High complexity uncertainty examples

Hello all,

I am looking for some examples of very complex uncertainty calculations...Partially for my own learning, and partially to develop some training material for my staff. I was hoping someone may have something they can share.

Or maybe this should just be a thread for the most complex uncertainty calcs you have had to do?

Anyway, Anything using more obscure statistical distributions, combining different measurement units, or having such low uncertainties as to consider more obscure environmental factors, such as local gravity would be amazing to take a look at.

For reference: I am starting to move from spreadsheets to SunCal (Sandia's uncertainty calculator), and am working mainly in mechanical and electrical measurement and testing (so bio/chem stuff like HPLCs aren't really my sphere).

The most complex application of uncertainty I've ever subjected myself to was when trying to calculate the condition number of a (non-singular) 2x2 matrix. The matrix had two different fractional elements with different uncertainties (the other two elements were unity minus one of the other two). I don't recommend this exercise for a class.

I've had more fun with simple (Bayesian) calculations of posterior probability density functions by introducing different sorts of uncertainties (either in the data or in the prior).

Tidge,

Thanks for the response.

Yeah, I don't want to dive too deeply into vector measurands and covariance matricies.

I will probably try and put together some examples with a range of distributions and keep to scalar uncertainties...And with Suncal, I may push a little on Monte Carlo simulations as a tool as well.

Section 15 of this HP/Agilent document has a nice explanation of the many components that go into a proper measurement and uncertainty statement.
Accuracy and Repeatability

Here's a screenshot of the uncertainty budget I created for the metrology lab here. Keep in mind, we're not an accredited lab- we're a diecast manufacturer. This exercise was for my own understanding, and it was my first attempt at an uncertainty budget. I was able to construct a graph that showed k=2 Expanded Uncertainty as a function of Length of Measurement, and derive an equation of the form U = SQRT(aL^2 + b^2) where b was the Initial Uncertainty at Length 0.

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