# Destructive Tensile Test Sampling Gage R&R

T

#### Tyred Worker

Hi all,

I'm new to this so I apologise if my terminology, or anything else, is incorrect.

We are going to perform a gage r&r on a tensometer using strips of cured rubber. Our process involves 5 different compounds that are tested in this way, the specifications of which are all pretty similar. We plan to use 3 operators to test 10 parts each, across 3 trials. My initial questions are in regard to the sampling regime.

Is it correct to allocate 2 parts from each compound to each operator for each trial of 10 parts?

Is it correct to manufacture all the parts to be tested from the same 5 lots (i.e. Compound 1 = 18 parts, 6 parts per operator. Compound 2 = 18 parts, 2 parts per operator per trial etc.)?

Any input would be much appreciated.

Tyred Worker

#### Hershal

##### Metrologist-Auditor
Trusted Information Resource
I am not the GR&R expert, but others here are and should be able to help you.

T

#### Tyred Worker

Thanks for the input.

Am I right in thinking that we are adopting the split-specimens approach? We basically have 5 large sheets of uncured rubber, of differing formulations, from which we can produce all the parts required for the gage r&r, there being an assumption of homogenity within the material.

I do have another question regarding the sampling which i'm not sure was covered in the blog entry but may be related to what I just commented on. We are using the 10 measurements per trial format and so are allocating 2 parts from the same lot for the 5 lots (formulations) across each trial. Is this the correct way to do it, or should we be allocating 1 part from different lots of the same formulation, i.e. 1 part from lot A of formulation X, 1 part from lot B of formulation X, 1 part from lot A of formulation Y, 1 part from lot B of formulation Y etc..

I hope this makes sense.

Andy

#### Miner

##### Forum Moderator
Yes. You are using the Split Specimens approach.

The goal is that all specimens that represent a single part (i.e., the split specimens) be as homogeneous as possible. These should be cut from the same sheet as physically close as possible. The specimens that represent different parts should contain the additional variation that would be typical for manufacturing. Ideally, these would be sheets from different batches of the same formulation.

You also need to analyze these as a nested ANOVA.

T

#### Tyred Worker

Excellent. Thank you very much for your help. I had a suspicion we should be creating parts from different batches.

We'll perform the testing and see how the nested ANOVA analysis turns out.

Andy

T

#### Tyred Worker

Hi,

We have done the study and I've posted the results below.

Gage R&R (Nested) for CA01

Source DF SS MS F P
OPERATOR 2 0.09689 0.048443 0.1544 0.858
SAMPLE (OPERATOR) 27 8.47095 0.313739 18.2761 0.000
Repeatability 60 1.03000 0.017167
Total 89 9.59784

Gage R&R
%Contribution
Source VarComp (of VarComp)
Total Gage R&R 0.017167 14.80
Repeatability 0.017167 14.80
Reproducibility 0.000000 0.00
Part-To-Part 0.098857 85.20
Total Variation 0.116024 100.00

Study Var %Study Var
Source StdDev (SD) (6 * SD) (%SV)
Total Gage R&R 0.131022 0.78613 38.47
Repeatability 0.131022 0.78613 38.47
Reproducibility 0.000000 0.00000 0.00
Part-To-Part 0.314416 1.88650 92.31
Total Variation 0.340623 2.04374 100.00

Number of Distinct Categories = 3

I have attached the relevant charts.

If I am interpreting this correctly, 38.47% of the total variability within the system is attributed to the measuring device. As this is >30%, and the number of distinct categories is <5, the situation is not acceptable.

I have a couple of questions.

Could the relatively narrow range of data produced by our parts contribute to what is a poor performance? If so, would it be acceptable to re-run the study but create parts from material we do not test using this method? Within the original study each formulation we manufacture that is tested using this traction method is represented. It would be very simple to create parts that produce data very different to that produced by the original study, albeit they would represent a formulation that is not tested using this particular traction method.

A colleague has suggested that, seeing as how the traction test method calls for an average of data from 5 parts to be reported, perhaps we should be replicating this when it comes to reporting results in our gage r&r studies, i.e. 1 gage r&r reported part result equals 5 actual parts tested. I am very doubtful as to the wisdom of this but would just like some confirmation either way.

