Quality Core Tools Certification

MSA Measurement System Analysis

Rev a

Ing. Ricardo Espinosa Álvarez, CQE, CSQP, CRE, CSSBB, CMQ / OE, CPIM, CSCP
ASQ Certified Black Belt
Certified Specialist in Core Tools by AIAG
ISO9001: 2015 Certified Lead Auditor by Exemplar Global
Certified Auditor of Suppliers IATF 16949: 2016 by AIAG
VDA 6.3 Certified Auditor
Email: ricardo_espinosa@kaizensigma.com
www.kaizensigma.com
LinkedIn: Ricardo Espinosa Alvarez

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Contents

• MSA of continuous variables

• Calibration
• Resolution study
• Stability study
• Accuracy study. GM Method
• Type 1 study
• Bias and linearity study
• GR&R study Range method
• GR&R ANOVA Crossed
• GR&R ANOVA Nested
• MSA by attributes

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 MSA of continuous variables

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MSA concept

• The evaluation of measurement systems consists of determining the capacity and stability of
measurement systems through studies of:
• Stability
• Accuracy
• Linearity
• Repeatability
• Reproducibility

Reference: AIAG Measurement Systems Analysis Fourth Edition June, 2010

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 Bias and variance

• The most commonly used statistical properties to characterize the quality of the information are the
bias (bias) and the variance of the measurement system.
• Bias refers to the location of the data in relation to the reference value.
• Variance refers to the spread of the data.

bias= 𝑥 − (reference value)

Bias
Average readings
(Accuracy)

Value of
reference

Variance (Precision)
Reference: AIAG Measurement Systems Analysis Fourth Edition June, 2010
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Accuracy and precision

Accurate Not accurate

x xxx
xx xx x

Precise x xxx
xx xx x

x
x x
Not precise x x
x x x x x
x
x x x
x x
x x
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 MSA studies
Calibration 10: 1 Control Bias study Type 1 Bias and Study
resolution chart study linearity GR&R
study study

Bias X X X X

Accuracy
Stability X
(Bias)

Linearity X X
MSA
Resolution X X

Repeatability X X X

Precision
(Variance)
Reproducibility X

uncertainty X

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MSA studies of continuous variables

Calibration

Resolution

Stability

Accuracy

Type 1

Linearity

GR&R
Range method

GR&R
ANOVA method
(Crossed)

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 How to conduct an MSA

1. Verify the calibration of the instrument

2. Define and document the measurement procedure
3. Train measurement system operators
4. Plan the number of operators, parts and trials
5. Select the operators for the study
6. Select and number the study pieces
7. Be present during the study
8. The study is done in the units of the plan
9. Perform blind measurements and in random order
10. Verify correct data capture
11. Record possible sources of variation
12. Analyze the data
13. Get conclusions
14. Take actions
15. Document the study

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Calibration

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 MSA studies of continuous variables

Calibration

Resolution

Stability

Accuracy

Type 1

Linearity

GR&R
Range method

GR&R
ANOVA method
(Crossed)

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Importance of calibration

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 How is uncertainty estimated?

• To estimate the uncertainty of measurement, you must first identify the sources of the uncertainties.
Then estimate the influence of each of these sources of uncertainty.
• All sources of uncertainty are combined to obtain the combined uncertainty and multiplied by the
coverage factor (usually k = 2) associated with a confidence level (95%).

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How is uncertainty estimated?

• Regardless of the sources of uncertainty, there are two ways to estimate uncertainty:

• Type A: it is done using statistical methods, from repeated measurements.

• Type B: obtained from other information such as calibration certificates, manufacturer's specifications,
calculations, publications.

• A combination of both forms of estimation of measurement uncertainty is required.

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 Types of uncertainty
𝑈 = 𝑘𝑢
Expanded

𝑢 = 𝑢 +𝑢
Combined

Type A Type B
Random errors Systematic errors
𝑈 Δ𝑎 Δ𝑎
𝑢 = 𝑢 = 𝑢 =
The us is statistically evaluated 𝑘 12 24
𝑠
∑ 𝑥 −𝑥 𝑢 =
𝑠 =
𝑛−1
𝑛

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MSA Summary
MSA Study Matrix
GR&R Range GR&R ANOVA GR&R ANOVA MSA Attributes
Calibration Resolution Stability Accuracy Study Type 1 Linearity
method Crossed Nested (Concordance)
3 operators 1
1 operator 1 3 operators 1
Tolerance / 1 operator 1 1 operator 1 1 operator 1 instrument 10 pieces
instrument 1 2 operators 1 instrument 15 pairs
resolution ≥10 instrument 1 instrument 1 instrument 5 covering the 3 operators 50 pieces
Recommended Uncertainty pattern 5 times instrument 5 pieces of parts spanning
and Process standard standard measured standards tolerance of the measured 3 times 25 OK and
method calculation per shift for 4 measured once per product tolerance, 5
variation / measured 10 50 times (Minitab measured 12 product, measured 3 25 NOT OK (Example AIAG)
w eeks (100 operator pairs measured by
resolution ≥10 times Example) times each times by each
readings) each operator
operator

% GR & R:
Tolerance /
<10% is % GR & R: <10%
resolution % agreement:
Acceptable 10% is Acceptable 10%
≥10 and The 95% bias Bias: p-value> ≥ 90% Acceptable ≥ 80%
AIAG acceptance No out of to 30% to 30% Acceptable
None Process interval None 0.05 Linearity: p- None Marginal <80% Not
criteria control points Acceptable with with improvement
variation / contains zero. value> 0.05 Acceptable Kappa: <0.4 Bad>
improvement plan. > 30% Not
resolution 0.75 Good to excellent
plan. > 30% Not Acceptable ndc≥ 5
≥10
Acceptable

Practical:% GR &
Practical:% GR &
R: <10% is % GR & R: <10% is
GM: Uncertainty VDA: GM: Bias less VDA: Cg> 1.33 R: <10% is
Practical: No GM: Bias and Acceptable 10% Acceptable 10% to Practical:% agreement: ≥
<5% of Resolution than 10% of and Cgk> 1.33 Acceptable 10% to
Other acceptance points outside linearity <10% to 30% 30% Acceptable with 90% Acceptable ≥ 80%
product <5% of the tolerance Resolution <5% 30% Acceptable
criteria the control of product Acceptable with improvement plan. > Marginal <80% Not
tolerance product of the of product with improvement
limits tolerance improvement 30% Not Acceptable Acceptable
(Example) tolerance product tolerance plan. > 30% Not
plan. > 30% Not ndc≥ 5
Acceptable ndc ≥ 5
Acceptable

1 instrument for
1 instrument for each 1 instrument for each
Number of studies each type of 1 measuring system for each
All instruments All instruments As required All instruments All instruments As required type of measurement type of measurement
(recommended) measurement type of measuring system
system system
system

Frequency (AIAG /
N/A N/A N/A N/A N/A N/A N/A N/A N/A N/A
IATF)

Every training and

Frequency 1 time at start Every line Every line Calibration or training
Calibration periods Every line release Every line release before GR&R Calibration periods annual
(recommended) of use release release periods
ANOVA
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 Resolution study

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MSA studies of continuous variables

Calibration

Resolution

Stability

Accuracy

Type 1

Linearity

GR&R
Range method

GR&R
ANOVA method
(Crossed)

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 Resolution

• Smallest unit of scale of an instrument

Lower resolution

Resolution = 1

Higher resolution

Resolution = 0.1

Reference: AIAG Measurement Systems Analysis Fourth Edition June, 2010

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Properties of a good measurement system

• Adequate resolution. Measurement increments should be small relative to process variation or

specification limits.

Reference: AIAG Measurement Systems Analysis Fourth Edition June, 2010

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 Product tolerance

Tolerance =
USL-LSL
Nominal

LSL USL
Lower Upper
specification limit specification
limit

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Empirical Rule 10 to 1

Tolerancia
The smallest unit of the
instrument should divide the
tolerance or variation of the
process into 10 or more
parts (whichever is less)

6σ
LIE LSE ≥ 10
6σ Resolution
Tolerancia

Product tolerance
≥ 10
Resolution

LIE LSE
6σ
Reference: AIAG Measurement Systems Analysis Fourth Edition June, 2010
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 Example of empirical rule 10 to 1
Instrument: Caliper
Product: Shaft
Characteristic: Diameter

Specification: 150±100 mm
USL= 250 mm
LSL= 50 mm
Tolerance= 200 mm
Std dev= 14.73 mm
Resolution: 1 mm

TOL/Res= 200 Resolution acceptable

6Sigma/Res= 88.4 Resolution acceptable

1 132
2 156
3 124
4 147
5 137
6 161
7 141
8 167
9 142
10 166

Std dev= 14.728 mm

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Inadequate resolution

• Another good indication of poor resolution is on a normal probability plot, where the data is stacked in
groups rather than flowing along the 45-degree line.

