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# Nested Gauge R&R (destructive)

Gauge R&R (Gauge Repeatability and Reproducibility) is a measurement system analysis. It analysis the amount of measurement variation introduced by a measurement system, which consists of the measuring instrument it self and the operators using the instrument. ## The variation in a measurement system analysis.

1. Repeatability: variation from the measurement instrument
2. Reproducibility: variation from the operators using the instrument
3. Overall Gage R&R, which is the combined effect of 1 and 2

## Type of Gauge R&R

This document is about Nested Gauge R&R and is used when the measurement is destructive. When using a test that is non destructive Use the Crossed Gauge R&R.  Nested (destructive) Crossed (non destructive)

Because the destructive character of the testing method, instead of repeatedly testing one part several times by one operator. In the nested Gauge R&R more parts that are assumed to be similar are tested.

### Parts in a Nested Gauge R&R

• This could be parts out of the same batch, compared with part out of an other batch.
• Batches made with differed process settings with known effect.

## Usage

1. Select GRR in the statistical mode drop-down menu 2. Select destructive Gauge R&R 3. Generate the measurement GRR => Generate GRR array • The amount of operators, parts (batches) and replicates must be bigger than 2
4. Organize Gauge R&R
• Select parts or batches that represents the process variation (if you take 3 batches take one from the low, middle and the high part of the variation.
• Select operators preferable operators that are normally doing this measurements.
• Use one Gauge (machine, production line).
• You must be able to assume that all parts out of the batch are identical enough to say the they are all the same like one part.
5. Conduct the Gauge R&R
6. Min p: Not used in a Nested Gauge R&R.
7. Sigma: is used in the %Gauge R&R tolerance (standard 6 sigma).

## Interpretation

• For a GRR % Var and %Tolerance the thumb rule is:
• Less than 10% Good
• Between 10% and 30% The measurement system is acceptable but this depends on the application. Cost of improving measurement system, yield, cost of repair, etc.
• Above 30% the measurement system is not acceptable should bee improved.
• If there is a big variation due to the operators, train the the operators to improve the measurement.
• Gage R&R and measure accuracy are two different things!

## Formula

### Calculating Anova #### Operator    #### Part (Operator)      #### Error   #### Total  ### Gauge R&R      ## Legend Degrees of freedom Sum of squares error Correction factor Degrees of freedom one factor Total amount levels one factor Sum of squares of one factor

## Example

Looking to this example the Gauge R&R is sufficient 9.51% this is smaller than 10% for a good Gauge R&R. In the example there are tolerance borders (-10...90) so the %Tol is leading.
There is a significant difference between the different parts, and not between the operators. Looking to the graph this is also visible. The interaction is also not significant.

If there are no tolerance borders then the Gauge R&R was just good but it is wise to improve the measurement method so Data file

### Anova

Operator: if Operators is significant it is wise to improve the measurement instructions and train the operators.

### Gauge R&R

Reproducibility: If the influence of the Reproducibility is high it is wise to review the measurement instruction and training of the operators.
Repeatability: If the influence of the repeatability is high it is wise review how the measurement is done.