# Do you know what is Gage Repeatability?

## Gage repeatability and reproducibility, shortly Gage R&R, is a statistical tool that measures the variation in the measurement system caused by the measurement device and the people taking the measurement.

Measurement system variation can be characterized by location (stability, bias, linearity) and width or spread (repeatability and reproducibility).

Gage repeatability and reproducibility (GR&R) study can be implemented for most manufacturing-related measurement systems. It may be used:

- for judging new measuring equipment as a criterion,
- for comparison of measuring devices,
- as indicator which shows the possibility of improving performance of measuring instruments,
- for comparison of one measuring equipment before and after repair,
- as required component for evaluating process variation and the acceptability level for a production process.
- as indicator of training in how to use measuring instruments.

*How to estimate total measurement variation?*

*How to estimate total measurement variation?*

Repeatability is the variation in measurement obtained:

- with one measuring instrument,
- when operated several times by the same operator,
- when measuring an identical characteristic on the same part.

**The standard deviation for repeatability (σ _{e}) is estimated by:**

where *R* is the average range of the repeated measurements.

Reproducibility is the variation in the average of measurements:

- made by different operators who are for example controllers, production operators etc. all who work with the gauge,
- using the same measuring gauge,
- when measuring the identical characteristic on the same part.

Operator variation, or reproducibility, is estimated by determining the overall average for each appraiser and then finding the range (R_{0}) by subtracting the smallest operator average from the largest.

**The standard deviation for reproducibility (σ _{0}) is estimated by:**

The measurement system variation (R&R) or gage R&R is represented by σ_{R&R}.

*Part-to-Part Variation*

Part-to-part variation also makes a contribution to the total variation in a measurement and can be determined from the measurement system data or an independent process capability study. If the measurement system study is used, the part standard deviation σ_{p} (PV) is estimated by R_{p} /d_{2}*. R_{p} can be estimated as the average range of part measurements.

*Total Variation*

Total variation (TV or σ_{TV}) for the study is calculated by summing the square of both the repeatability and reproducibility (R&R) variation and the part-to-part variation PV, and taking the square root, as follows:

The contribution of the equipment variation contribution EV is calculated as 100(EV/TV). The contribution of other factors to the total variation TV can be similarly calculated, as follows:

*Types of gage R&R*

**Use the gage R&R study that is designed for the type and number of factors that you have.**

**Crossed gage R&R study**A study in which each operator measures each part. This study is called*crossed*because the same parts are measured by each operator multiple times. Often, you will use a crossed gage R&R study to determine how much of your process variation is due to measurement system variation.**Nested gage R&R study**A study in which only one operator measures each part, usually because the test destroys the part. This study is called*nested*because one or more factors is nested under another factor and, thus, not crossed with the other factors.**Expanded gage R&R study**A study in which one or more of the following conditions exists:- More than two factors, usually, operator, gage, and part
- Fixed or random factors
- Both crossed and nested factors
- An unbalanced design

This study is called *expanded* because you can use it in several types of situations.

*Evaluation of results*

### If the percentage of process variation is:

- less than 10% - the measurement system is acceptable
- between 10% and 30% - the measurement system is conditionally acceptable but the improvement is expected (it depends on the application, the cost of the measurement device, cost of repair or the other factors)
- more than 30% - the measurement system is not acceptable, it has to be improved

### If the percentage of variance components is:

- less than 1% - the measurement system is acceptable
- between 1% and 9% - the measurement system is conditionally acceptable but the improvement is expected (it depends on the application, the cost of the measurement device, cost of repair or the other factors)
- more than 9% - the measurement system is not acceptable, it has to be improved.

očuť ťiež: kresle v obývačke. ANestskej

**Gage R&R for Destructive Testing**

### Destructive versus non-destructive tests

- During non-destructive measurements we can collect data for GR&R studies by measuring the same part or sample several times, using the same measurement device, with measurements conducted by the same appraiser.
- During destructive measurements we cannot use the same part or sample again obviously, because it is consumed or destroyed.
- Since we cannot repeat measurements on the same part or sample, we must use techniques to separate sample-to-sample variation from actual measurement system variation.

### With a destructive measurement system there are two choices for assessing repeatability:

· Find a nondestructive test that correlates with the results of the destructive test and use it instead.

· Collect parts that are so similar in the property to be measured that it can be assumed they have identical measurements.

*Searching for a substitute*

Sometimes it is not possible to find a nondestructive substitute measurement system. In these cases is the best practice to find parts that are so uniform in the property to be measured so it can be assumed they are the same part.

*Example*

We have to measure the penetration on bullet-proof vests. The only way to do this is to shoot at it and see if the bullet penetrates the vest. Whether or not it does, the vest is irreparably damaged. This is a destructive measurement system for which there is no nondestructive substitute.

In a typical study, each part (vest) would be measured six times, twice by each of three operators. Because the part can only be measured once, six identical vests for each “part” to be measured are needed. These vests are required to be made from the same roll of material, using material that is as close on the roll as possible to avoid within lot variation in the material. Perhaps by looking at other testing data for the material, it can be verified that the variation in the material meets the requirements. Additionally, the vests will have to be sewn together as identically as possible, including stitch placement and spacing. This will require care above and beyond normal production procedures. The more careful the preparation, the more accurate the results will be.

A gage R&R study can now be performed on the vest measurement system in the normal way with this exception-each time a part is called for, use one of the six identical vests representing that part. Make the analysis of the data in the usual way as if it were a nondestructive study. Whether or not a suitable substitute measurement system is found, one will have greater uncertainty in the results. If using a nondestructive substitute, there will be some additional uncertainty in the correlation with the original method. The statisticians can help with this correlation.

If you must proceed with the original measurement system, you will not be able to separate the repeatability from the variation in the “identical” parts-the six vests, in this case. Repeatability will always be overestimated. In this case is not som important.

*Crossed gage R&R versus nested gage R&R*

*Crossed gage R&R versus nested gage R&R*

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

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

*Crossed Gage R&R for Destructive Testing*

*Crossed Gage R&R for Destructive Testing*

Suppose you are preparing a Gage R&R study with 3 operators where each operator measures each part twice. This requires 3x2=6 measurements per part. For your destructive test you can have at least 6 specimens which are considered as the same part. In this case you can use a crossed Gage study just like you would for a non-destructive test.

*Nested Gage R&R for Destructive Testing*

*Nested Gage R&R for Destructive Testing*

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

Each operator measures a different set of parts. Therefore, each part is “nested” within operator rather than “crossed” since each part is unique to an operator. Diagram below shows another view of crossed versus nested studies.

If we suppose, 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.

Author: Jana Loskotova