Fehlerpropagationsverfahren

Fehlerpropagationsverfahren, also known as error propagation or propagation of uncertainty, is a method used in science and engineering to estimate the uncertainty in a calculated quantity based on the uncertainties of the input variables. When a quantity is determined by a formula involving other quantities, each with its own uncertainty, the uncertainty in the final result is a combination of these input uncertainties.

The core idea behind Fehlerpropagationsverfahren is to determine how variations in the input variables affect the output. This is typically achieved through partial derivatives. For a function f(x, y, ...), where x, y, ... are input variables with uncertainties σx, σy, ..., the uncertainty in f, denoted as σf, can be approximated by the following formula: σf² ≈ (∂f/∂x)²σx² + (∂f/∂y)²σy² + ... This formula assumes that the input uncertainties are independent.

The process involves calculating the partial derivative of the function with respect to each input variable, squaring these derivatives, and multiplying them by the square of the respective input uncertainties. These terms are then summed up. The square root of this sum gives the estimated uncertainty in the calculated quantity.

Fehlerpropagationsverfahren is crucial for reporting results accurately. It provides a quantitative measure of confidence in a measurement or calculation, allowing scientists and engineers to understand the reliability of their findings and to make informed decisions based on experimental data. It is widely applied in fields like physics, chemistry, metrology, and experimental design.