# Range method
![Bouton-tableur](baseUrl/gagerr/range/Bouton-tableur.jpg)

The range method is particularly used in the industry as its calculations can easily be done by hand.

This method makes it possible to calculate measurement systems' repeatability and reproducibility but does not allow for interaction calculations, which limits its reach.  The calculations carried out in this method are based on the calculation of the intra-sample standard deviation from the range.

The principle of the calculation is the following:

![1 - Illustration](baseUrl/gagerr/range/1-Illustration.png)


Consider the entirety of measurements for each part by each operator as a sample.  In this way the intra-sample variability represents the repeatability of the measurement system that is calculated by:

![equation](sigma_{"repeatability"}=bar(R)/d_2^"*")


## More details
Next the measurements average of each operator is considered as a sample, which makes it possible to calculate the reproducibility of the measurement system by:
![equation](sigma_{"operators"}=R_{bar(X)}/d_2^"*")

The details of these calculations are provided in the following example:

![Exemple GRR](baseUrl/gagerr/range/Exemple-GRR.jpg)


Repeatability calculation:
![equation](sigma_{"repeatability"}=bar(R)/d_2^"*"=1.266/1.128=1.123)


Reproducibility calculation:
![equation](sigma_{"operators"}=R_{bar(X)}/d_2^"*"=1.35/1.912=0.706)

![equation](sigma_{"reproducibility"}=sqrt(sigma_{"operators"}^2-sigma_{"repeatability"}^2/(n*r))=sqrt(0.706^2-1.12^2/(10*2))=0.66)


Variability calculation of the measurement system:![equation](sigma_{"instruments"}^2=sigma_{"repeatability"}^2+sigma_{"reproducibility"}^2)
![equation](sigma_{"instruments"}=sqrt(1.123^2+0.66^2)=1.30)



We can therefore deduce:
![equation]("GRR"%=(6*sigma)/(IT)=(6*1.30)/40=19.53%)
![equation]("Cpc"=(IT)/(6*sigma)=5.12)




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Range method

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Eine Komplettlösung für Industrie 4.0