feilspredning

Feilspredning, a Norwegian term, translates to "error propagation" or "propagation of uncertainty" in English. It refers to the process of determining how uncertainties in the measurements of physical quantities affect the uncertainty in a calculated result. When a quantity is derived from other quantities through a mathematical formula, any uncertainty in the input values will inevitably lead to an uncertainty in the output value.

The principles of error propagation are fundamental in experimental science and engineering. They provide a systematic way to quantify the reliability of a computed result based on the precision of the initial measurements. Various mathematical methods exist to perform error propagation, with the most common approach involving the use of partial derivatives of the function relating the input variables to the output variable.

For a function $f(x, y)$ where $x$ and $y$ are measured quantities with uncertainties $\Delta x$ and $\Delta y$ respectively, the uncertainty in $f$, denoted as $\Delta f$, can be approximated using the following formula:

$\Delta f \approx \sqrt{(\frac{\partial f}{\partial x}\Delta x)^2 + (\frac{\partial f}{\partial y}\Delta y)^2}$

This formula assumes that the errors in the input variables are independent. If the errors are correlated, a more complex formula involving covariance terms is required. Understanding and applying feilspredning allows scientists and engineers to make informed decisions about the significance of their results and to identify which measurements contribute most to the overall uncertainty. It is a crucial step in assessing the quality and validity of experimental data and derived quantities.