Using AI tools to learn uncertainty#
Get a free PDF of one of the recommended sources, e.g. https://www.esscolab.com/uploads/files/measurement-guide.pdf
Upload this PDF to one of the AI tools, and ask questions, e.g.
https://askyourpdf.com/conversations/d/2d36eb11-2d38-46e5-bbf0-e62027ed9112
Question: can you show me a real calculation example?
Answer: Sure! Here is a real calculation example to demonstrate the estimation and calculation of overall uncertainty in measurements:
Let us say we want to measure the length of a piece of string using a tape measure. We take 10 repeated readings and calculate the mean and standard deviation of these readings.
Type A Evaluation:
Mean of the 10 readings: x = 5.017 m
Estimated standard deviation of the mean: s/n = 0.007 m
Type B Evaluation:
Uncertainty due to the tape measure: ±0.25 mm
Uncertainty due to the string not lying straight: ±0.03 m
Uncertainty due to the temperature effect: ±0.58 mm
Combining Uncertainties:
Summation in quadrature for Type A and Type B uncertainties:
0.007 m (Type A) squared = 0.000049 m^2
0.25 mm (Type B) squared = 0.000625 m^2
0.03 m (Type B) squared = 0.0009 m^2
0.58 mm (Type B) squared = 0.0003364 m^2
Combined standard uncertainty = square root of the sum of the squared uncertainties = 0.0253 m
Expressing the Uncertainty:
Using a coverage factor of k = 2 (for a 95% confidence level):
Expanded uncertainty = combined standard uncertainty * k = 0.0253 m * 2 = 0.0506 m
Therefore, the overall uncertainty in the measurement of the length of the string is 0.0506 meters.
SOURCES:
Page 20: Measurement Good Practice Guide No. 11 (Issue 2)
Page 27: Measurement Good Practice Guide No. 11 (Issue 2)
what are 8 steps to estimate and express uncertainty?#
The eight steps to estimate and express uncertainty in measurements are as follows:
Determine the objective of the measurement and identify the necessary measurements and calculations to obtain the final result.
Perform the required measurements.
Estimate the uncertainty of each input quantity that contributes to the final result and express them in similar terms.
Determine if the errors of the input quantities are independent of each other. If not, additional calculations or information may be needed.
Calculate the measurement result, including any known corrections such as calibration factors.
Combine the individual uncertainties to find the combined standard uncertainty using appropriate methods (e.g., summation in quadrature).
Express the uncertainty using a coverage factor, along with the size of the uncertainty interval, and state the level of confidence.
Document the measurement result, uncertainty, and the methodology used to obtain them.
SOURCES:
Page 19: Measurement Good Practice Guide No. 11 (Issue 2)
Page 27: Measurement Good Practice Guide No. 11 (Issue 2)
Additional sources#
Thanks to this blog:
https://www.isobudgets.com/best-measurement-uncertainty-guide-for-beginners/
NPL MGPG No. 11 – A Beginner’s Guide to Uncertainty of Measurement https://www.isobudgets.com/pdf/documents/04_NPL_MGPG_No11.pdf
UKAS M3003 – The Expression of uncertainty and Confidence in Measurement https://www.isobudgets.com/pdf/documents/02_UKAS_M3003.pdf
EA 4/02 – Expression of the Uncertainty of Measurement in Calibration https://www.isobudgets.com/pdf/documents/05_EA_4-02.pdf
BIPM JCGM 100:2008 – Guide to the Expression of Uncertainty in Measurement https://www.isobudgets.com/pdf/documents/03_BIPM_JCGM100.pdf
NIST Technical Note 1297 – Guidelines for the Evaluating and Expressing the Uncertainty of NIST Measurement Results https://www.isobudgets.com/pdf/documents/01_NIST_TN1297.pdf
https://www.isobudgets.com/pdf/documents/07_NASA_NHBK873919-3.pdf