The document describes a gage reliability and repeatability (Gage R&R) study conducted to evaluate a measurement system. Ten parts were each measured twice by three different operators at different locations. Analysis of variance showed significant interaction between operators and parts, indicating the measurements were affected by who took them and where. Most variability was due to differences between parts rather than repeatability or reproducibility. However, the measurement system's variability exceeded 10% of the total tolerance, suggesting it needs improvement to reliably distinguish part measurements.

1. Null Hypothesis
Difference in measurements is unrelated
to change of location of scale.

2. Gage R&R Study
Method
Parts: 10 Operators: 3
Replicates: 2 Total runs: 60
RAUL DARIO GERMAN
Each one of the operators measured ten parts twice in random order. Each
operator placed the scale in a different location in the plant.

3. Gage R&R Study - ANOVA Method
Two-Way ANOVA Table With Interaction
Source DF SS MS F P
Parts 9 0.0002437 0.0000271 21.1329 0.000
Operators 2 0.0000089 0.0000045 3.4855 0.053
Parts * Operators 18 0.0000231 0.0000013 2.4028 0.016
Repeatability 30 0.0000160 0.0000005
Total 59 0.0002917
α to remove interaction term = 0.05
If the p-value for the operator and part interaction is 0.05 or
higher, the interaction is not significant.
The p-value for the operator and part interaction is less than 0.05.
This means that operator-part interaction exists.
Low p-values are indications of strong evidence against the null
hypothesis.

4. Gage R&R Study - ANOVA Method
Variance Components
%Contribution
Source VarComp (of VarComp)
Total Gage R&R 0.0000011 19.88
Repeatability 0.0000005 9.94
Reproducibility 0.0000005 9.94
Operators 0.0000002 2.97
Operators*Parts 0.0000004 6.97
Part-To-Part 0.0000043 80.12
Total Variation 0.0000054 100.00
Ideally, very little of the variability should be due to repeatability
and reproducibility. Differences between parts (Part-to-Part) should
account for most of the variability.
When the %Contribution from part-to-part variation is high, the
measurement system can reliably distinguish between parts.

5. Gage R&R Study - ANOVA Method
Gage Evaluation
Study Var %Study Var %Tolerance
Source StdDev (SD) (6 × SD) (%SV) (SV/Toler)
Total Gage R&R 0.0010328 0.0061968 44.58 105.63
Repeatability 0.0007303 0.0043818 31.52 74.69
Reproducibility 0.0007303 0.0043818 31.52 74.69
Operators 0.0003991 0.0023944 17.23 40.81
Operators*Parts 0.0006116 0.0036697 26.40 62.55
Part-To-Part 0.0020736 0.0124419 89.51 212.08
Total Variation 0.0023166 0.0138996 100.00 236.93
Because the %Study Var and the %Tolerance are greater than 10%,
we conclude that the measurement system needs improvement.