 0.0001633
Total 29 0.0073367

Gage R&R

%Contribution
Source VarComp (of VarComp)
Total Gage R&R 0.0001633 60.12
Repeatability 0.0001633 60.12
Reproducibility 0.0000000 0.00
Part-To-Part 0.0001083 39.88
Total Variation 0.0002717 100.00

Study*Var %Study*Var
Source StdDev (SD) (6***SD) (%SV)
Total Gage R&R 0.0127802 0.0766812 77.54
Repeatability 0.0127802 0.0766812 77.54
Reproducibility 0.0000000 0.0000000 0.00
Part-To-Part 0.0104083 0.0624500 63.15
Total Variation 0.0164823 0.0988939 100.00

Well it looks like my repeatability sucks. Which is what I suspected. these ATE's are as older than my in-laws. If you move them your readings go to in a hand basket.

I knew I wouldn't have any repro, my part-to-part is a source of interest. These are nearly 'identical 'parts. So where's this variance coming from?

R

#### Rob Nix

Daniel,

First things first. MSA is for ensuring measurement system (ATE) integrity, that is, that it reads consistently the correct measurement. THEN the parts you test should be analyzed over time using SPC to ensure control. THEN you test lots of parts in order to determine capability (Cpk).

I'm not sure what you were getting at. Perhaps it is a "chicken or egg" scenario where R&R cannot be determined without a controlled process, and without a repeatable gage you cannot determine control.

Jstain,

What type of parts and what measurement characteristic is being checked? Sometimes the dynamics of the part, e.g. heat, viscosity, leakage, durometer, etc. changes WHILE the testing is being done.

By the way, Shattuck Rd. is less than 3 miles from where I'm at on Wheeler St.

D

#### dfirka

Rob,

Yes, I was just looking at it from a mere theoretical sandpoint, with the following experiment in mind:

- take "p" parts from the current process in a representative way, over a short period of time;
- measure them "n" times with the different instruments we will use to control the process.
- estimate GRR and PV

and my reasoning was on the rationale to use that data to estimate process capability in addition to assess the measurement system capability.

Thxs

J

#### JStain - 2008

First things first. MSA is for ensuring measurement system (ATE) integrity, that is, that it reads consistently the correct measurement. (Cpk).
I will probaly suprise you, but your local power provider has never tested it's meter (your house meter) testers for accuracy. I am in the "calibration" (read sticker factory) laboratory. We have these testers (18 of them) which they use to "certify" that the meters that are on your house are accuarate.

When I calibrated them I noticed the readings were all over the map. I asked has anyone ever tested (gage R&R) to see if these boards are repeatable. I get that glazed over look and shrugs as a response.

THEN the parts you test should be analyzed over time using SPC to ensure control. THEN you test lots of parts in order to determine capability (Cpk).
i know what you mena here, perhaps I'm a little ahead of myself.

I mentioned the Cpk, only that I suspect nobodys looked at if these boards are actualy capable of mesuring to the accuracy they "claim".

To be fair this company's probably about a 1 to 1.5 sigma company. maybe I'm asking too much.

But, having only 5 parts will give a very "uncertain" estimation of the variance. This variance itself is a random variable which has confidence intervals that decrease as the number of parts increase.
With nothing to lose but time, how many would be a good number dfirka?

By the way, Shattuck Rd. is less than 3 miles from where I'm at on Wheeler St.
They live north of Bay st. I remember when all that was farm country. My cousin lives down by Davenport south of Bay street, it's on the way that we stop to get bread.

D

#### dfirka

Jstain said:
With nothing to lose but time, how many would be a good number dfirka?
:blowup

The most common ANOVA design used in GRR is a "random-effects model" with two factors. I dont know of a closed formula to calculate the sample size for kind of designs.

In the recent (excellent) paper by Burdick et al (link at the end), the authors appliy two different methods to compute the 95% confidence interval for the variance estimates.

They use a study with 3 appraisers, 10 parts an 3 repetitions.

I was appalled by the huge uncertainty calculated for the variance estimate: for example, the point estimate for the "parts" variance was 48.2, but the 95% interval was [22.6 - 161.6].

So a word of caution should be raised regarding the usual recommendations of three appraisers to analyse the A.V. in GRR studies, this amount could produce misleading decisions based in very weak data.

Back to the question> So how many parts should we take? Without any formula the only way out is the old "trial an error" methodology: adding parts until we get confidence limits that makes us happy (we have to stop somewhere, infinite parts are the only way to certainty).

Instead of the aggregation of parts, Burdick suggested using past historical data to get the confidence intervals by simulation.

I'm sorry I cannot say : take 10 parts

Is also sad that popular statistical software dont tell us the confidence limits of the results.

Daniel

Burdick et al Paper: http://www.asq.org/pub/jqt/past/vol35_issue4/pdf/qtec-35-4-342.pdf

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