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I have an issue I need to figure out at work and I’ll try explain to the best of my ability.

In basic terms I need to figure out a multiplier value + a floor value (if required) for an audit coming up.

Let's say a certificate of a volt meter has readings of 1V, 5V and 10V on its 10V Range. The uncertainties are 1uV, 5uV and 10uV

On this example its easy because I could figure this out without a floor value by doing the following = 1uV is 1ppm / 0.0001%. If you multiply 1, 5 and 10V by 0.000,001 (0.0001%) then you will get figures of 1uV, 5uV, 10uV etc

However, if the uncertainties are non linear i.e. 1V = 1.7uV, 5V = 5uV, 10V = 10uV then I need to add a floor figure and then calculate a multiplier.

Any ideas that will work with multiple ranges rather than just the example question? My apologies if I have skewed the explanation, it’s been a long day.

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Kaf2023

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If I understand it correctly, it seems like you want to calculate a multiplier value and a floor value (when needed) for non-linear uncertainties. You should be able to use a general approach that works for multiple ranges and non-linear uncertainties. See below for my ideas:

So, assuming you can define a function that represents the relationship between the measured voltage and the uncertainty, we have:

Multiplier = Measured Uncertainty / Uncertainty Function

Use below when the multiplier values are not sufficient to account for the uncertainty, as you mentioned:

Floor Value = Desired Uncertainty - (Multiplier * Measured Voltage)

For each measured voltage, apply the multiplier and add the floor value (if required) to calculate the final uncertainty for the audit. You can apply this method to multiple ranges by repeating the process for each range you want to audit.

You can use a mathematical approach that solves a system of equations. For each range, you can create an equation using the above. For your example, you'll have:

M * 1V + F = 1.7uV
M * 5V + F = 5uV
M * 10V + F = 10uV

Now, you can use a mathematical solver or software to solve this system of equations simultaneously and find values for M and F that satisfy all the above equations.

I hope this answers your question.

Kav10

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