Quality Progress - September 2017 - 46

F E AT U R E

MEASUREMENT
caused by different operators.
+ Whether the measurement system can
discriminate between different parts.
+ Whether the measurement system variability is small compared to the process
variability.

Three GR&R studies

GR&R is a method
used to evaluate
the repeatability
and reproducibility
of a measurement
system because
measurement systems
can themselves
cause variations in
measurements.

There are three GR&R studies-crossed,
nested and expanded-each with a different
objective. Choosing which GR&R study to
perform depends on how much data are
available and whether the measurement
test is destructive.
1. Crossed GR&R study. In this study,
each operator measures each part. It is
called crossed GR&R because the same parts are measured multiple times by each operator (see Figure 3). It's
used to determine how much process variation is due to
measurement system variation.
Crossed GR&R is used in nondestructive scenarios-
when parts are not destroyed during measurement and
can be measured twice.
Example. Measuring the length of a part-the part is
not changed during the measurement.
The two methods commonly used to analyze the
results of a crossed GR&R study are the average and
range method, and ANOVA.
2. Nested GR&R study. This method is used when only
one operator measures each part, usually because the
test destroys the part (see Figure 4). This study is called
nested because one or more factors are nested under
another factor and not crossed with the other factors.
Nested GR&R is used in destructive testing scenarios,
such as impact testing and chemical analysis. A critical

sample again.
3. Expanded GR&R study. Standard GR&R studies (that is,
crossed and nested) assess the effects of two factors in
the measurement system-typically operator and part
(see Figure 5). In many cases, the effects of operator and
part are not sufficient to provide a complete understanding of the measurement system, so a third variable
(typically gage) is added to the standard GR&R study.
When three or more factors are included in the analysis, the study is called expanded GR&R (see Figure 6). An
expanded GR&R study can be done if one or more of the
following conditions exists:
+ More than two factors are being assessed. The study
analyzes not just parts and operators, but also up to eight
additional factors, such as gage, lab or location.
+ There are missing data points. An expanded GR&R study
can be performed even with incomplete data and unbalanced studies.
+ There are fixed or random factors for greater flexibility.

FIGURE 4

FIGURE 5

Nested GR&R study
Operator 1

Operator 2

factor of a nested GR&R study is to identify
a batch of material that is so close to the
original it reasonably can be assumed
the parts in the batch are the same part.
The key to being able to run a destructive
GR&R study is the assumption that a batch
is homogeneous.
ANOVA is used to analyze the results of
a destructive GR&R study. The average and
range method cannot be used.
Example. Testing the amount of force
required to open a bag of potato chips,
heat-treating steel tubes and testing the
strength of a rope until it breaks. In these
examples, the sample is destroyed during
testing, making it impossible to test the

Standard GR&R study
Standard GR&R

Operator 3

Gage variation
(repeatability)
Part
1

Part
2

Part
3

Part
4

GR&R = gage repeatability and reproducibility

Part
5

Variation due to measurement
procedure (reproducibility)

Part
6
Operator-tooperator variation

Operator-toparts variation

GR&R = gage repeatability and reproducibility

46 QP

September 2017 ❘ qualityprogress.com


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Table of Contents for the Digital Edition of Quality Progress - September 2017

Seen and Heard
Progress Report
Mr. Pareto Head
Career Coach
Expert Answers
Field Notes
Data Disruption
The Deal With Big Data
Better Intelligence
A Study in Measurement
Innovation Imperative
Statistics Spotlight
Standard Issues
ASQ's 2017 Quality Resource Guide
Marketplace
Footnotes
Back to Basics
Quality Progress - September 2017 - Intro
Quality Progress - September 2017 - cover1
Quality Progress - September 2017 - cover2
Quality Progress - September 2017 - 1
Quality Progress - September 2017 - 2
Quality Progress - September 2017 - 3
Quality Progress - September 2017 - 4
Quality Progress - September 2017 - 5
Quality Progress - September 2017 - Seen and Heard
Quality Progress - September 2017 - 7
Quality Progress - September 2017 - Progress Report
Quality Progress - September 2017 - 9
Quality Progress - September 2017 - Mr. Pareto Head
Quality Progress - September 2017 - 11
Quality Progress - September 2017 - Career Coach
Quality Progress - September 2017 - 13
Quality Progress - September 2017 - 14
Quality Progress - September 2017 - Expert Answers
Quality Progress - September 2017 - Field Notes
Quality Progress - September 2017 - 17
Quality Progress - September 2017 - 18
Quality Progress - September 2017 - 19
Quality Progress - September 2017 - Data Disruption
Quality Progress - September 2017 - 21
Quality Progress - September 2017 - 22
Quality Progress - September 2017 - 23
Quality Progress - September 2017 - 24
Quality Progress - September 2017 - 25
Quality Progress - September 2017 - The Deal With Big Data
Quality Progress - September 2017 - 27
Quality Progress - September 2017 - 28
Quality Progress - September 2017 - 29
Quality Progress - September 2017 - 30
Quality Progress - September 2017 - 31
Quality Progress - September 2017 - 32
Quality Progress - September 2017 - 33
Quality Progress - September 2017 - Better Intelligence
Quality Progress - September 2017 - 35
Quality Progress - September 2017 - 36
Quality Progress - September 2017 - 37
Quality Progress - September 2017 - 38
Quality Progress - September 2017 - 39
Quality Progress - September 2017 - 40
Quality Progress - September 2017 - 41
Quality Progress - September 2017 - A Study in Measurement
Quality Progress - September 2017 - 43
Quality Progress - September 2017 - 44
Quality Progress - September 2017 - 45
Quality Progress - September 2017 - 46
Quality Progress - September 2017 - 47
Quality Progress - September 2017 - Innovation Imperative
Quality Progress - September 2017 - 49
Quality Progress - September 2017 - 50
Quality Progress - September 2017 - Statistics Spotlight
Quality Progress - September 2017 - 52
Quality Progress - September 2017 - 53
Quality Progress - September 2017 - Standard Issues
Quality Progress - September 2017 - 55
Quality Progress - September 2017 - 56
Quality Progress - September 2017 - 57
Quality Progress - September 2017 - ASQ's 2017 Quality Resource Guide
Quality Progress - September 2017 - 59
Quality Progress - September 2017 - 60
Quality Progress - September 2017 - 61
Quality Progress - September 2017 - 62
Quality Progress - September 2017 - 63
Quality Progress - September 2017 - 64
Quality Progress - September 2017 - 65
Quality Progress - September 2017 - 66
Quality Progress - September 2017 - 67
Quality Progress - September 2017 - Marketplace
Quality Progress - September 2017 - 69
Quality Progress - September 2017 - Footnotes
Quality Progress - September 2017 - 71
Quality Progress - September 2017 - Back to Basics
Quality Progress - September 2017 - cover3
Quality Progress - September 2017 - cover4
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