Reference: AIAG Measurement Systems Analysis Fourth Edition June, 2010

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 MSA Summary
MSA Study Matrix
GR&R Range GR&R ANOVA GR&R ANOVA MSA Attributes
Calibration Resolution Stability Accuracy Study Type 1 Linearity
method Crossed Nested (Concordance)
3 operators 1
1 operator 1 3 operators 1
Tolerance / 1 operator 1 1 operator 1 1 operator 1 instrument 10 pieces
instrument 1 2 operators 1 instrument 15 pairs
resolution ≥10 instrument 1 instrument 1 instrument 5 covering the 3 operators 50 pieces
Recommended Uncertainty pattern 5 times instrument 5 pieces of parts spanning
and Process standard standard measured standards tolerance of the measured 3 times 25 OK and
method calculation per shift for 4 measured once per product tolerance, 5
variation / measured 10 50 times (Minitab measured 12 product, measured 3 25 NOT OK (Example AIAG)
w eeks (100 operator pairs measured by
resolution ≥10 times Example) times each times by each
readings) each operator
operator

% GR & R:
Tolerance /
<10% is % GR & R: <10%
resolution % agreement:
Acceptable 10% is Acceptable 10%
≥10 and The 95% bias Bias: p-value> ≥ 90% Acceptable ≥ 80%
AIAG acceptance No out of to 30% to 30% Acceptable
None Process interval None 0.05 Linearity: p- None Marginal <80% Not
criteria control points Acceptable with with improvement
variation / contains zero. value> 0.05 Acceptable Kappa: <0.4 Bad>
improvement plan. > 30% Not
resolution 0.75 Good to excellent
plan. > 30% Not Acceptable ndc≥ 5
≥10
Acceptable

Practical:% GR &
Practical:% GR &
R: <10% is % GR & R: <10% is
GM: Uncertainty VDA: GM: Bias less VDA: Cg> 1.33 R: <10% is
Practical: No GM: Bias and Acceptable 10% Acceptable 10% to Practical:% agreement: ≥
<5% of Resolution than 10% of and Cgk> 1.33 Acceptable 10% to
Other acceptance points outside linearity <10% to 30% 30% Acceptable with 90% Acceptable ≥ 80%
product <5% of the tolerance Resolution <5% 30% Acceptable
criteria the control of product Acceptable with improvement plan. > Marginal <80% Not
tolerance product of the of product with improvement
limits tolerance improvement 30% Not Acceptable Acceptable
(Example) tolerance product tolerance plan. > 30% Not
plan. > 30% Not ndc≥ 5
Acceptable ndc ≥ 5
Acceptable

1 instrument for
1 instrument for each 1 instrument for each
Number of studies each type of 1 measuring system for each
All instruments All instruments As required All instruments All instruments As required type of measurement type of measurement
(recommended) measurement type of measuring system
system system
system

Frequency (AIAG /
N/A N/A N/A N/A N/A N/A N/A N/A N/A N/A
IATF)

Every training and

Frequency 1 time at start Every line Every line Calibration or training
Calibration periods Every line release Every line release before GR&R Calibration periods annual
(recommended) of use release release periods
ANOVA
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Stability study

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 MSA studies of continuous variables

Calibration

Resolution

Stability

Accuracy

Type 1

Linearity

GR&R
Range method

GR&R
ANOVA method
(Crossed)

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Properties of a good measurement system

• The measurement system must be in statistical control. Under repeatable conditions, variation in the
measurement system is due only to common causes and not special causes. This is known as statistical
stability and is evaluated by graphical methods.

Reference: AIAG Measurement Systems Analysis Fourth Edition June, 2010

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 Variation types

Variation due to common causes

Variation due to special causes ? ?

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Common causes

• Many sources of variation that consistently act on the process

• They produce a stable and repeatable distribution over time, known as a state of statistical control.
• The result of the process is stable.

Reference: AIAG Statistical Process Control Second Edition July, 2005

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 Special causes

• Factors that cause variation that affects only a part of the result of the process.
• They are intermittent and unpredictable
• Special causes are identified by one or more points outside the control limits or non-random patterns
of points within the control limits.
• The process is not stable
• They can be harmful (remove) or beneficial (make permanent)

? ?

Reference: AIAG Statistical Process Control Second Edition July, 2005

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Process Stability

A stable process shows a control chart with no out-of-control points

Longitud de perno
U C L=3.4728
3.46
Sample M ean

3.44
_
_
3.42 X=3.4227

3.40

3.38
LC L=3.3726
1 3 5 7 9 11 13 15 17 19 21 23 25
Sample

0.20
U C L=0.1838

0.15
Sample Range

0.10 _
R=0.0869

0.05

0.00 LC L=0
1 3 5 7 9 11 13 15 17 19 21 23 25
Sample

Reference: AIAG Measurement Systems Analysis Fourth Edition June, 2010

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 How to select the control chart

Type of
measurement

Continuous
Attribute
variable

n=1 n: 2-8 n> 8 Defective unit Defects

I-MR X-R X-S p np c or

Sample Constant Constant Constant Constant Constant Constant Constant

size or variable or variable

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Average control chart rules

Rule 1
Any point outside of limit controls
10.00

9.00 LCS

8.00
Average

7.00
LC
6.00

5.00 LCI

4.00
1 3 5 7 9 11 13 15 17 19 21 23 25
Sample

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 Range control chart rules

Rule 1
Any point outside of limit controls
1.6

1.4

1.2
LCS
1
Range

0.8

0.6

0.4
R
0.2

0
LCI
1 3 5 7 9 11 13 15 17 19 21 23 25
Sample

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Xbar-R stability study

• Obtain a production part in the middle range of the measurements as a standard sample for stability
analysis.
• Measure the standard sample 3-5 times on a periodic basis (daily, weekly) at different times.
• Plot the information on an Average-Range control chart
• Establish control limits and evaluate unstable or out-of-control conditions using standard control chart
analysis

1 operator
1 instrument
1 piece measured multiple
times in a period of time
Reference: AIAG Measurement Systems Analysis Fourth Edition June, 2010
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 Xbar-R stability study

Average Plot: The Change in Bias

Over Time

Range Plot: The Change in

Repeatability Over Time

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Xbar-R stability study example

Day Time Measurement 1 Measurem ent 2 Measurement 3 Measurem ent 4 Measurement 5
• Example: You want to evaluate a certain tube 1 1 0.249 0.246 0.248 0.247 0.249

diameter measuring instrument. There is one 2

3
0.25
0.249
0.248
0.25
0.247
0.25
0.248
0.25
0.249
0.252
piece, which is used to carry out 100 2
4
1
0.248
0.246
0.25
0.251
0.248
0.252
0.25
0.249
0.244
0.251
measurements by a single operator for five 2 0.252 0.245 0.252 0.249 0.247

days, four times a day and five times each 0.251 0.249 0.253 0.247 0.248
3
4 0.252 0.249 0.247 0.249 0.25
time. Evaluate the stability of the measurement 3 1
2
0.251
0.248
0.249
0.255
0.25
0.25
0.251
0.252
0.25
0.252
system 3 0.25 0.25 0.253 0.249 0.248
4 0.251 0.25 0.247 0.249 0.25
4 1 0.249 0.252 0.249 0.25 0.251
2 0.252 0.247 0.25 0.248 0.251
3 0.252 0.25 0.252 0.248 0.253
4 0.248 0.25 0.251 0.254 0.25
5 1 0.25 0.25 0.252 0.249 0.248
2 0.251 0.248 0.247 0.247 0.248
3 0.249 0.246 0.25 0.248 0.252
4 0.249 0.249 0.253 0.251 0.25

Stability.xls
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 Xbar-R stability study example

Stat> Control Charts> Variable charts for

subgroups> Xbar-R

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Xbar-R stability study example

