I'm trying to calibrate a proximity sensor A with another proximity sensor B. Say sensor B uncertainty is already known from the data sheet. However, for sensor A the uncertainty is nowhere to be found.

So I try to calibrate sensor A with the measurement value of sensor B, and create a regression line from the voltage data of sensor A vs distance measured with sensor B. How do I determine the uncertainty of sensor A?

Do I need to check again on how much is the difference between measured value of sensor A and B? Or is the uncertainty of sensor A follows the calibration device, in which in this case is sensor B? Or, is there any equation that I need to follow to determine the uncertainty?

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  • 3
    $\begingroup$ This is fine place for the question IMHO. $\endgroup$
    – joojaa
    Sep 20, 2021 at 5:07
  • $\begingroup$ why do you need to get that uncertainty measurement for sensor A? It seems to me a bit unorthodox to use another (non calibrated sensor B), when it would make sense to use fixed distances. $\endgroup$
    – NMech
    Sep 20, 2021 at 10:32
  • $\begingroup$ Break down different sources of error. Non-linearity, noise, hysteresis, thermal/ electrical/ environmental/ other cross sensitivities, ADC chain, sensitivity to non equilibrium condition, drift with aging, fouling. These are within your one specimen. They can be expressed as deviation from best-fit line, or at some typical reference point. Then there is specimen-to-specimen variation within a manufacturing batch, and batch to batch. Learn the details of the technology, and your application, pick the categories that will affect you, then design the appropriate experiment to characterize it. $\endgroup$
    – Pete W
    Sep 20, 2021 at 13:49

2 Answers 2


This is definitely not an answer to your problem. It more like a long comment.

The main question for me is: why do you need to get that uncertainty measurement for sensor A?

A few points of note:

  1. Each sensor (or measurement line) has its own uncertainty values. I.e. the datasheet reference value of uncertainty for sensor B, is not necessarily the same that you would find if you calibrated that sensor in an accredited laboratory.

  2. A good reference for generic uncertainty is "Guide to expression of uncertainty in measurement ". This is a generic document that provides useful procedures and directions.

With respect to your problem (although its not clear what you are trying to achieve), to measure the uncertainty of a proximity sensor I would have expected that the standard procedure would require the use of fixed distances (not the measurement from another sensor).

The uncertainty of sensor A ($u_A$) in that context would mean to me that for a fixed distance, sensor A would return a value with a $\pm u_A$. And yes you can compare that to another sensor, but its more definitive if you use a fixed distance (at least IMHO).

I have the above perspective because I have the following experience which (at least in my opinion) I consider relevant/comparable. My experience was with checking the calibration of an anemometer in wind measurements with a backup anemometer in a ISO-17025 accredited laboratory (in another lifetime). In that case a calibrated anemometer would be periodically be used to check that the tested anemometer has not suffered a significant change in calibration parameters. However, in that procedure, the tested anemometer was not considered recalibrated, and although the uncertainty of the measurement is calculated it is not used outside of a "GO, NO-GO" decision type system.


In a typical calibration setup, a Test Accuracy Ratio is decided upon based on the qualities and innate accuracies of the two devices (the calibration standard B and the calibrated item A in your case). This is often 4 to 1, 5 to 1, or 10 to 1. So if the standard has an uncertainty of ±0.01 inches, a 10 to 1 ratio would mean that the calibrated item is assigned an uncertainty of only ±0.1 inches. This can be true even if A and B are exactly the same make and model of sensor, and it accounts for variability in the calibration equipment and operator procedure, and the fact that the standard B is kept in a lab and periodically compared with an even more accurate standard, while the A item is not.

The ideal situation is that the calibration standard is much more accurate than you actually need, so your item uncertainty values can be conservative in this respect and still fulfill your need.


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