Gage R&R (measurement system analysis)

Paste readings of several parts taken by several operators to see how much of the variation comes from the gage and from people, and whether the measurement system can control the process.

Pre-sizing and estimating tool: results do not replace design, calculations or reports signed by a licensed professional, nor verification against the applicable codes and standards.

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Study data

One measurement per line: part; operator; trial; measurement

Part; Operator; Trial; Measurement
1; A; 1; 0.29
2; A; 1; -0.56
3; A; 1; 1.34
4; A; 1; 0.47
5; A; 1; -0.80
6; A; 1; 0.02
7; A; 1; 0.59
8; A; 1; -0.31
9; A; 1; 2.26
10; A; 1; -1.36
1; A; 2; 0.41
2; A; 2; -0.68
3; A; 2; 1.17
4; A; 2; 0.50
5; A; 2; -0.92
6; A; 2; -0.11
7; A; 2; 0.75
8; A; 2; -0.20
9; A; 2; 1.99
10; A; 2; -1.25
1; A; 3; 0.64
2; A; 3; -0.58
3; A; 3; 1.27
4; A; 3; 0.64
5; A; 3; -0.84
6; A; 3; -0.21
7; A; 3; 0.66
8; A; 3; -0.17
9; A; 3; 2.01
10; A; 3; -1.31
1; B; 1; 0.08
2; B; 1; -0.47
3; B; 1; 1.19
4; B; 1; 0.01
5; B; 1; -0.56
6; B; 1; -0.20
7; B; 1; 0.47
8; B; 1; -0.63
9; B; 1; 1.80
10; B; 1; -1.68
1; B; 2; 0.25
2; B; 2; -1.22
3; B; 2; 0.94
4; B; 2; 1.03
5; B; 2; -1.20
6; B; 2; 0.22
7; B; 2; 0.55
8; B; 2; 0.08
9; B; 2; 2.12
10; B; 2; -1.62
1; B; 3; 0.07
2; B; 3; -0.68
3; B; 3; 1.34
4; B; 3; 0.20
5; B; 3; -1.28
6; B; 3; 0.06
7; B; 3; 0.83
8; B; 3; -0.34
9; B; 3; 2.19
10; B; 3; -1.50
1; C; 1; 0.04
2; C; 1; -1.38
3; C; 1; 0.88
4; C; 1; 0.14
5; C; 1; -1.46
6; C; 1; -0.29
7; C; 1; 0.02
8; C; 1; -0.46
9; C; 1; 1.77
10; C; 1; -1.49
1; C; 2; -0.11
2; C; 2; -1.13
3; C; 2; 1.09
4; C; 2; 0.20
5; C; 2; -1.07
6; C; 2; -0.67
7; C; 2; 0.01
8; C; 2; -0.56
9; C; 2; 1.45
10; C; 2; -1.77
1; C; 3; -0.15
2; C; 3; -0.96
3; C; 3; 0.67
4; C; 3; 0.11
5; C; 3; -1.45
6; C; 3; -0.49
7; C; 3; 0.21
8; C; 3; -0.49
9; C; 3; 1.87
10; C; 3; -2.16

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Crossed, balanced study: every operator measures every part the same number of times, in random order. Typical: 10 parts, 3 operators, 2 or 3 trials.

Method

Calculation method

Remove interaction if p >

Study variation spread

Characteristic tolerance

Lower limit (LSL)

Upper limit (USL)

In the same unit as the measurements. Leave USL ≤ LSL to skip %GRR of tolerance.

—%GRR of total variation

—

Variance components

Components of variation

Contribution to variance, % of study variation and % of tolerance for each source.

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Average of each part by operator

Parallel, close lines mean good reproducibility; crossing lines indicate interaction.

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Method, assumptions and references

Equations used

Average and range: EV = R̄ · K1; AV = √[(X̄diff · K2)² − EV² ÷ (n · r)]; PV = Rp · K3; K = 1/d₂ or 1/d₂*

ANOVA: σ²_EV = MS_error; σ²_int = (MS_op×part − MS_error) ÷ r; σ²_AV = (MS_op − MS_op×part) ÷ (n · r); σ²_PV = (MS_part − MS_op×part) ÷ (k · r)

GRR = √(EV² + AV²); TV = √(GRR² + PV²); %GRR = 100 · GRR ÷ TV; %Tol = 100 · 6 · GRR ÷ (USL − LSL); ndc = ⌊1.41 · PV ÷ GRR⌋

Assumptions and limits

Crossed, balanced study, parts chosen to cover the process range, readings in random order. Negative components are set to zero.
K1 = 1/d₂ (0.8862 for 2 trials, 0.5908 for 3); K2 and K3 = 1/d₂* for one subgroup (0.7071 and 0.5231 for 2 and 3 operators; 0.3146 for 10 parts), as in the MSA manual.
Destructive (nested) and attribute studies need other methods. The system must be stable and have a resolution of at least 1/10 of process variation.

Standards and technical documents

AIAG. Measurement Systems Analysis (MSA) Reference Manual, 4th ed., 2010
ISO 22514-7:2021: Statistical methods in process management — Capability and performance — Part 7: Capability of measurement processes
Burdick, R. K.; Borror, C. M.; Montgomery, D. C. Design and Analysis of Gauge R&R Studies. ASA-SIAM, 2005
Montgomery, D. C. Introduction to Statistical Quality Control, 8th ed. Wiley, 2019, ch. 8
IATF 16949:2016, clause 7.1.5.1.1: Measurement systems analysis

U.S. regulations

ANSI/ISO/ASQ Q10012-2003: Measurement management systems — Requirements for measurement processes and measuring equipment
ANSI/NCSL Z540.3-2006: Requirements for the Calibration of Measuring and Test Equipment
21 CFR Part 820 (QMSR, incorporating ISO 13485:2016): control of monitoring and measuring equipment

Frequently asked questions

What %GRR is acceptable?

Up to 10% the system is acceptable; 10% to 30% may be accepted depending on the application; above 30% it is unacceptable. In the MSA manual example, %GRR is 26.7% by average and range.

ANOVA or average and range?

ANOVA uses all the data, separates the operator × part interaction and is preferred by the MSA manual. Average and range is simpler and gives similar values when there is no interaction.

What is ndc?

The number of distinct categories the gage can separate: 1.41 × PV ÷ GRR. Below 5, the system cannot be used to control the process.

How many parts and operators?

Typically 10 parts, 3 operators and 2 or 3 trials, 60 to 90 readings in total, in random order and without the operator seeing previous readings.

Variance components?

Components of variation?

Average of each part by operator?

Next step

Method, assumptions and references

Equations used

Assumptions and limits

Standards and technical documents

U.S. regulations

Frequently asked questions

Variance components

Components of variation

Average of each part by operator