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 MSA Summary
MSA Study Matrix
GR&R Range GR&R ANOVA GR&R ANOVA MSA Attributes
Calibration Resolution Stability Accuracy Study Type 1 Linearity
method Crossed Nested (Concordance)
3 operators 1
1 operator 1 3 operators 1
Tolerance / 1 operator 1 1 operator 1 1 operator 1 instrument 10 pieces
instrument 1 2 operators 1 instrument 15 pairs
resolution ≥10 instrument 1 instrument 1 instrument 5 covering the 3 operators 50 pieces
Recommended Uncertainty pattern 5 times instrument 5 pieces of parts spanning
and Process standard standard measured standards tolerance of the measured 3 times 25 OK and
method calculation per shift for 4 measured once per product tolerance, 5
variation / measured 10 50 times (Minitab measured 12 product, measured 3 25 NOT OK (Example AIAG)
w eeks (100 operator pairs measured by
resolution ≥10 times Example) times each times by each
readings) each operator
operator

% GR & R:
Tolerance /
<10% is % GR & R: <10%
resolution % agreement:
Acceptable 10% is Acceptable 10%
≥10 and The 95% bias Bias: p-value> ≥ 90% Acceptable ≥ 80%
AIAG acceptance No out of to 30% to 30% Acceptable
None Process interval None 0.05 Linearity: p- None Marginal <80% Not
criteria control points Acceptable with with improvement
variation / contains zero. value> 0.05 Acceptable Kappa: <0.4 Bad>
improvement plan. > 30% Not
resolution 0.75 Good to excellent
plan. > 30% Not Acceptable ndc≥ 5
≥10
Acceptable

Practical:% GR &
Practical:% GR &
R: <10% is % GR & R: <10% is
GM: Uncertainty VDA: GM: Bias less VDA: Cg> 1.33 R: <10% is
Practical: No GM: Bias and Acceptable 10% Acceptable 10% to Practical:% agreement: ≥
<5% of Resolution than 10% of and Cgk> 1.33 Acceptable 10% to
Other acceptance points outside linearity <10% to 30% 30% Acceptable with 90% Acceptable ≥ 80%
product <5% of the tolerance Resolution <5% 30% Acceptable
criteria the control of product Acceptable with improvement plan. > Marginal <80% Not
tolerance product of the of product with improvement
limits tolerance improvement 30% Not Acceptable Acceptable
(Example) tolerance product tolerance plan. > 30% Not
plan. > 30% Not ndc≥ 5
Acceptable ndc ≥ 5
Acceptable

1 instrument for
1 instrument for each 1 instrument for each
Number of studies each type of 1 measuring system for each
All instruments All instruments As required All instruments All instruments As required type of measurement type of measurement
(recommended) measurement type of measuring system
system system
system

Frequency (AIAG /
N/A N/A N/A N/A N/A N/A N/A N/A N/A N/A
IATF)

Every training and

Frequency 1 time at start Every line Every line Calibration or training
Calibration periods Every line release Every line release before GR&R Calibration periods annual
(recommended) of use release release periods
ANOVA
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Accuracy study

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 MSA studies of continuous variables

Calibration

Resolution

Stability

Accuracy

Type 1

Linearity

GR&R
Range method

GR&R
ANOVA method
(Crossed)

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Accuracy study

1 operator
Bias
1 instrument
1 reference
standard measured
multiple times

Reference Average readings

value

Average bias is the difference between the average of

readings and the reference value

Reference: AIAG Measurement Systems Analysis Fourth Edition June, 2010

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 Accuracy study
GM method

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Accuracy study

Diameter 1 operator
LSL= 50.000 mm
USL= 250.000 mm
1 instrument
Tolerance= 200.000 mm

Reference= 118.000
1 reference standard

Reading Reference Bias % Bias

1 112 118.000 -6.000 -3.00% Bias acceptable
2 124 118.000 6.000 3.00% Bias acceptable
3 124 118.000 6.000 3.00% Bias acceptable
4 114 118.000 -4.000 -2.00% Bias acceptable
5 125 118.000 7.000 3.50% Bias acceptable
6 118 118.000 0.000 0.00% Bias acceptable
7 122 118.000 4.000 2.00% Bias acceptable
8 120 118.000 2.000 1.00% Bias acceptable
9 118 118.000 0.000 0.00% Bias acceptable
10 118 118.000 0.000 0.00% Bias acceptable

Average bias= 1.500

% Bias/Tol= 0.8% Bias acceptable

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 MSA Summary
MSA Study Matrix
GR&R Range GR&R ANOVA GR&R ANOVA MSA Attributes
Calibration Resolution Stability Accuracy Study Type 1 Linearity
method Crossed Nested (Concordance)
3 operators 1
1 operator 1 3 operators 1
Tolerance / 1 operator 1 1 operator 1 1 operator 1 instrument 10 pieces
instrument 1 2 operators 1 instrument 15 pairs
resolution ≥10 instrument 1 instrument 1 instrument 5 covering the 3 operators 50 pieces
Recommended Uncertainty pattern 5 times instrument 5 pieces of parts spanning
and Process standard standard measured standards tolerance of the measured 3 times 25 OK and
method calculation per shift for 4 measured once per product tolerance, 5
variation / measured 10 50 times (Minitab measured 12 product, measured 3 25 NOT OK (Example AIAG)
w eeks (100 operator pairs measured by
resolution ≥10 times Example) times each times by each
readings) each operator
operator

% GR & R:
Tolerance /
<10% is % GR & R: <10%
resolution % agreement:
Acceptable 10% is Acceptable 10%
≥10 and The 95% bias Bias: p-value> ≥ 90% Acceptable ≥ 80%
AIAG acceptance No out of to 30% to 30% Acceptable
None Process interval None 0.05 Linearity: p- None Marginal <80% Not
criteria control points Acceptable with with improvement
variation / contains zero. value> 0.05 Acceptable Kappa: <0.4 Bad>
improvement plan. > 30% Not
resolution 0.75 Good to excellent
plan. > 30% Not Acceptable ndc≥ 5
≥10
Acceptable

Practical:% GR &
Practical:% GR &
R: <10% is % GR & R: <10% is
GM: Uncertainty VDA: GM: Bias less VDA: Cg> 1.33 R: <10% is
Practical: No GM: Bias and Acceptable 10% Acceptable 10% to Practical:% agreement: ≥
<5% of Resolution than 10% of and Cgk> 1.33 Acceptable 10% to
Other acceptance points outside linearity <10% to 30% 30% Acceptable with 90% Acceptable ≥ 80%
product <5% of the tolerance Resolution <5% 30% Acceptable
criteria the control of product Acceptable with improvement plan. > Marginal <80% Not
tolerance product of the of product with improvement
limits tolerance improvement 30% Not Acceptable Acceptable
(Example) tolerance product tolerance plan. > 30% Not
plan. > 30% Not ndc≥ 5
Acceptable ndc ≥ 5
Acceptable

1 instrument for
1 instrument for each 1 instrument for each
Number of studies each type of 1 measuring system for each
All instruments All instruments As required All instruments All instruments As required type of measurement type of measurement
(recommended) measurement type of measuring system
system system
system

Frequency (AIAG /
N/A N/A N/A N/A N/A N/A N/A N/A N/A N/A
IATF)

Every training and

Frequency 1 time at start Every line Every line Calibration or training
Calibration periods Every line release Every line release before GR&R Calibration periods annual
(recommended) of use release release periods
ANOVA
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Type 1 Study

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 MSA studies of continuous variables

Calibration

Resolution

Stability

Accuracy

Type 1

Linearity

GR&R
Range method

GR&R
ANOVA method
(Crossed)

© Copyright by Kaizen Sigma. 49

Type I Study

• Use Type I Study to assess the capability of a measurement process. This study assesses the combined
effects of bias and repeatability based on multiple measurements of the same part.
• A Type 1 Study should be performed prior to other repeatability and reproducibility studies.

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 How to conduct a type 1 study

• Type 1 Study
• Measure the standard in the analyzed measurement system, 25-50 consecutive times, removing and
placing the standard.
• Measure the standard 10 times on an alternate measurement system (Micrometer, CMM, etc.) and
obtain the average. This is the reference value in Minitab analysis.
• Analyze in Minitab
• Analyze and eliminate the sources of variation in the measurement system.

