1. Redeveloping the GUM.validate Function
in the metRology Package for R
Jillian Kasner
Advisors: Will Guthrie and Hung-kung Liu
Statistical Engineering Division
Information Technology Laboratory
4 August 2015
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2. Background
 Motivating Example: Uncertainty of 3D Printers
– Experiment design
 15 x 15 x 10 mm and 30 x 30 x20 mm boxes
 Four boxes of each size/day
 Randomized run order
 Ten days
– Makerbot Replicator 2 Specifications
 0.011 mm for the x- and y- axis
 0.0025 mm for the z-axis
 Uncertainty Analysis and Metrology
– Types and Causes of Measurement Error
 metRology package for R
– GUM Function
– GUM.validate Function
 Changes to GUM.validate function
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3. Measurement Error: 3D Printed Objects
 Type A Uncertainty
– Random Measurement Error
– Normal Distribution
 Type B Uncertainty
– Caliper Calibration Error
– Uniform Distribution
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4. Possible Bias
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5. Uncertainty Analysis with
metRology for Microsoft Excel
Certain commercial equipment, instruments, or materials are identified in this talk in order to specify research procedures adequately. Such
identification is not intended to imply recommendation or endorsement by the National Institute of Standards and Technology, nor is it intended to
imply that the materials or equipment identified are necessarily the best available for the purpose.
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6. Using Copulas in GUM.validate
 Need to account for correlation between variables in
validation, just as in the original uncertainty analysis
– Copulas are used to make a joint multivariate distribution
from any set of individual marginal starting distributions
 The input correlation matrix used to generate random
values using a copula may need to be adjusted to
give the desired output correlation
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7. Optimization of Output Correlation Matrix
Different Correlation Matrices Same Correlation Matrix
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Optimization Improved the Output
Correlation Matrix
• 60% of the time in the graph above
• 56.5% of the time out of 200 runs
Optimization Improved the Output
Correlation Matrix
• 55% of the time in the graph above
• 56.5% of the time out of 200 runs

8. Summary of 3D Printer Experiment Results
 Confidence Intervals for Standard Deviation of 3D Printer Output
 Bias
 Size Dependence
– Mean (effect) and Variability (no effect)
 Caliper Calibration
– At the end of the summer, I remeasured each box with the original
caliper and a new caliper, which showed no significant differences
– Also, measured gage blocks to verify calibrations of both calipers
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Axis Variability Lower Bound Point Estimate Upper Bound
x-axis True Standard Deviation 0.0649 mm 0.0751 mm 0.089 mm
y-axis True Standard Deviation 0.0801 mm 0.0926 mm 0.1099 mm
z-axis True Standard Deviation 0.0548 mm 0.0634 mm 0.0751 mm

9. Summary
 Background Learning
– Previous GUM.validate and GUM Functions
– Uncertainty Analysis in Metrology
 Studied the course materials for the NIST Fundamentals of
Uncertainty Analysis short course
– Programming in R
 Changes to GUM.validate for Uncertainty Analysis
– Added Copulas for Simulation of Validation Data
– Added Code to Optimize Copula Correlation Matrix
– Added Beta Distribution
 Illustrates adding any distribution
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10. Acknowledgements
 My advisor, William Guthrie and Hung-kung Liu, for
all of their help and support.
 The Statistical Engineering Division staff, especially
Stephany Bailey, for their assistance throughout the
summer.
 The NIST SURF Directors and SURF Program
Coordinator Dr. Brandi Toliver for running the
program.
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