How to combine instrument uncertainty with deviation

In summary, the conversation discusses using a digimatic indicator tool to measure the thickness of an uneven film. The tool has a digital screen with 1 um display, but the accuracy is only 3 um according to the specifications. To account for the unevenness, the speaker has taken 10 measurements at different points of the film. The question is how to calculate the error when reporting the average thickness, and the suggestion is to refer to the machine's specifications and use half of the instrument resolution as the uncertainty for each individual reading.
  • #1
Celder
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0
Here's my problem: I have been using a digimatic indicator tool to measure the thickness of a somewhat uneven film. The digimatic indicator has a digital screen that shows up to 1 um, but according to specifications the accuracy is only 3 um. To account for the uneveness I have taken 10 measurements at different points of the film.

My question is: When I report the average thickness, how should I calculate the error?
 
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  • #2
Welcome to PF;
Check the machine spec to see what they mean by "accuracy".
Rule of thumb is to take the uncertainty on each individual reading to be half the instrument resolution.
It is not unusual for you to have to use equipment which has a higher resolution than the uncertainty in the measurement - i.e. you cannot use a stopwatch to 1/100s accuracy but it displays to that resolution.
What do you normally do with the stopwatch measurements?
 

1. How do I calculate the combined uncertainty of an instrument and a deviation?

The combined uncertainty of an instrument and a deviation can be calculated by using the root-sum-square (RSS) method. This involves taking the square root of the sum of the squares of the individual uncertainties.

2. Can I simply add the instrument uncertainty and the deviation together?

No, simply adding the instrument uncertainty and the deviation will not accurately represent the combined uncertainty. This is because the uncertainty of the instrument and the deviation are typically not independent of each other and cannot be directly added.

3. Is it necessary to consider the uncertainty of both the instrument and the deviation?

Yes, it is important to consider the uncertainty of both the instrument and the deviation in order to accurately represent the total uncertainty of the measurement. Neglecting one or the other can result in an inaccurate measurement.

4. How can I minimize the combined uncertainty of an instrument and a deviation?

The combined uncertainty can be minimized by reducing the uncertainties of both the instrument and the deviation. This can be achieved through using more precise instruments and minimizing sources of error in the deviation.

5. Are there any limitations to combining instrument uncertainty and deviation?

Yes, there are limitations to combining instrument uncertainty and deviation. This method assumes that the uncertainties are normally distributed and that there are no correlations between the two sources of uncertainty. Additionally, it may not accurately represent the uncertainty in cases where the instrument and the deviation have significant non-linear effects on the measurement.

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