# A Simple Guide to Gage R&R for Destructive Testing

Measurement systems analysis (MSA) is essential to the success of any data analysis. If you cannot rely on the tool you’re using to take measurements, then why bother collecting data to begin with? It would be like trying to lose weight while relying on a scale that doesn’t work. What’s the point in weighing yourself?

Minitab Statistical Software offers many types of tools that you can use to assess your measurement system, including:

• Gage R&R Study (Crossed)
• Gage R&R Study (Nested)
• Attribute Agreement Analysis

## Destructive Testing Defined

In MSA studies for continuous measurements (e.g. weight, length, volume) using non-destructive testing, each part can be measured repeatedly. In this case, we can use crossed Gage studies. However, sometimes we must conduct an MSA where the test required to take the measurement destroys the object or physically changes the characteristic that is being measured. Examples include impact testing and chemical analysis. Picture frozen chickens being hurled at aircraft windshields or testing the amount of force required to open a bag of potato chips.

So what analysis do we use when the test is destructive? Like many questions that arise where statistics are concerned, the answer is, of course, “it depends.”

## Crossed Gage R&R for Destructive Testing

Suppose you are conducting a Gage R&R study with 3 operators where each operator measures each part twice. This requires 3x2=6 measurements per part. Suppose for your destructive test you can obtain at least 6 specimens that are sufficiently similar to be considered the same part. Even though the 6 specimens are truly not the same part, as long as they’re similar enough to be considered the same part, then you can use a crossed Gage study just like you would for a non-destructive test.

This homogeneity assumption is critical to obtain meaningful results because Minitab presumes they are the same, identical part. In Minitab, you label the parts with the same ID (e.g., Part 1) even though they are physically different parts, as shown in the worksheet.

Note: The order of the measurements shown in the Minitab worksheet does not reflect the order in which the data should be collected. Parts should be measured in a random order to reduce time-related biases, such as operator fatigue or instrument drift. Randomizing the part order also ensures that operators do not easily recall previous measurements for the parts.

## Nested Gage R&R for Destructive Testing

Suppose again that you are conducting a Gage R&R study for a destructive test with 3 operators and 2 replicates per part. But suppose it is not feasible to obtain 6 specimens that are similar enough to be considered the same part, rather only 2 specimens. Then in this case, you must use a nested analysis.

Each operator measures a different set of parts. Therefore, each part is said to be “nested” within operator rather than “crossed” since each part is unique to an operator. Let’s look at a diagram for another view of crossed versus nested studies.

Presuming each operator is going to measure each part twice, the crossed example shows 2 operators each measuring the same 6 parts for a total of 24 measurements (2 operators x 6 parts x 2 replicates). In the nested scenario where we again have 2 replicates, each part (e.g. P1) actually represents 2 physically different parts that are similar enough be considered identical. With 2 operators each measuring 3 parts twice, there would be a total of 12 measurements (2x3x2) in this case.

## Crossed vs. Nested Summary

If you want to conduct a reliable statistical analysis, then assessing your measurement system is critical. In the case of destructive testing, your first step is to choose between a crossed and nested study. Ask yourself:

• How many parts can I obtain that are similar enough to be considered identical?
• How many operators will participate in the study?
• How many times is each operator going to measure the “same” part? Two times? Three times? Etc.

Once you have the answers to these questions, you can then determine whether a crossed or nested study is more appropriate. Regardless of which you choose, both analyses will provide meaningful results, and both can be easily conducted using Minitab. For specific Gage R&R examples using Minitab, see our articles on crossed and nested studies.

Name: Ilksen Cosar • Wednesday, October 23, 2013

Hello Michelle,
I got confused with the term "destructive test". As far as I know, a destructive test can not be performed on the same part twice. That is what makes it so difficult to see the variation in destructive tests. Could you please explain further?
Thanks,

Name: Michelle Paret • Thursday, October 24, 2013

Ilksen, you make a valid point that a destructive test cannot be performed on the same part twice. That is why the homogeneity assumption is critical for Gage R&R. Parts must be sufficiently similar to be considered the same part (even though they are not physically the same part). I hope this helps to clarify what I was trying to explain in the post.

Name: Himanshu Kumar • Thursday, November 14, 2013

Can I consider Rockwell Hardness test as destuctive test.? It can be performed on same part but at different locations.

Name: Michelle Paret • Thursday, November 21, 2013

Himanshu, as long as the different locations meet the homogeneity assumption, then it should be acceptable to identify them as the same "part" in your Minitab analysis. There may be other aspects of the study that need to be considered, such as how operators will know how to identify these "locations".

Name: Robert • Thursday, January 30, 2014

what if we are doing destructive Gage R&R and no two parts are identical? is there any way to show the repeatability? if not the measurement system will be very high, is there anyway to come up with rationale?

Name: Michelle Paret • Friday, January 31, 2014

Robert, even if no two parts are exactly identical, are there parts similar enough to be treated as if they're the same part? If you would like to have a discussion regarding this topic, please don't hesitate to contact our Technical Support team (click Contact Us below to get the phone# for your country).

Name: Justin • Tuesday, March 18, 2014

What if its a load bearing destructive test. Either the part can hold a certain weight or it cannot. There's no way of knowing until you test them. Say for Instance when you do the test all of the parts you select can hold the weight. Your Gage R&R would show all of the operators agree perfectly with each other and the standard. What then? Do you use a bigger sample size?

Name: Michelle Paret • Friday, March 21, 2014

Gage R&R is an important step in data analysis. However, the load bearing destructive test that you describe doesn't sound like one in which there could be error in the measurement system - either the the part holds or it doesn't. What would be the goal of using a Gage R&R in this instance? It sounds like the operators would also get the correct answer, and therefore, you know you can trust your data.

Name: Edgar • Friday, April 4, 2014

Hi Michelle,

For destructive MSA, would you consider doing a T-Test and F-Test instead of a crossed or nested GR&R?

Name: Michelle Paret • Tuesday, April 8, 2014

Hi Edgar,

Calculations for destructive (and non-destructive) MSA are based on ANOVA, which includes related F-tests. Since there are mutliple factors and multiple levels for each factor, I don't think the t-test would be sufficient for MSA.

Please let me know if you have any other questions.

Name: venkatesh • Monday, June 9, 2014

Hi, Good Day to You.
I just need a clarification. Consider we are measuring some electrical characteristic like output voltage of an IC in the unit under test, where the repeatability is not guaranteed by the IC itself as it can produce different voltages across the trials but within the tolerances specified by the IC manufacturer (Eg: 5V +/- 0.5V). In these case %gage R&R fails to meet