When does the calibration uncertainty contribute to a measurement uncertainty?

In summary, when considering the uncertainty of a measurement made by an instrument with a known calibration, it is important to take into account all sources of uncertainty, including the calibration uncertainty. However, in many cases, the uncertainty associated with the calibration process may be significantly lower than the uncertainty associated with the instrument being calibrated. It is possible to combine the calibration tolerance and the calibration uncertainty using the root sum of squares method to obtain a standard uncertainty for the device at calibration, but this may not be accurate unless all calibration parameters are taken into account. Using controls with known outcomes may provide a more precise measurement in cases where the instrument is capable of higher precision.
  • #1
fonz
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Often a calibration certificate for an instrument has the error found during the calibration as well as the uncertainty associated calibration itself.

I'm reasearching uncertainty calculations using the GUM 1995 method and I haven't found one yet that includes the uncertainty of the calibration result as a source of measurement uncertainty for a particular instrument. Only uncertainty derived from the error found by the calibration process is used. Is there a reason for this? Is it likely because in most cases there is a Test Accuracy / Uncertainty Ratio greater than 4:1?
 
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  • #2
I suspect it will depend on where you are looking and what you are calibrating. The uncertainty associated with the calibration "experiment" itself will in many cases (pretty much all electrical instruments) be way lower (in some cases a couple of orders of magnitude) than the uncertainty associated with the instrument being calibrated.
That said, if you look up some papers from journals such as Metrologia you will find cases where every part of the error budget is taken into account.
 
  • #3
f95toli said:
I suspect it will depend on where you are looking and what you are calibrating. The uncertainty associated with the calibration "experiment" itself will in many cases (pretty much all electrical instruments) be way lower (in some cases a couple of orders of magnitude) than the uncertainty associated with the instrument being calibrated.
That said, if you look up some papers from journals such as Metrologia you will find cases where every part of the error budget is taken into account.

Hi thanks for the reply. That is essentially my understanding and I think that the common requirement for a Test Accuracy / Uncertainty Ratio of 4:1 or even 10:1 validates your statement.

It has got me thinking though. When considering the uncertainty of a measurement made by an instrument with a known calibration. Is is correct to assume the error quoted by a calibration certificate can be considered a standard uncertainty or expanded uncertainty and if so, at what level of confidence? For example, I have shown an image of a typical calibration chart for a pressure sensor. The calibration tolerance is shown in blue, and the calibration points highlighted in green along with the error bars representing the uncertainty of the calibration itself. Is it correct to say that the contribution of uncertainty due to the accuracy of this device on any measurement made by it is within +/-2% of span? If so, at what level of confidence?

Calibration Uncertainty.PNG
 
  • #4
The short answer is "always." All sources of uncertainty always contribute to the total uncertainty of a measurement, including calibration uncertainty. The question, as you've already discussed, is whether that calibration uncertainty is negligible compared to the rest of the sources. When you do a root sum of squares to add uncertainties, small contributions fade away pretty quickly.
 
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  • #5
Would it be appropriate to assume a rectangular probability distribution for the calibration tolerance (blue line in the previous figure) and combine it with the expanded uncertainty of the calibration (green error bars) using the root sum squares method to obtain a standard uncertainty for the device at calibration?

If the 'as-found' calibration error is much less than the calibration tolerance then I suppose that is quite conservative so potentially the largest calibration error could be used and assumed to be a rectangular probability distribution. Combining that with the standard uncertainty of the calibration itself using RSS would then derive a standard uncertainty taking into account the calibration of the device and the uncertainty of the calibration itself. It seems sensible to me but it's not made clear in the GUM.
 
  • #6
fonz said:
If the 'as-found' calibration error is much less than the calibration tolerance then I suppose that is quite conservative so potentially the largest calibration error could be used and assumed to be a rectangular probability distribution. Combining that with the standard uncertainty of the calibration itself using RSS would then derive a standard uncertainty taking into account the calibration of the device and the uncertainty of the calibration itself. It seems sensible to me but it's not made clear in the GUM.
I think this is not a good strategy unless you have more data about the calibration. For instance there might be a systematic change (say perhaps Temperature in your example) that would shift that green line to the other side of the calibration tolerance. Unless you know that the calibration data includes the entire calibration parameter space this is not a good practice.
If you need numbers better than the 2% band, it looks as though the instrument is capable of higher precision, but you would need to supply a correction factor using "controls" i.e. known outcomes. This is often done for medical diagnostic devices
 

1. How does calibration uncertainty affect measurement uncertainty?

Calibration uncertainty refers to the potential error or variability in the calibration process of a measuring instrument. This uncertainty can contribute to the overall measurement uncertainty, as it can affect the accuracy and precision of the instrument's readings. Therefore, it is important to consider calibration uncertainty when calculating measurement uncertainty.

2. When should calibration uncertainty be taken into account?

Calibration uncertainty should be taken into account whenever a measurement is being made using a calibrated instrument. This includes both initial calibrations and routine calibrations to ensure the accuracy and reliability of the instrument's readings. Ignoring calibration uncertainty can lead to inaccurate measurements and potentially faulty data.

3. How is calibration uncertainty calculated?

Calibration uncertainty is typically calculated by comparing the readings of the instrument before and after calibration. The difference between these readings can be used to determine the level of uncertainty in the calibration process. Other factors, such as the calibration method and the instrument's specifications, may also be considered in the calculation.

4. Can calibration uncertainty be reduced?

Yes, calibration uncertainty can be reduced by using more precise and accurate calibration methods, regularly calibrating the instrument, and properly maintaining the instrument. Additionally, using multiple calibration standards and performing multiple calibrations can also help to reduce calibration uncertainty.

5. What are the consequences of ignoring calibration uncertainty?

Ignoring calibration uncertainty can lead to inaccurate measurements and potentially faulty data. This can have serious consequences, especially in scientific research or in industries where precise measurements are crucial. It is important to always consider and account for calibration uncertainty to ensure the reliability and accuracy of measurements.

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