This document discusses gage repeatability and reproducibility (Gage R&R) studies. It defines gage R&R as a method to check if a gage is capable of precise and reliable measurements. It also defines key terms like repeatability, reproducibility, accuracy, and variations. The document provides examples of simple and more complex Gage R&R studies using a micrometer and width measurement. It analyzes the results in terms of variation contributions and control charts. Companies generally aim for gage variation to be less than 30% or 10% of total process variation depending on the gage's purpose.

1. Gage
Repeatability &
Reproducibility

2. Introduction
• What is a Gage R&R
• Definitions
• Standards that companies use
• Examples of Gage R&Rs

3. What will not be covered
• The Equations for Gage R&R
– There are many statistics programs
– Go to www.google.com and type in Gage
R&R and there are work sheets

4. Example
Thickness
0.0440
0.0430
Reading
0.0420
0.0410
0.0400
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30
Count

5. What is a Gage R&R?
• A method to check whether a gage is
capable of making the appropriate
measurements.
• Doing an Analysis of Variation (ANOVA)
of a group of readings to ensure
measurement precision and reliability
• The gage is a constant

6. What is a Gage R&R?
• A measurement is characterized by
Location (accuracy, stability and linearity
metrics) and Spread (repeatability and
reproducibility).
• A Gage R&R measures spread

7. Definitions
• Variation
– the differences within a piece, from piece to piece,
measurement to measurement, and other variation
such as process step to process step, etc.
• Every process has variation including in
the measuring gage
• Want to make sure that variation in the
gage is acceptable

8. Definitions
• Accuracy
– Bias. Difference between an average of a
number of measurements and the true value
• Gage must be accurate
• Test for accuracy is calibration
• The Gage must be calibrated

9. Definitions
• Repeatability
– Precision. The ability to repeat the
measurements by the same operator at or
near the same time
• Reproducibility
– Reliability. The ability to reproduce the
measurements by different operators at
different times.

10. Methodology

11. Standards
• What are some standards that companies
such as GE are using for acceptable
gages?

12. Standards
• For gages that are used to make pass/fail
decisions < 30% of the process variation
can come from the gage
• For gages that are used to measure
improvements in the process < 10% of the
process variation can come from the gage

13. Any Questions?

14. Examples from the simplest
measuring gages to more
complicated equipment

15. Example of a simple Gage R&R
• A micrometer is tested by having 3 people
measure 5 to 10 parts 3 times each in
random order

16. Part Individual Readings
Inspector Number 1st set 2nd set 3rd set
Nick 1 4.822 4.823 4.826
2 4.81 4.811 4.813
3 4.808 4.814 4.81
4 4.796 4.795 4.813
5 4.818 4.817 4.816
6 4.811 4.815 4.812
7 4.816 4.801 4.813
8 4.809 4.817 4.81
9 4.809 4.808 4.811
10 4.811 4.802 4.808

17. Part Individual Readings
Inspector Number 1st set 2nd set 3rd set
Roy 1 4.826 4.827 4.817
2 4.803 4.811 4.815
3 4.834 4.812 4.794
4 4.8 4.808 4.803
5 4.816 4.834 4.811
6 4.804 4.796 4.812
7 4.821 4.806 4.813
8 4.814 4.827 4.824
9 4.811 4.815 4.813
10 4.806 4.816 4.81

18. Part Individual Readings
Inspector Number 1st set 2nd set 3rd set
Greg 1 4.845 4.821 4.813
2 4.831 4.819 4.812
3 4.808 4.815 4.819
4 4.814 4.807 4.814
5 4.812 4.81 4.816
6 4.828 4.82 4.813
7 4.812 4.81 4.809
8 4.799 4.79 4.819
9 4.804 4.809 4.801
10 4.809 4.791 4.8

19. Results
• Gage R&R
• %Contribution
• Source Sigma2 (of Sigma2)
•
• Total Gage R&R 7.29E-05 79.12
• Repeatability 6.20E-05 67.27
• Reproducibility 1.09E-05 11.85
• Operator 0.00E+00 0.00
• Operator*Sample 1.09E-05 11.85
• Part-To-Part 1.92E-05 20.88
• Total Variation 9.21E-05 100.00

20. Results
Gage name: Micrometer
Date of study:
Gage R&R (ANOVA) for Measurement Reported by: Dave Potty
Tolerance:
Misc:
Components of Variation By Sample
100 4.85
%Contribution
4.84
4.83
Percent
50 4.82
4.81
4.80
0 4.79
Gage R&R Repeat Reprod Part-to-Part Sample 1 2 3 4 5 6 7 8 9 10
R Chart by Operator By Operator
Greg Nick Roy 4.85
0.04
Sample Range
4.84
0.03 UCL=0.03183
4.83
0.02 4.82
R=0.01237 4.81
0.01
4.80
0.00 LCL=0
4.79
0 Operator Greg Nick Roy
Xbar Chart by Operator Operator*Sample Interaction
4.83 Greg Nick Roy Operator
Greg
UCL=4.825
ean
4.82 Nick
4.82
Average
Roy
Sample M
Mean=4.812
4.81 4.81
4.80 LCL=4.800 4.80
0 Sample 1 2 3 4 5 6 7 8 9 10

21. Example of a more complicated
Gage R&R
• We had a continuous measurement of
width of a flat wire
• We measure a standard 10 times and
compared the measurements

22. Calculation
T o ta l o f o b s e rv e d
W ith in p a r t V a r ia tio n V a r ia tio n
M e a s u r e m e n t V a r ia tio n

23. Data
Average 4.7473 4.7479 4.7485 4.7484 4.7483 4.7484 4.7477 4.7480 4.7493 4.7486
SD 0.0309 0.0058 0.0064 0.0055 0.0065 0.0056 0.0067 0.0056 0.0060 0.0056
Count 990 1008 983 979 986 984 987 979 987 976

24. Width
Grand Average = 4.748
Grand SD = 0.011
Wire variation = 0.005
Measurement variation = 0.010
99% CB = 5.15 * σ measurement variation
99% CB = 0.051

25. Summary
Width
Measurement variation 0.051
Tolerance 0.250
GRR (tolerance) 20.4%

26. Review
• What is a Gage R&R
• Definitions
• Standards that companies use
• Examples of Gage R&Rs

27. Any Questions?

28. Thank You!