# What is the R&R pledge?

The R&R guarantee is used to qualify a measurement process. This means checking that the variability of the measurement process is compatible with the variability of the quantity to be measured.

It is considered necessary to have a ratio of 4 between the variability of the parts and the variability of the measurement. This ratio is expressed as Cpc production:

$\text{Cpc production}=\frac{text{production dispersion}}{text{measurement dispersion}}$

The production Cpc therefore depends on the dispersion of the parts. However, when we want to characterise a measuring instrument, we would like this characterisation to be independent of production variability. We are therefore going to introduce a new type of variable, which allows us to characterise the measuring instrument not in terms of part dispersion, but in terms of the part tolerance interval.
In the same way that capability is calculated, the measuring instrument will be characterised:
• Or by Cpc (Control Process Capability):

$\text{Cpc}=\frac{\text{tolerance interval}}{\text{measurement dispersion}}> 4$

• GRR% (Repeatability and Reproducibility):

$\text{GRR%}=\frac{text{measurement dispersion}}{\text{tolerance interval}}< 30%$

As you can see, the two indicators represent the same thing and we have the relationship :

$\text{GRR%}=\frac{1}{Cpc}$

Here are the generally accepted rules:

CpcGRR%
Unacceptable<3>30%
Limit process>3 and < 420%
Acceptable>4<20%
Excellent>8<10%

## Calculating the dispersion of a measuring instrument

To calculate the dispersion of a measurement process, a repeatability and reproducibility test is used.

The repeatability and reproducibility test aims to characterise the overall dispersion of the measurement process by separating what is repeatability (i.e. the dispersion of the measurement repetition) from what is reproducibility (i.e. a difference between several operators).

To carry out this test you need :
Standard test: 3 operators each measure 10 parts 3 times each
Rapid test: 3 operators each measure 10 parts 1 time each (this test does not separate repeatability and reproducibility)

Once the measurements have been made, there are two methods for calculating the dispersion of the measurement medium:

ANAVAR method : A more accurate method, which calculates repeatability and reproducibility and detects whether there are interactions between parts and operators.

RANGE method : A more approximate method, easy to calculate with an Excel spreadsheet, but which does not detect any part/operator interaction.
We recommend that you use the ANAVAR calculation method, as it is the most accurate.

## Range method

The range method is particularly used in industry because its calculations can easily be done by hand.
This method can be used to calculate the repeatability and reproducibility of the measurement process. However, it does not allow interaction to be calculated, which limits its scope. The calculations in this method are based on calculating an intra-sample standard deviation from the ranges.
The calculation principle is as follows:

All the measurements of each part by each operator are considered to be a sample. In this way, the intra-sample variability represents the repeatability of the measurement process, which is calculated by :

$\sigma_{repetablity}=\frac{\overline{R}}{d_{2}^{*}}$

We then consider the averages of each operator's measurements as a sample. This makes it possible to calculate the reproducibility of the measurement process by :
$\sigma_{operator}=\frac{R_{\overline{X}}{d_{2}^{*}}$

## ANAVAR method

La ANAVAR method is more complex:

To calculate the GRR and Cpc using the ANAVAR method, we use the Fisher test:

Sources of variabilitySum of squaresDegree of freedom
PartsSSBb-1
Interaction (Operator/part)SSAB(a-1)(b-1)
InstrumentSSEab(n-1)
TotalTSSN-1

with:

a = number of operators
b = number of pieces
n = number of repetitions
N = total number of measurements = abn

This method is therefore much more complex to implement, but it allows interaction to be calculated as a source of dispersion, which is not possible with the RANGE method. It is therefore more accurate.

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