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The method of averaging and ranges is one of two methods most used to identify the precision of a measuring system and its capability to a demand.

## 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 Repeatability-EV

The répétabilité́ of the measuring equipment is calculated from the average of the ranges :

EV = Rcross /d2

• Rcross : Average of the range
• d2 : 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 d2 1,16 1,693

Complete Duncan Table for d2

## 2. Calculate Reproducibility-AV

Reproducibility is composed of the variability due to the operator to which the repeatability of the latter contains is subtracted.

AV = √ ((RM/d2*)2 -(EV2/g))

• RM= Mmax – Mmin 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.
• d2* : is to be taken in Duncan’s painting with the result below:
 Short Version Long Version m 2 3 g 10 30 d2* 1,41 1,91

Complete Duncan Table for d2*

## 3. Calculating the Gage R & R

The overall dispersion of the measuring equipment shall be calculated according to the following formula:

Gage R & R = √ (AV2+ EV2)

## 4. Calculating the variability of parts-PV

The dispersion of the parts is measured, excluding the effect of the measurement error, according to the following formula:

PV = √ ((MoyMax-MoyMin)/d2* *)2 -(EV2/Nb operator * NB tests by operators)

d2* * 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 d2* * = 2.48
• in long version: 10 parts to be measured therefore d2* * = 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 & R2+ PV2)

## 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

https://www.aiag.org/scriptcontent/index.cfm