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}}

- 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:

Cpc | GRR% | |
---|---|---|

Unacceptable | <3 | >30% |

Limit process | >3 and < 4 | 20% |

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.

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.

## Range method

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}^{*}}

## 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 variability | Sum of squares | Degree of freedom |
---|---|---|

Operator | SSA | a-1 |

Parts | SSB | b-1 |

Interaction (Operator/part) | SSAB | (a-1)(b-1) |

Instrument | SSE | ab(n-1) |

Total | TSS | N-1 |

with:

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.

## To calculate your Gage R&R easily, you can use our statistics module:

### Data Analysis

Build your R&R pledge in just a few clicks.

Ellistat is a software package compatible with the MSA standard for validating a measurement process by checking the repeatability and reproducibility (Gage R&R) of the instrument and verifying its accuracy.