I work at a factory plant where they use a mass balance.
The problem is that there is an huge difference between the input and output of one element. There are several people working on this problem but I focus more on the analytical side of the process.
The input is one product and the output consist of several different products
The concentration of each product is based on different analyses.
For example titration, gc analysis and a density measurement.
The results from all those different analysis are combined to calculate this mass balance.
Of course each analysis has its own uncertainty. And I want to combine each uncertainty into one combined uncertainty. Is it possible to use an simple formulae as shown in the file?
And is it possible to do this also for the measurement error?
Any advice on how to approach this would be very helpful.
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Jasper van der Plas You need to know the relationship in the form of output=f(inputs). Then you can calculate the standard uncertainty (SU) of the output based on the law of propagation of uncertainty, which may give you a simple formula. Measurement error is quantified by uncertainty. For detailed discussion, you may refer to Article A unified theory of measurement errors and uncertainties
Yes, it is possible to apply a formula as simple as the one in the image as long as you adhere to the GUM Guide. From what you show in the figure you are applying the law of propagation of uncertainty that is correct. But you should take into account type B and type A uncertainties. Write me and tell me more details about the problem so I can help you better. Best Regards
If you are familiar with MATLAB, I can recommend you this toolbox developed by colleagues of my institute: https://www.aau.at/en/smart-systems-technologies/sensors-and-actuators/downloads/an-uncertainty-toolbox-2/
Please refer to the documentation. besides classical GUM it also performs Monte Carlo simulations and unscented transform, which may be helpful for some cases, where the simplifications of GUM may not lead to proper results.
Nevertheless, like both comments above, I do also recommend you a deep understanding of each variable and their relationships to each other. I.e. check if all input paramters may be (linearly) correlated to degree.