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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

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