Introduction
The method of averages and ranges allows to have a good precision in the analysis of a measuring system. Located between the method by analysis of variance and the method of the ranges, it identifies the variability due to the operators, the parts and the measuring system.
1. Calculate RepeatabilityEV
The répétabilité́ of the measuring equipment is calculated from the average of the ranges :
EV = R_{cross} /d_{2}
 R_{cross} : Average of the range
 d_{2} : identifies itself in Duncan’s chart below where:
 g: number of parts to be tested multiplied by the number of tester.
 m: number of measurements per operator and per parts.
What gives us:
Short Version 
Long Version 

m 
2 
3 
g 
10 
30 
d_{2} 
1,16 
1,693 
Complete Duncan Table for d_{2}
2. Calculate ReproducibilityAV
Reproducibility is composed of the variability due to the operator to which the repeatability of the latter contains is subtracted.
AV = √ ((R_{M}/d_{2}^{*})^{2 }(EV^{2}/g))
 R_{M}= M_{max} – M_{min} where M is the average of the measurements for each operator. The most important average obtained by one operator minus the minimum average obtained by another operator is subtracted.
 d_{2}* : is to be taken in Duncan’s painting with the result below:
Short Version 
Long Version 

m 
2 
3 
g 
10 
30 
d_{2}^{*} 
1,41 
1,91 
Complete Duncan Table for d_{2}^{*}
3. Calculating the Gage R & R
The overall dispersion of the measuring equipment shall be calculated according to the following formula:
Gage R & R = √ (AV^{2}+ EV^{2})
4. Calculating the variability of partsPV
The dispersion of the parts is measured, excluding the effect of the measurement error, according to the following formula:
PV = √ ((MoyMaxMoyMin)/d_{2}^{* *})^{2} (EV^{2}/Nb operator * NB tests by operators)
d_{2}^{* *} is to be taken in the first row of the table and the column corresponds in this case to the number of parts measured either:
 Short Version: 5 parts to be measured therefore d_{2}^{* *} = 2.48
 in long version: 10 parts to be measured therefore d_{2}^{* *} = 3.18
Duncan Complete Table for d2 * *
5. Calculation of total Variation – TV
The total Variation corresponds to the variability of all elements, equipment, man and parts. It is calculated according to the following formula:
TV = √ (Gage R & R^{2}+ PV^{2})
Source
A. J. Duncan (1986)Quality Control and industrial statistics
D. Durat, M. Pillai (2005) – Quality in production: from ISO 9000 to Six Sigma
K. Horell (1991)Introduction to Measurement Capability analysis
Boeing (1998) – Advanced Quality System Tools
D. S. Ermer (2006) – Improved Gage R & R Measurement studies
A. de Frenne (2008) – Analysis of the measurement system