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Type I Study
• Example: An electrode manufacturer wants to Diameter
evaluate the measurement system that
12.3057
measures the outer diameter of electrode
shafts to determine if the system accurately 12.3009
measures the shaft within the tolerance of 0.05 12.3037
mm. 12.2975
• An operator measures a reference shaft with a 12.3056
known outside diameter of 12.305 mm 50 12.3033
times. 12.3030
12.2965
12,2986
12.3031
12,3051
12.3056
12.3036
12,3091
12.3029

Type 1 study data

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 Type I Study

Stat>Quality Tools>Gage Study>Type 1 gage

study

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Type I Study

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 Capability

𝐾 ∗ 𝑇𝑜𝑙𝑒𝑟𝑎𝑛𝑐𝑒 0.2 ∗ 0.050

C = = = 0.46
6 ∗ 𝑆𝑡𝑑𝑒𝑣 6 ∗ 0.003631

𝐾 𝐵𝑖𝑎𝑠 0.2 −0.00231

Cgk = ∗ 𝑇𝑜𝑙 − = ∗ (0.050) − = 0.25
2 3 ∗ 𝑆𝑡𝑑𝑒𝑣 2 3 ∗ (0.003631)

K 0.20
%Var(Repe𝑎𝑡𝑎𝑏𝑖𝑙𝑖𝑡𝑦) = 𝑥100 = 𝑥100 = 43.57%
C 0.46

K 0.20
%Var(Repeteatability 𝑎𝑛𝑑 𝐵𝑖𝑎𝑠) = 𝑥100 = 𝑥100 = 81.10%
Cgk 0.25

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MSA Summary
MSA Study Matrix
GR&R Range GR&R ANOVA GR&R ANOVA MSA Attributes
Calibration Resolution Stability Accuracy Study Type 1 Linearity
method Crossed Nested (Concordance)
3 operators 1
1 operator 1 3 operators 1
Tolerance / 1 operator 1 1 operator 1 1 operator 1 instrument 10 pieces
instrument 1 2 operators 1 instrument 15 pairs
resolution ≥10 instrument 1 instrument 1 instrument 5 covering the 3 operators 50 pieces
Recommended Uncertainty pattern 5 times instrument 5 pieces of parts spanning
and Process standard standard measured standards tolerance of the measured 3 times 25 OK and
method calculation per shift for 4 measured once per product tolerance, 5
variation / measured 10 50 times (Minitab measured 12 product, measured 3 25 NOT OK (Example AIAG)
w eeks (100 operator pairs measured by
resolution ≥10 times Example) times each times by each
readings) each operator
operator

% GR & R:
Tolerance /
<10% is % GR & R: <10%
resolution % agreement:
Acceptable 10% is Acceptable 10%
≥10 and The 95% bias Bias: p-value> ≥ 90% Acceptable ≥ 80%
AIAG acceptance No out of to 30% to 30% Acceptable
None Process interval None 0.05 Linearity: p- None Marginal <80% Not
criteria control points Acceptable with with improvement
variation / contains zero. value> 0.05 Acceptable Kappa: <0.4 Bad>
improvement plan. > 30% Not
resolution 0.75 Good to excellent
plan. > 30% Not Acceptable ndc≥ 5
≥10
Acceptable

Practical:% GR &
Practical:% GR &
R: <10% is % GR & R: <10% is
GM: Uncertainty VDA: GM: Bias less VDA: Cg> 1.33 R: <10% is
Practical: No GM: Bias and Acceptable 10% Acceptable 10% to Practical:% agreement: ≥
<5% of Resolution than 10% of and Cgk> 1.33 Acceptable 10% to
Other acceptance points outside linearity <10% to 30% 30% Acceptable with 90% Acceptable ≥ 80%
product <5% of the tolerance Resolution <5% 30% Acceptable
criteria the control of product Acceptable with improvement plan. > Marginal <80% Not
tolerance product of the of product with improvement
limits tolerance improvement 30% Not Acceptable Acceptable
(Example) tolerance product tolerance plan. > 30% Not
plan. > 30% Not ndc≥ 5
Acceptable ndc ≥ 5
Acceptable

1 instrument for
1 instrument for each 1 instrument for each
Number of studies each type of 1 measuring system for each
All instruments All instruments As required All instruments All instruments As required type of measurement type of measurement
(recommended) measurement type of measuring system
system system
system

Frequency (AIAG /
N/A N/A N/A N/A N/A N/A N/A N/A N/A N/A
IATF)

Every training and

Frequency 1 time at start Every line Every line Calibration or training
Calibration periods Every line release Every line release before GR&R Calibration periods annual
(recommended) of use release release periods
ANOVA
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 Bias and linearity study

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MSA studies of continuous variables

Calibration

Resolution

Stability

Accuracy

Type 1

Linearity

GR&R
Range method

GR&R
ANOVA method
(Crossed)

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 Linearity

• Linearity is defined as the difference in accuracy (bias) between the master and the observed average
over the entire operating range of the instrument.

1 operator
Bias 2
1 instrument
Bias 1
Various parts covering
the range of the
instrument
Multiple measurements
of the same part
VR Lower part Top of the 1 pattern reading
of the range range

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Linearity

• Linearity can be evaluated using the following guidelines:

• Select g> = 5 parts whose measurements, due to process variation, cover the operating range of the
instrument.
• Measure each part by inspection layout to determine its reference value and to confirm that the
instrument's operating range is covered.
• Measure each part m> = 10 times on the instrument analyzed by one of the operators who normally
use the instrument.
• Select parts randomly to minimize recall of operator bias in measurements

Reference: AIAG Measurement Systems Analysis Fourth Edition June, 2010

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 Linearity

• Results study- Graph

• Calculate the bias of the parts for each measurement and the average bias for each part:

bias= 𝑥 − (reference value)

• Plot the individual biases and the average biases with respect to the reference values on a line graph.

Reference: AIAG Measurement Systems Analysis Fourth Edition June, 2010

© Copyright by Kaizen Sigma. 61

Linearity

• Graph the line “bias = 0” and review the graph for indications of special causes and acceptance of
linearity.
• For the linearity of the system to be acceptable, the line "bias = 0" must be completely within the
confidence interval.

Reference: AIAG Measurement Systems Analysis Fourth Edition June, 2010

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 Linearity

Hypothesis test for

linearity:
The bias line = 0 must be within the
Ho: Slope= 0
CI Confidence Interval
Ha: Slope ≠ 0

If p˃0.05
Acceptable
linearity
Hypothesis
testing for
accuracy:
Ho: Bias= 0
Ha: Bias ≠ 0
If p˃0.05
Acceptable
bias

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Linearity

• Example: An operator measured the thickness of five pieces, 12 times each, with the instrument to be
tested, and once with the standard (master instrument). The parts were selected in such a way as to
cover the operating range of the instrument (measuring instrument). The specification of the part is
0.6 to 1 mm. The information is shown in the following table. Determine the linearity and accuracy of
the instrument

Reading Reading Reading Reading Reading Reading Reading Reading Reading Reading Reading Reading
P a rt Reference 1 2 3 4 5 6 7 8 9 10 11 12
P1 0.60 0.593 0.624 0.632 0.590 0.580 0.610 0.603 0.595 0.600 0.602 0.598 0.608
P2 0.70 0.681 0.711 0.720 0.694 0.700 0.691 0.710 0.723 0.691 0.700 0.700 0.704
P3 0.80 0.795 0.810 0.791 0.814 0.800 0.788 0.798 0.796 0.800 0.810 0.798 0.802
P4 0.90 0.933 0.940 0.910 0.880 0.892 0.887 0.913 0.891 0.874 0.882 0.905 0.895
P5 1.00 0.992 0.990 0.990 0.980 1.000 1.000 1.014 1.022 1.010 0.990 1.010 0.988

MSA.xls data

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 Linearity

Data> Stack> Columns

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Linearity

Stat> Quality Tools> Measurement Study> Measurement

System Linearity and Bias Study

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 Linearity
Outcome
Hypothesis test for
linearity:
The bias line = 0 must be within the
Ho: Earring= 0
CI Confidence Interval
Ha: Slope ≠ 0

If p˃0.05
Acceptable
linearity
Hypothesis
testing for
accuracy:
Ho: Bias= 0
Ha: Bias ≠ 0
If p˃0.05
Acceptable
bias

