Sensor and transmitter, combined error.

Hi all,
I'm reading temperature in the 0-300ºF range.
If I have a sensor (let's say it's a RTD) with an error dX (let's say 0.5ºF) and I use a transmitter whose error is dY (let's say 0.3ºF), what would be the combined (total) error in my reading?

Thanks!

You don't know, you can estimate a range:

-0.8..0.8.

boneless said:

You don't know, you can estimate a range:

-0.8..0.8.

Click to expand...

So you think the total error is the sum of the errors? That was my first thought, but I am not sure.

It can be, but does not have to be.

I doubt that your error will be a static +0.5 from the RTD and a static +0.3 from the transmitter.

It usually is something like +/-.00001/F

There are different kinds of error. However, the easiest to calculate is the worst case, which is dX + dY.

Other factors to consider are the statistical distribution of the errors (are the errors uniform distribution, normal, or something else) and sensitivity of the error (is the amount of error dependent on something like temperature?). If you know those, there is a lot more math that can be done to shrink the "total error".

You also need to consider the accuracy/resolution of the instrument or analogue input you are using to make the measurement. All of the seperate elements can add up to a significant error if you are not careful.

mk42 said:

There are different kinds of error. However, the easiest to calculate is the worst case, which is dX + dY.

Click to expand...

I agree, and the worst case is what I'm worried about.

just do a standard deviation calculation

The Beginner's Guide to Uncertainty of Measurement is published by National Physical Laboratory (whoever they are).

https://www.wmo.int/pages/prog/gcos/documents/gruanmanuals/UK_NPL/mgpg11.pdf

I don't really have these issues with what I do, but I do recall that the field distinguishes between error and uncertainty.



It isn't clear whether your values are errors, that you've measured against a certified standard, or values from an accuracy statement from a spec sheet (the Guide covers the misapplied use of 'accuracy' vs uncertainty).

I believe that measured errors are additive, so that if the one is off by +0.5 and the other off by +0.2, the total error is the sum of +0.7, because that's what you'd 'see' at the output of the transmitter. A 100.0° input would produce an RTD output of 100.5°, for which the transmitter would output 100.7° (transmitter 'sees' 100.5 but has a +0.2 error)

The Guide's approach is that uncertainty is determined by multiple measurements and therefore statistical methods are used to come up with an uncertainty value. They state that accuracy statements are not uncertainty statements. They might not be, but I've seen people use root mean square of multiple accuracy values to determinetotal/system accuracy/uncertainty.

Error spec will be in C. But, you can improve accuracy by doing a system calibration.
I'll assume a 100 Ohm Platinum RTD. With RTD's, the largest error is caused by deviation from linear. You can improve your system's accuracy by using a lookup table and adding correction factors. Look at this Certificate of Calibration. The response is within .01 C from 0-25C, linear with a -.01 offset from 25-50C, then drifts up as we get hotter.
RTD accuracy decreases with temperature. See figure 2 here.

For your amplifier, I would expect accuracy to change over it's temperature range. Accuracy should be much better if it's in a controlled temperature environment. There is still a possibility of drift over time, so periodic calibration is required.