A nested Gage R&R can be useful for studying destructive measurements. As obtaining a measurement destroys the sample being measured, repeating and reproducing measurements on the same item is not possible.
A nested Gage study depends on the ability to be able to use groups of samples that, if not identical, are at least similar.
The worksheet Gage nested contains a dataset loosely based around breaking the strength of a block of chocolate. A block of chocolate is assumed to be homogenous and is split into three identical bars. 12 blocks of chocolate are divided among the two operators with six blocks per operator. Each operator measures all the bars within its set of six blocks.
We will use the Gage R&R Study (Nested) option to investigate the measurement system error and sample variation.
The following instructions will run the nested Gage R&R study on the data for a destructive test:
- Open the file
Gage nested.mtwby using Open Worksheet option from the File menu. - Navigate to Stat | Quality Tools | Gage Study and click on Gage R&R Study (Nested).
- Enter
Blockin the Part or batch numbers field. - Enter
Operatorin the Operators field. - Enter
Strength(N)in the Measurement data field. - Click on OK to run the study.
The output from the nested Gage study will contain the same components as the crossed studies. We should have results that give us the percent study variable for the total Gage R&R, repeatability, reproducibility, part to part variation, and total variation.
We did not specify any tolerances or historical standard deviations, percent tolerance and percent process are not generated. As with the crossed studies, these could be entered from Options. See the Gage R&R Study (Crossed) option for more on these results.
The crossed Gage R&R estimates the reproducibility by comparing the results via the Operators field on the same samples. Differences by operator on a sample give reproducibility. In the nested design, operators measure different samples. In this case, we are estimating the operator effect on the difference between the means of all the measurements. This variation of the operator is found from a nested ANOVA, where the parts are nested within the operator.
When using a nested study on destructive tests, variation within the batch or samples that should be identical will be confounded with the repeatability. As long as the variation within the batch is small, the study works fine. If the variation within the batch is high, then we cannot tell if the repeatability is due to variation within the sample or the measurement system.