Estimating Measurement Uncertainty

Learn how to estimate measurement uncertainty in accordance with the GUM method and the iterative PUMA method.

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This has been one of the most valuable training courses that I have taken. I found it to be well thought out, straightforward in presentation and course content. I now have a thorough understanding of uncertainty contributors and the budgeting process. I would recommend this course to anyone collecting data measurements and the assessments of their accuracy. Thank you for making this course available.

R. Alex Eddington

I was hesitant at first about purchasing Dr. Henrik S. Nielsen's on-line Estimating Measurement Uncertainty course however I elected to go ahead and purchase it anyway. I'm sure glad I made that decision. In the course, Dr. Henrik succinctly covers everything I wanted to know about the topic and which I was able to put to use in my profession right away. Don't worry if you don't have an in-depth statistics background. You do not need it for this course. The math only gets tricky in a couple of spots and Dr. Henrik clearly describes what is going on. The course and the handouts provided by Dr. Nielsen are top-notch.

Don MacArthur

Estimating Measurement Uncertainty is a basic activity in measurement laboratories and on production lines in modern industry. ISO 9000, QS 9000 and ISO/TS 16949 have put increased focus on this issue with new, specific requirements. Accounting for the measurement uncertainty is also a prerequisite for a calibration laboratory to gain accreditation to ISO 17025.

The “Guide to the Expression of Uncertainty in Measurement” (GUM) is a reference type document containing much theory and advanced mathematics, which makes it very difficult to apply at an industrial level.

The training course teaches uncertainty estimation based on the PUMA method, documented in ISO 14253-2, which is a simplified, iterative method based on GUM. The PUMA method is much more straightforward and easier to apply than GUM itself. The course focuses on the physical understanding of the measurement task and makes only very limited use of complex mathematical and statistical tools.

The course also teaches the use of uncertainty budgets to optimize measurement processes in terms of uncertainty and cost. This is a very powerful aspect of the course, which can lead to significant savings.


Just finished the course, highly recommended to anyone who has an interest in estimating uncertainty measurement. I find the topic strangely interesting now! Thanks to the Dr. for putting the course together and making the topic approachable & understandable.

Adrian Thompson

Your Instructor


Henrik S. Nielsen
Henrik S. Nielsen

Dr. Henrik S. Nielsen is the president of HN Metrology Consulting and HN Proficiency Testing, the first accredited proficiency testing provider catering to dimensional inspection and calibration laboratories in the US.

His areas of expertise include geometrical product specifications, dimensional metrology, uncertainty estimation and quality assurance for calibration laboratories. He teaches seminars on all of these subjects though various organizations.

Dr. Nielsen is the chairman of ISO Technical Committee 213 “Geometrical Product Specifications and Verification” and has been an expert serving on related committees since 1988. He has served as project leader and author of several ISO standards.

Prior to founding HN Metrology Consulting in 1998, Dr. Nielsen was the Technical Manager of Corporate Standards at Cummins Engine Co. in Columbus, Indiana. Dr. Nielsen holds a M. Sc. In Mechanical Engineering and a Ph. D. in Metrology, both from the Technical University of Denmark.


Surely a great and practical course on uncertainty. Dr. Nielsen does a great job in making the complex subject into quite simple pieces using some common examples in metrology. I recommend this course to both beginner and advanced users of uncertainty.

Gautham Nagendra

Course Curriculum


  Course Introduction
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  The Concept of Uncertainty
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  Identifying Uncertainty Contributors
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  Modelling the Measurement Process
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  The GUM Method
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  Uncertainty Budgeting
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  The PUMA Method
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  Course Summary
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This course was perfect in getting me beyond the words and to an understanding of the concepts and the players involved.

John Griffin

Frequently Asked Questions


When does the course start and finish?
The course starts now and never ends! It is a completely self-paced online course - you decide when you start and when you finish.
How long do I have access to the course?
How does lifetime access sound? After enrolling, you have unlimited access to this course for as long as you like - across any and all devices you own.
What if I am unhappy with the course?
We would never want you to be unhappy! If you are unsatisfied with your purchase, contact us in the first 30 days and we will give you a full refund.

I thought this course was very good and gave me an overall improved understanding of uncertainty.

Curtis L. Robb

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I am a beginner to uncertainty and the course was excellent in getting me oriented quickly. I do think working through a real life example after each section was especially helpful in applying the theory.

Michael Shuttlesworth, P.E.