© Copyright by Kaizen Sigma. 67

MSA Summary
MSA Study Matrix
GR&R Range GR&R ANOVA GR&R ANOVA MSA Attributes
Calibration Resolution Stability Accuracy Study Type 1 Linearity
method Crossed Nested (Concordance)
3 operators 1
1 operator 1 3 operators 1
Tolerance / 1 operator 1 1 operator 1 1 operator 1 instrument 10 pieces
instrument 1 2 operators 1 instrument 15 pairs
resolution ≥10 instrument 1 instrument 1 instrument 5 covering the 3 operators 50 pieces
Recommended Uncertainty pattern 5 times instrument 5 pieces of parts spanning
and Process standard standard measured standards tolerance of the measured 3 times 25 OK and
method calculation per shift for 4 measured once per product tolerance, 5
variation / measured 10 50 times (Minitab measured 12 product, measured 3 25 NOT OK (Example AIAG)
w eeks (100 operator pairs measured by
resolution ≥10 times Example) times each times by each
readings) each operator
operator

% GR & R:
Tolerance /
<10% is % GR & R: <10%
resolution % agreement:
Acceptable 10% is Acceptable 10%
≥10 and The 95% bias Bias: p-value> ≥ 90% Acceptable ≥ 80%
AIAG acceptance No out of to 30% to 30% Acceptable
None Process interval None 0.05 Linearity: p- None Marginal <80% Not
criteria control points Acceptable with with improvement
variation / contains zero. value> 0.05 Acceptable Kappa: <0.4 Bad>
improvement plan. > 30% Not
resolution 0.75 Good to excellent
plan. > 30% Not Acceptable ndc≥ 5
≥10
Acceptable

Practical:% GR &
Practical:% GR &
R: <10% is % GR & R: <10% is
GM: Uncertainty VDA: GM: Bias less VDA: Cg> 1.33 R: <10% is
Practical: No GM: Bias and Acceptable 10% Acceptable 10% to Practical:% agreement: ≥
<5% of Resolution than 10% of and Cgk> 1.33 Acceptable 10% to
Other acceptance points outside linearity <10% to 30% 30% Acceptable with 90% Acceptable ≥ 80%
product <5% of the tolerance Resolution <5% 30% Acceptable
criteria the control of product Acceptable with improvement plan. > Marginal <80% Not
tolerance product of the of product with improvement
limits tolerance improvement 30% Not Acceptable Acceptable
(Example) tolerance product tolerance plan. > 30% Not
plan. > 30% Not ndc≥ 5
Acceptable ndc ≥ 5
Acceptable

1 instrument for
1 instrument for each 1 instrument for each
Number of studies each type of 1 measuring system for each
All instruments All instruments As required All instruments All instruments As required type of measurement type of measurement
(recommended) measurement type of measuring system
system system
system

Frequency (AIAG /
N/A N/A N/A N/A N/A N/A N/A N/A N/A N/A
IATF)

Every training and

Frequency 1 time at start Every line Every line Calibration or training
Calibration periods Every line release Every line release before GR&R Calibration periods annual
(recommended) of use release release periods
ANOVA
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 GR&R study

© Copyright by Kaizen Sigma. 69

Properties of a good measurement system

• For product control, the variability of the measurement system should be small compared to the
specification limits. Evaluate the measurement system against the tolerance of the characteristic.

6𝜎 &
• %𝐺𝑅𝑅
For process control, the = of the measurement
variability 𝑥100 system must demonstrate effective resolution
𝑇𝑜𝑙𝑒𝑟𝑎𝑛𝑐𝑒
and be small compared to the variation of the manufacturing process. Evaluate the measurement
system against the 6 sigmas of process variation and / or the total variation of the MSA study.

𝜎 &
%𝐺𝑅𝑅 = 𝑥100
𝜎

Reference: AIAG Measurement Systems Analysis Fourth Edition June, 2010

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 Terminology

• Repeatability
• Variation in measurements obtained with a measuring instrument when used multiple times by an
operator when measuring the identical characteristic in the same part
• Reproducibility
• Variation in the average of measurements made by different operators using the same instrument
when measuring a characteristic in a part
• GRR or Gage R&R
• Instrument repeatability and reproducibility: the combined estimation of repeatability and
reproducibility of the measurement system.

Reference: AIAG Measurement Systems Analysis Fourth Edition June, 2010

© Copyright by Kaizen Sigma. 71

Repeatability

• Repeatability or precision is the variation in measurements made by a single operator on the same part
and with the same measuring instrument.

VR 1 operator
1 instrument
1 piece measured
several times
Repeatability

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 Reproducibility
•Reproducibility is the variation between the means of the
measurements made by several operators with the same
parts and with the same measuring instrument.

Good reproducibility Poor reproducibility

Operator 1 Operator 2 Operator 3 Operator 1 Operator 2 Operator 3

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Measurement Index -% GR&R

𝜎 & 6𝜎 &
%𝐺𝑅𝑅 = 𝑥100 %𝐺𝑅𝑅 = 𝑥100
𝜎 𝑇𝑜𝑙𝑒𝑟𝑎𝑛𝑐𝑖𝑎

• Estimate whatand Percentage of total variation comes from

measurement error.
• Includes both repeatability and reproducibility

Reference: AIAG Measurement Systems Analysis Fourth Edition June, 2010

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 GRR criteria

GRR Decision Comments

Less than Generally considered Recommended, especially useful for
10% acceptable classifying parts or when process
control is required
10% to 30% May be acceptable for The decision should be made, for
some applications example, on the importance of the
measure, cost of the measuring
instrument, cost of rework or repair.
Should be approved by the customer
Greater than Considered Every effort should be made to
30% unacceptable improve the measurement system.
This condition can be remedied by a
suitable measurement strategy. For
example, using the average of several
readings of the same part
characteristic to reduce measurement
variation.

Reference: AIAG Measurement Systems Analysis Fourth Edition June, 2010

© Copyright by Kaizen Sigma. 75

Number of Different Categories

𝜎
N𝑑𝑐 = 1.41
𝜎 &

• It is the number of divisions that the measurement system can measure through process variation.
• Indicates how well the process variation (runs and improvements) can be detected.
• There must be 5 or more different categories for the measurement system to be acceptable.

Reference: AIAG Measurement Systems Analysis Fourth Edition June, 2010

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 Number of Different Categories

1 Data Category

3
Categori
es
10
Categories

Reference: AIAG Measurement Systems Analysis Fourth Edition June, 2010

© Copyright by Kaizen Sigma. 77

Repeatability and Reproducibility

• Acceptable methods:
• Range method
• Average and Range method (including control chart method)
• ANOVA method

• All of these techniques are subject to the prerequisite of statistical stability.

Reference: AIAG Measurement Systems Analysis Fourth Edition June, 2010

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 GR&R study
Range method

© Copyright by Kaizen Sigma. 79

MSA studies of continuous variables

Calibration

Resolution

Stability

Accuracy

Type 1

Linearity

GR&R
Range method

GR&R
ANOVA method
(Crossed)

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 Range method

• Provides a quick approximation of the measurement variability.

• It only provides the general analysis of the measurement system.
• Does not break down variability into repeatability and reproducibility
• It is typically used as a quick check to ensure that the GRR has not changed.
• This approach has the potential to detect an unacceptable measurement system 80% of the time with
a sample size of 5 and 90% of the time with a sample size of 10.

