How to Estimate Uncertainty for a Physical Quantity with Dependent Variables?

Click For Summary
SUMMARY

The discussion focuses on estimating the uncertainty of a physical quantity A defined by the equation A=(74.5 B^2*(M+N))^{1/3}, where B, M, and N have specified relative uncertainties. The correlation between the uncertainties of M and N, which depend on B, is crucial for accurate calculations. If the correlation is negligible, M and N can be treated as independent. The uncertainty in B is given as 0.0002, while M and N are estimated with a 15% error margin.

PREREQUISITES
  • Understanding of uncertainty propagation in physical quantities
  • Familiarity with dependent and independent variables in mathematical modeling
  • Knowledge of logarithmic functions and their applications
  • Basic proficiency in using uncertainty analysis software tools
NEXT STEPS
  • Learn about uncertainty propagation methods in physical sciences
  • Study the application of correlation coefficients in uncertainty analysis
  • Explore software tools for uncertainty estimation, such as MATLAB or Python libraries
  • Investigate advanced techniques for modeling dependent variables in uncertainty calculations
USEFUL FOR

Researchers, physicists, and engineers involved in experimental design and data analysis, particularly those working with dependent variables and uncertainty estimation in physical measurements.

bznm
Messages
181
Reaction score
0
I have a physical quantity A defined as ##A=(74.5 B^2*(M+N))^{1/3}##

where B, M, N and relative uncertainties are given. And M and N are dependent on B.
Could you show me how to calculate and estimation for the uncertainty on A?

Thanks a lot
 
Last edited:
Physics news on Phys.org
You will need to know the correlation between the uncertainties on M and N and the uncertainties on B. If you think this is small, you can treat them as independent.
 
M and N are function of B (ie for example ##log M=(0.755 \pm 0.059)*log B+(0.416\pm 0.024)## The value of B is given by a software, and its uncertainty is 0.0002.
The values of M and N are extimated using relations like the one that I have just written, and it is assumed that the error is 15%.
How can I estimate the uncertainty on A?
 

Similar threads

  • · Replies 5 ·
Replies
5
Views
3K
  • · Replies 4 ·
Replies
4
Views
4K
  • · Replies 3 ·
Replies
3
Views
2K
Replies
15
Views
2K
  • · Replies 1 ·
Replies
1
Views
2K
Replies
2
Views
2K
  • · Replies 1 ·
Replies
1
Views
3K
  • · Replies 22 ·
Replies
22
Views
2K
  • · Replies 1 ·
Replies
1
Views
2K
  • · Replies 4 ·
Replies
4
Views
2K