Any input would be most appreciated.

Andy

#### Miner

##### Forum Moderator
Is this test used for inspection to a tolerance, or is it used for SPC?

If it is used for inspection, you should enter the tolerance range and evaluate the results using %Tol. You can also disregard the %SV and ndc.

If you will use it for SPC, then you do need to address the poor %SV and ndc. Regarding your proposal, the batch to batch variation must reflect the variation that would be seen in your manufacturing process for that specific formulation. Forcing additional variation into the study that does not represent the actual process variation is not correct. Regarding the suggestion to use the average of multiple measurements, this is a viable last-ditch option to improve the results. However, for this to be valid and honest, you must be willing to revise your test method to require using the average on a permanent basis, not just to pass the R&R study.

T

#### Tyred Worker

Hi Alan,

Yes, this test is used for inspection to a tolerance. I have performed evaluations based on two different specification limits, which generated the following numbers:

Gage R&R (Nested) - "A" CA02 specification limits

Source DF SS MS F P
OPERATOR 2 0.1203 0.060148 0.1685 0.846
SAMPLE (OPERATOR) 27 9.6372 0.356934 16.7461 0.000
Repeatability 60 1.2789 0.021314
Total 89 11.0364
% Contribution
Source VarComp (of VarComp)
Total Gage R&R 0.021314 16.00
Repeatability 0.021314 16.00
Reproducibility 0.000000 0.00
Part-To-Part 0.111873 84.00
Total Variation 0.133188 100.00

Process tolerance = 2.45

Study Var %Study Var %Tolerance
Source StdDev (SD) (6 * SD) (%SV) (SV/Toler)
Total Gage R&R 0.145995 0.87597 40.00 35.75
Repeatability 0.145995 0.87597 40.00 35.75
Reproducibility 0.000000 0.00000 0.00 0.00
Part-To-Part 0.334474 2.00685 91.65 81.91
Total Variation 0.364949 2.18969 100.00 89.38

Number of Distinct Categories = 3

Gage R&R (Nested) - "B" CA02 specification limits

Source DF SS MS F P
OPERATOR 2 0.1203 0.060148 0.1685 0.846
SAMPLE (OPERATOR) 27 9.6372 0.356934 16.7461 0.000
Repeatability 60 1.2789 0.021314
Total 89 11.0364

%Contribution
Source VarComp (of VarComp)
Total Gage R&R 0.021314 16.00
Repeatability 0.021314 16.00
Reproducibility 0.000000 0.00
Part-To-Part 0.111873 84.00
Total Variation 0.133188 100.00

Process tolerance = 1.2

Study Var %Study Var %Tolerance
Source StdDev (SD) (6 * SD) (%SV) (SV/Toler)
Total Gage R&R 0.145995 0.87597 40.00 73.00
Repeatability 0.145995 0.87597 40.00 73.00
Reproducibility 0.000000 0.00000 0.00 0.00
Part-To-Part 0.334474 2.00685 91.65 167.24
Total Variation 0.364949 2.18969 100.00 182.47

Number of Distinct Categories = 3

Note: I have had to perform the evaluations based upon a different parameter than I reported previously...we do not have specification limits for the previous parameter.

I read on a thread elsewhere on the site that the %Tolerance values reflect a probability of experiencing a Type I or Type II error with respect to those specification limits. If this is correct, does this then mean that with the higher process tolerance we have a 35.5% chance of experiencing one of the errors and with the narrower process tolerance we have a 73% chance?? That seems unacceptably high!!!

Andy

#### Miner

##### Forum Moderator
The attached image is of a Gage Performance Curve. The line is the Probability of Acceptance. An ideal gage with no variation would have a square function with a probability of zero outside the spec limits and a probability of 1 inside the spec limits.

Unfortunately, no gage is ideal. Therefore, there is a zone of uncertainty where this probability transitions from zero to 1. The more gage variation, the wider this zone.

The second image is a misclassification plot. This better illustrates the Type 1 and 2 errors. A Type 1 error is the probability is calling a good part bad, and the Type 2 error is the probability of calling a bad part good.

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