Reference: AIAG Measurement Systems Analysis Fourth Edition June, 2010

© Copyright by Kaizen Sigma. 81

Range method

∑𝑅
A𝑣𝑒𝑟𝑎𝑔𝑒 R =
𝑛
𝑅
𝐺𝑅𝑅 =
𝑑∗

𝐺𝑅𝑅
%𝐺𝑅𝑅 = 100 ∗
𝑃𝑟𝑜𝑐𝑒𝑠𝑠 𝑠𝑡𝑎𝑛𝑑𝑎𝑟𝑑 𝑑𝑒𝑣𝑖𝑎𝑡𝑖𝑜𝑛

Reference: AIAG Measurement Systems Analysis Fourth Edition June, 2010

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 Range Method Example

Part Operator A Operator B Range

1 0.85 0.80 0.05
2 0.75 0.70 0.05
3 1.00 0.95 0.05
4 0.45 0.55 0.10
5 0.50 0.60 0.10

Process standard deviation = 0.0777

Short GR&R data

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MSA Summary
MSA Study Matrix
GR&R Range GR&R ANOVA GR&R ANOVA MSA Attributes
Calibration Resolution Stability Accuracy Study Type 1 Linearity
method Crossed Nested (Concordance)
3 operators 1
1 operator 1 3 operators 1
Tolerance / 1 operator 1 1 operator 1 1 operator 1 instrument 10 pieces
instrument 1 2 operators 1 instrument 15 pairs
resolution ≥10 instrument 1 instrument 1 instrument 5 covering the 3 operators 50 pieces
Recommended Uncertainty pattern 5 times instrument 5 pieces of parts spanning
and Process standard standard measured standards tolerance of the measured 3 times 25 OK and
method calculation per shift for 4 measured once per product tolerance, 5
variation / measured 10 50 times (Minitab measured 12 product, measured 3 25 NOT OK (Example AIAG)
w eeks (100 operator pairs measured by
resolution ≥10 times Example) times each times by each
readings) each operator
operator

% GR & R:
Tolerance /
<10% is % GR & R: <10%
resolution % agreement:
Acceptable 10% is Acceptable 10%
≥10 and The 95% bias Bias: p-value> ≥ 90% Acceptable ≥ 80%
AIAG acceptance No out of to 30% to 30% Acceptable
None Process interval None 0.05 Linearity: p- None Marginal <80% Not
criteria control points Acceptable with with improvement
variation / contains zero. value> 0.05 Acceptable Kappa: <0.4 Bad>
improvement plan. > 30% Not
resolution 0.75 Good to excellent
plan. > 30% Not Acceptable ndc≥ 5
≥10
Acceptable

Practical:% GR &
Practical:% GR &
R: <10% is % GR & R: <10% is
GM: Uncertainty VDA: GM: Bias less VDA: Cg> 1.33 R: <10% is
Practical: No GM: Bias and Acceptable 10% Acceptable 10% to Practical:% agreement: ≥
<5% of Resolution than 10% of and Cgk> 1.33 Acceptable 10% to
Other acceptance points outside linearity <10% to 30% 30% Acceptable with 90% Acceptable ≥ 80%
product <5% of the tolerance Resolution <5% 30% Acceptable
criteria the control of product Acceptable with improvement plan. > Marginal <80% Not
tolerance product of the of product with improvement
limits tolerance improvement 30% Not Acceptable Acceptable
(Example) tolerance product tolerance plan. > 30% Not
plan. > 30% Not ndc≥ 5
Acceptable ndc ≥ 5
Acceptable

1 instrument for
1 instrument for each 1 instrument for each
Number of studies each type of 1 measuring system for each
All instruments All instruments As required All instruments All instruments As required type of measurement type of measurement
(recommended) measurement type of measuring system
system system
system

Frequency (AIAG /
N/A N/A N/A N/A N/A N/A N/A N/A N/A N/A
IATF)

Every training and

Frequency 1 time at start Every line Every line Calibration or training
Calibration periods Every line release Every line release before GR&R Calibration periods annual
(recommended) of use release release periods
ANOVA
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 GR&R
ANOVA Crossed Method

© Copyright by Kaizen Sigma. 85

MSA studies of continuous variables

Calibration

Resolution

Stability

Accuracy

Type 1

Linearity

GR&R
Range method

GR&R
ANOVA
(Crossed)
method

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 GR&R ANOVA Crossed Method

• Study method.
• Obtain a sample of n≥10 parts that represent the current or expected range of the process variation.
• Refer the operators as A, B, C, etc. and number the parts from 1 to n in such a way that the numbers
are not visible to operators.
• Calibrate the instrument if this is part of the normal measurement system procedure. Have the
operator A measure n parts in random order and record the results on row 1.
• Make operators B and C measure the same n parts without seeing each other's readings. Enter the
results on lines 6 and 11, respectively.

Reference: AIAG Measurement Systems Analysis Fourth Edition June, 2010

© Copyright by Kaizen Sigma. 87

GR&R ANOVA Crossed Method

• Example: It is desired to carry out a repeatability and reproducibility study, for which 3 operators and a
calibrator were selected to measure the thickness of certain seals, whose specification is 3 to 5 mm.
These seals were measured three times by each operator. See data table.
•

Trial Operator P1 P2 P3 P4 P5 P6 P7 P8 P9 P10

1 A 3.640 3.935 3.845 4.165 4.281 3.433 3.804 3.931 4.146 4.228
2. A 3.575 3.930 3.882 4.225 4.309 3.446 3.845 3.906 4.153 4.218
3. A 3.617 3.899 3.793 4.183 4.252 3.368 3.788 3.898 4.198 4.247
1 B 3.588 3.918 3.850 4.162 4.227 3.406 3.803 3.866 4.147 4.221
2. B 3.629 3.907 3.849 4.208 4.234 3.394 3.804 3.849 4.098 4.219
3. B 3.631 3.945 3.851 4.235 4.278 3.396 3.800 3.875 4.124 4.213
1 C 3.577 3.881 3.853 4.177 4.265 3.433 3.811 3.851 4.141 4.224
2. C 3.583 3.872 3.781 4.161 4.239 3.380 3.800 3.886 4.152 4.211
3. C 3.629 3.874 3.797 4.175 4.199 3.400 3.787 3.852 4.125 4.225

MSA

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 GR&R ANOVA Crossed Method

Data>Stack>Columns

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GR&R ANOVA Crossed Method

Stat>Quality Tools>Gage Study>Gage R&R

Study (Crossed)

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 GR&R ANOVA Crossed Method

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GR&R ANOVA Crossed Method

Resultado 𝜎 =𝜎 +𝜎 &

𝜎 & =𝜎 +𝜎

𝜎 =𝜎 +𝜎 ∗

𝜎 &
%𝐺𝑅𝑅 = 𝑥100
𝜎

6𝜎 &
%𝐺𝑅𝑅 = 𝑥100
𝑇𝑜𝑙𝑒𝑟𝑎𝑛𝑐𝑒

<10=Acceptable
10-30=Marginal
>30=Non aceptable
ndc = 1.41
𝜎
Ndc shall be 5 or more
𝜎
92
&
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 GR&R ANOVA Crossed Method

Gage R&R (ANOVA) Report for Valor

Reported by:
Gage name: The largest bar must be the Tolerance:
Date of study:variation from piece to piece Misc:

Components of Variation Valor by Pieza

100 % Contribution 4.4
% Study Var
% Tolerance
Percent

4.0
50

3.6

0 1 10 2 3 4 5 6 7 8 9
There should be no Gage R&R Repeat Reprod Part-to-Part
Pieza
out-of-control points R Chart by Operador
A B C Valor by Operador
UCL=0.1051
Sample Range

0.10 4.4

0.05 _
R=0.0408 4.0

0.00 LCL=0
3.6
1 1 0 2 3 4 5 6 7 8 9 1 10 2 3 4 5 6 7 8 9 1 1 0 2 3 4 5 6 7 8 9

Pieza A B C
More than Operador
50% of Xbar Chart by Operador
A B C
Pieza * Operador Interaction
points must 4.4
Sample Mean

UCL=3.966 4.4
be outside 4.0
__
X=3.924
Operador
A

the limits of B

Average
4.0 C
3.6 LCL=3.883
control
1 1 0 2 3 4 5 6 7 8 9 1 10 2 3 4 5 6 7 8 9 1 1 0 2 3 4 5 6 7 8 9 3.6

Pieza 1 10 2 3 4 5 6 7 8 9
Pieza

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MSA Summary
MSA Study Matrix
GR&R Range GR&R ANOVA GR&R ANOVA MSA Attributes
Calibration Resolution Stability Accuracy Study Type 1 Linearity
method Crossed Nested (Concordance)
3 operators 1
1 operator 1 3 operators 1
Tolerance / 1 operator 1 1 operator 1 1 operator 1 instrument 10 pieces
instrument 1 2 operators 1 instrument 15 pairs
resolution ≥10 instrument 1 instrument 1 instrument 5 covering the 3 operators 50 pieces
Recommended Uncertainty pattern 5 times instrument 5 pieces of parts spanning
and Process standard standard measured standards tolerance of the measured 3 times 25 OK and
method calculation per shift for 4 measured once per product tolerance, 5
variation / measured 10 50 times (Minitab measured 12 product, measured 3 25 NOT OK (Example AIAG)
w eeks (100 operator pairs measured by
resolution ≥10 times Example) times each times by each
readings) each operator
operator

