## Calibration Uncertainty

## Calibration Uncertainty

(OP)

I'm researching uncertainty calculations based on the GUM method. I have a question about estimating the standard uncertainty of an instrument based on it's calibration. In the examples I have seen, a manufacturer will quote a certain reference accuracy and state the statistical significance. Rosemount for example use 3sigma and hence it is fairly trivial to convert that to standard uncertainty given a calibration certificate.

Where I am unsure is for calibrations made on-site or in a workshop for example. Some good calibrators often display the calibration curve as well as the uncertainty associated with the calibration as in the example below for a pressure sensor.

What would be an acceptable way to quote the standard uncertainty of this device's calibration in an uncertainty estimate for any measurement made by it? Is it correct to assume that since the tolerance is +/-2% of span (and is within this tolerance) that this has a rectangular probability distribution and therefore the standard uncertainty due to this calibation is derived in the usual way (2%/√3)? Is rectangular too conservative and if so, what confidence level should be applied if it were assumed to be distributed normally?

Also, does the uncertainty of the calibration process itself need to be taken into account i.e. the green error bars as shown in the figure?

Where I am unsure is for calibrations made on-site or in a workshop for example. Some good calibrators often display the calibration curve as well as the uncertainty associated with the calibration as in the example below for a pressure sensor.

What would be an acceptable way to quote the standard uncertainty of this device's calibration in an uncertainty estimate for any measurement made by it? Is it correct to assume that since the tolerance is +/-2% of span (and is within this tolerance) that this has a rectangular probability distribution and therefore the standard uncertainty due to this calibation is derived in the usual way (2%/√3)? Is rectangular too conservative and if so, what confidence level should be applied if it were assumed to be distributed normally?

Also, does the uncertainty of the calibration process itself need to be taken into account i.e. the green error bars as shown in the figure?

## RE: Calibration Uncertainty

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## RE: Calibration Uncertainty

## RE: Calibration Uncertainty

TTFN (ta ta for now)

I can do absolutely anything. I'm an expert! https://www.youtube.com/watch?v=BKorP55Aqvg

FAQ731-376: Eng-Tips.com Forum Policies forum1529: Translation Assistance for Engineers Entire Forum list http://www.eng-tips.com/forumlist.cfm

## RE: Calibration Uncertainty

Calibration Tolerance = +/-2% (of span)

Expanded Uncertainty of Calibration (k = 2) = 0.1% (of span)

Standard Uncertainty of Calibration Tolerance = +/-2%/√3 = +/-1.16%

Standard Uncertainty of Calibration = +/-0.1%/2 = +/-0.05%

Standard Uncertainty of UUT = √(1.15^2) + (0.05)^2 )= +/-1.63% (of span)

Here, the uncertainty of the calibration would have to assume the largest uncertainty throughout the range which happens to be at the higher data point.

Having thought about this some more, I think that using the calibration tolerance is quite conservative. It might be more appropraite to use the largest calibration error and combine that with the calibration uncertainty using the root sum squares method as in the example. In this way, a well calibrated device is reflected in it's uncertainty.