% GR & R:
Tolerance /
<10% is % GR & R: <10%
resolution % agreement:
Acceptable 10% is Acceptable 10%
≥10 and The 95% bias Bias: p-value> ≥ 90% Acceptable ≥ 80%
AIAG acceptance No out of to 30% to 30% Acceptable
None Process interval None 0.05 Linearity: p- None Marginal <80% Not
criteria control points Acceptable with with improvement
variation / contains zero. value> 0.05 Acceptable Kappa: <0.4 Bad>
improvement plan. > 30% Not
resolution 0.75 Good to excellent
plan. > 30% Not Acceptable ndc≥ 5
≥10
Acceptable

Practical:% GR &
Practical:% GR &
R: <10% is % GR & R: <10% is
GM: Uncertainty VDA: GM: Bias less VDA: Cg> 1.33 R: <10% is
Practical: No GM: Bias and Acceptable 10% Acceptable 10% to Practical:% agreement: ≥
<5% of Resolution than 10% of and Cgk> 1.33 Acceptable 10% to
Other acceptance points outside linearity <10% to 30% 30% Acceptable with 90% Acceptable ≥ 80%
product <5% of the tolerance Resolution <5% 30% Acceptable
criteria the control of product Acceptable with improvement plan. > Marginal <80% Not
tolerance product of the of product with improvement
limits tolerance improvement 30% Not Acceptable Acceptable
(Example) tolerance product tolerance plan. > 30% Not
plan. > 30% Not ndc≥ 5
Acceptable ndc ≥ 5
Acceptable

1 instrument for
1 instrument for each 1 instrument for each
Number of studies each type of 1 measuring system for each
All instruments All instruments As required All instruments All instruments As required type of measurement type of measurement
(recommended) measurement type of measuring system
system system
system

Frequency (AIAG /
N/A N/A N/A N/A N/A N/A N/A N/A N/A N/A
IATF)

Every training and

Frequency 1 time at start Every line Every line Calibration or training
Calibration periods Every line release Every line release before GR&R Calibration periods annual
(recommended) of use release release periods
ANOVA
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 GR&R ANOVA Nested

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Destructive or non-repeatable tests

• Applies to homogeneous material or material that can be measured only once.

• It can be destructive tests
• Pairs of very similar pieces (consecutive) or 2 samples of homogeneous material are taken.

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 GR&R ANOVA Nested

• Study methodology:
• 3 Operators are selected
• It is done with a measuring instrument
• 15 pairs of pieces are taken and assigned to each operator (5 pairs to
each). Each pair is made of consecutive pieces.
• See the following scheme:

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GR&R ANOVA Nested

Lot Operator Operator Operator

A B C
Pair 1 Pair 6 Pair 11
Monday
Pair 2 Par 7 Pair 12
Tuesday Pieces or
samples from
Par 3 Par 8 Par 13 different batches
Wednesday (Batches should
be as different as
Pair 4 Pair 9 possible)
Pair 14

Thursday
Par 5 Pair 10 Par 15
Friday

Consecutive pieces or samples from the same

lot (They should be as similar as possible)

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 GR&R ANOVA Nested
15 pairs of pieces were taken for destructive testing and reproducibility analysis. Three
operators measured 5 pairs each. The specification is 10 to 20 mm.

Stat>Quality Tools>Gage Study>Gage R&R

Study (Nested)

Destructiva.xls
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GR&R ANOVA Nested

Resultado

𝜎 &
%𝐺𝑅𝑅 = 𝑥100
𝜎

6𝜎 &
%𝐺𝑅𝑅 = 𝑥100
𝑇𝑜𝑙𝑒𝑟𝑎𝑛𝑐𝑒

<10=Acceptable
10-30=Marginal
>30=Non aceptable

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 GR&R ANOVA Nested

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MSA Summary
MSA Study Matrix
GR&R Range GR&R ANOVA GR&R ANOVA MSA Attributes
Calibration Resolution Stability Accuracy Study Type 1 Linearity
method Crossed Nested (Concordance)
3 operators 1
1 operator 1 3 operators 1
Tolerance / 1 operator 1 1 operator 1 1 operator 1 instrument 10 pieces
instrument 1 2 operators 1 instrument 15 pairs
resolution ≥10 instrument 1 instrument 1 instrument 5 covering the 3 operators 50 pieces
Recommended Uncertainty pattern 5 times instrument 5 pieces of parts spanning
and Process standard standard measured standards tolerance of the measured 3 times 25 OK and
method calculation per shift for 4 measured once per product tolerance, 5
variation / measured 10 50 times (Minitab measured 12 product, measured 3 25 NOT OK (Example AIAG)
w eeks (100 operator pairs measured by
resolution ≥10 times Example) times each times by each
readings) each operator
operator

% GR & R:
Tolerance /
<10% is % GR & R: <10%
resolution % agreement:
Acceptable 10% is Acceptable 10%
≥10 and The 95% bias Bias: p-value> ≥ 90% Acceptable ≥ 80%
AIAG acceptance No out of to 30% to 30% Acceptable
None Process interval None 0.05 Linearity: p- None Marginal <80% Not
criteria control points Acceptable with with improvement
variation / contains zero. value> 0.05 Acceptable Kappa: <0.4 Bad>
improvement plan. > 30% Not
resolution 0.75 Good to excellent
plan. > 30% Not Acceptable ndc≥ 5
≥10
Acceptable

Practical:% GR &
Practical:% GR &
R: <10% is % GR & R: <10% is
GM: Uncertainty VDA: GM: Bias less VDA: Cg> 1.33 R: <10% is
Practical: No GM: Bias and Acceptable 10% Acceptable 10% to Practical:% agreement: ≥
<5% of Resolution than 10% of and Cgk> 1.33 Acceptable 10% to
Other acceptance points outside linearity <10% to 30% 30% Acceptable with 90% Acceptable ≥ 80%
product <5% of the tolerance Resolution <5% 30% Acceptable
criteria the control of product Acceptable with improvement plan. > Marginal <80% Not
tolerance product of the of product with improvement
limits tolerance improvement 30% Not Acceptable Acceptable
(Example) tolerance product tolerance plan. > 30% Not
plan. > 30% Not ndc≥ 5
Acceptable ndc ≥ 5
Acceptable

1 instrument for
1 instrument for each 1 instrument for each
Number of studies each type of 1 measuring system for each
All instruments All instruments As required All instruments All instruments As required type of measurement type of measurement
(recommended) measurement type of measuring system
system system
system

Frequency (AIAG /
N/A N/A N/A N/A N/A N/A N/A N/A N/A N/A
IATF)

Every training and

Frequency 1 time at start Every line Every line Calibration or training
Calibration periods Every line release Every line release before GR&R Calibration periods annual
(recommended) of use release release periods
ANOVA
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 MSA by attributes
Agreement Analysis

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MSA by attributes
50 pieces were taken for visual inspection and a Reproducibility and Repeatability analysis.
Three operators inspected each part three times each.

Operador A Operador B Operador C

Pieza A1 A2 A3 B1 B2 B3 C1 C2 C3 Referencia 26 0 1 0 0 0 0 0 0 1 0
1 1 1 1 1 1 1 1 1 1 1 27 1 1 1 1 1 1 1 1 1 1
2 1 1 1 1 1 1 1 1 1 1 28 1 1 1 1 1 1 1 1 1 1
3 0 0 0 0 0 0 0 0 0 0 29 1 1 1 1 1 1 1 1 1 1
4 0 0 0 0 0 0 0 0 0 0 30 0 0 0 0 0 1 0 0 0 0
5 0 0 0 0 0 0 0 0 0 0 31 1 1 1 1 1 1 1 1 1 1
6 1 1 0 1 1 0 1 0 0 1 32 1 1 1 1 1 1 1 1 1 1
7 1 1 1 1 1 1 1 0 1 1 33 1 1 1 1 1 1 1 1 1 1
8 1 1 1 1 1 1 1 1 1 1 34 0 0 1 0 0 1 0 1 1 0
9 0 0 0 0 0 0 0 0 0 0 35 1 1 1 1 1 1 1 1 1 1
10 1 1 1 1 1 1 1 1 1 1 36 1 1 0 1 1 1 1 0 1 1
11 1 1 1 1 1 1 1 1 1 1 37 0 0 0 0 0 0 0 0 0 0
12 0 0 0 0 0 0 0 1 0 0 38 1 1 1 1 1 1 1 1 1 1
13 1 1 1 1 1 1 1 1 1 1 39 0 0 0 0 0 0 0 0 0 0
14 1 1 0 1 1 1 1 0 0 1 40 1 1 1 1 1 1 1 1 1 1
15 1 1 1 1 1 1 1 1 1 1
41 1 1 1 1 1 1 1 1 1 1
16 1 1 1 1 1 1 1 1 1 1
42 0 0 0 0 0 0 0 0 0 0
17 1 1 1 1 1 1 1 1 1 1
43 1 0 1 1 1 1 1 1 0 1
18 1 1 1 1 1 1 1 1 1 1
19 1 1 1 1 1 1 1 1 1 1 44 1 1 1 1 1 1 1 1 1 1
20 1 1 1 1 1 1 1 1 1 1 45 0 0 0 0 0 0 0 0 0 0
21 1 1 0 1 0 1 0 1 0 1 46 1 1 1 1 1 1 1 1 1 1
22 0 0 1 0 1 0 1 1 0 0 47 1 1 1 1 1 1 1 1 1 1
23 1 1 1 1 1 1 1 1 1 1 48 0 0 0 0 0 0 0 0 0 0
24 1 1 1 1 1 1 1 1 1 1 49 1 1 1 1 1 1 1 1 1 1
25 0 0 0 0 0 0 0 0 0 0 50 0 0 0 0 0 0 0 0 0 0
26 0 1 0 0 0 0 0 0 1 0 0 = No Pasa
1 = Pasa

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 MSA by attributes
50 pieces were taken for visual inspection and MSA analysis by attributes. Three operators
inspected each part three times each.

Stat> Quality Tools> Attribute Agreement Study

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MSA by attributes

Effectiveness
≥90% Acceptable
≥80% Marginal
<80% Not acceptable

Kappa
<0.4 Bad
> 0.75 Good to excellent

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 MSA by attributes

Effectiveness
≥90% Acceptable
≥80% Marginal
<80% Not acceptable

Kappa
<0.4 Bad
> 0.75 Good to excellent

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MSA by attributes

Effectiveness
≥90% Acceptable
≥80% Marginal
<80% Not acceptable

Kappa
<0.4 Bad
> 0.75 Good to excellent

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 MSA Summary
MSA Study Matrix
GR&R Range GR&R ANOVA GR&R ANOVA MSA Attributes
Calibration Resolution Stability Accuracy Study Type 1 Linearity
method Crossed Nested (Concordance)
3 operators 1
1 operator 1 3 operators 1
Tolerance / 1 operator 1 1 operator 1 1 operator 1 instrument 10 pieces
instrument 1 2 operators 1 instrument 15 pairs
resolution ≥10 instrument 1 instrument 1 instrument 5 covering the 3 operators 50 pieces
Recommended Uncertainty pattern 5 times instrument 5 pieces of parts spanning
and Process standard standard measured standards tolerance of the measured 3 times 25 OK and
method calculation per shift for 4 measured once per product tolerance, 5
variation / measured 10 50 times (Minitab measured 12 product, measured 3 25 NOT OK (Example AIAG)
w eeks (100 operator pairs measured by
resolution ≥10 times Example) times each times by each
readings) each operator
operator

% GR & R:
Tolerance /
<10% is % GR & R: <10%
resolution % agreement:
Acceptable 10% is Acceptable 10%
≥10 and The 95% bias Bias: p-value> ≥ 90% Acceptable ≥ 80%
AIAG acceptance No out of to 30% to 30% Acceptable
None Process interval None 0.05 Linearity: p- None Marginal <80% Not
criteria control points Acceptable with with improvement
variation / contains zero. value> 0.05 Acceptable Kappa: <0.4 Bad>
improvement plan. > 30% Not
resolution 0.75 Good to excellent
plan. > 30% Not Acceptable ndc≥ 5
≥10
Acceptable

Practical:% GR &
Practical:% GR &
R: <10% is % GR & R: <10% is
GM: Uncertainty VDA: GM: Bias less VDA: Cg> 1.33 R: <10% is
Practical: No GM: Bias and Acceptable 10% Acceptable 10% to Practical:% agreement: ≥
<5% of Resolution than 10% of and Cgk> 1.33 Acceptable 10% to
Other acceptance points outside linearity <10% to 30% 30% Acceptable with 90% Acceptable ≥ 80%
product <5% of the tolerance Resolution <5% 30% Acceptable
criteria the control of product Acceptable with improvement plan. > Marginal <80% Not
tolerance product of the of product with improvement
limits tolerance improvement 30% Not Acceptable Acceptable
(Example) tolerance product tolerance plan. > 30% Not
plan. > 30% Not ndc≥ 5
Acceptable ndc ≥ 5
Acceptable

1 instrument for
1 instrument for each 1 instrument for each
Number of studies each type of 1 measuring system for each
All instruments All instruments As required All instruments All instruments As required type of measurement type of measurement
(recommended) measurement type of measuring system
system system
system

Frequency (AIAG /
N/A N/A N/A N/A N/A N/A N/A N/A N/A N/A
IATF)

Every training and

Frequency 1 time at start Every line Every line Calibration or training
Calibration periods Every line release Every line release before GR&R Calibration periods annual
(recommended) of use release release periods
ANOVA
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MSA by attributes
Agreement Study with Minitab Assistant

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 MSA Assistant by Attributes

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MSA Assistant by Attributes

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 MSA Assistant by Attributes

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MSA Assistant by Attributes

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 MSA Assistant by Attributes

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MSA Assistant by Attributes

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 MSA Summary
MSA Study Matrix
GR&R Range GR&R ANOVA GR&R ANOVA MSA Attributes
Calibration Resolution Stability Accuracy Study Type 1 Linearity
method Crossed Nested (Concordance)
3 operators 1
1 operator 1 3 operators 1
Tolerance / 1 operator 1 1 operator 1 1 operator 1 instrument 10 pieces
instrument 1 2 operators 1 instrument 15 pairs
resolution ≥10 instrument 1 instrument 1 instrument 5 covering the 3 operators 50 pieces
Recommended Uncertainty pattern 5 times instrument 5 pieces of parts spanning
and Process standard standard measured standards tolerance of the measured 3 times 25 OK and
method calculation per shift for 4 measured once per product tolerance, 5
variation / measured 10 50 times (Minitab measured 12 product, measured 3 25 NOT OK (Example AIAG)
w eeks (100 operator pairs measured by
resolution ≥10 times Example) times each times by each
readings) each operator
operator

% GR & R:
Tolerance /
<10% is % GR & R: <10%
resolution % agreement:
Acceptable 10% is Acceptable 10%
≥10 and The 95% bias Bias: p-value> ≥ 90% Acceptable ≥ 80%
AIAG acceptance No out of to 30% to 30% Acceptable
None Process interval None 0.05 Linearity: p- None Marginal <80% Not
criteria control points Acceptable with with improvement
variation / contains zero. value> 0.05 Acceptable Kappa: <0.4 Bad>
improvement plan. > 30% Not
resolution 0.75 Good to excellent
plan. > 30% Not Acceptable ndc≥ 5
≥10
Acceptable

Practical:% GR &
Practical:% GR &
R: <10% is % GR & R: <10% is
GM: Uncertainty VDA: GM: Bias less VDA: Cg> 1.33 R: <10% is
Practical: No GM: Bias and Acceptable 10% Acceptable 10% to Practical:% agreement: ≥
<5% of Resolution than 10% of and Cgk> 1.33 Acceptable 10% to
Other acceptance points outside linearity <10% to 30% 30% Acceptable with 90% Acceptable ≥ 80%
product <5% of the tolerance Resolution <5% 30% Acceptable
criteria the control of product Acceptable with improvement plan. > Marginal <80% Not
tolerance product of the of product with improvement
limits tolerance improvement 30% Not Acceptable Acceptable
(Example) tolerance product tolerance plan. > 30% Not
plan. > 30% Not ndc≥ 5
Acceptable ndc ≥ 5
Acceptable

1 instrument for
1 instrument for each 1 instrument for each
Number of studies each type of 1 measuring system for each
All instruments All instruments As required All instruments All instruments As required type of measurement type of measurement
(recommended) measurement type of measuring system
system system
system

Frequency (AIAG /
N/A N/A N/A N/A N/A N/A N/A N/A N/A N/A
IATF)

Every training and

Frequency 1 time at start Every line Every line Calibration or training
Calibration periods Every line release Every line release before GR&R Calibration periods annual
(recommended) of use release release periods
ANOVA
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• Thank you

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