Measurement uncertainty

The measurement uncertainty of the estimate or estimator of a physical quantity narrows a range of values ​​within which the true value of the measurand to be specified with a probability of ( is usually an indication for 95%). The result of a measurement is defined only by estimates and measurement uncertainty. The measurement uncertainty is specified without a sign. Measurement uncertainties are themselves estimates. Other names for measurement uncertainty are according to DIN 1319-3 standard uncertainty, standard uncertainty, or simply uncertainty. The previously used in similar contexts error term is not synonymous with the concept of measurement uncertainty.

Meaning and purpose of estimating measurement uncertainties is to define intervals that include the true values ​​of the measured variables or " locate " to.

In general, the uncertainty sets a symmetrically located at the estimated value of the measurement range, the estimate of known systematic errors has been freed. Known systematic measurement errors are not subject to the uncertainty estimate. The measurement result is represented by an expression of the form

Given.

The uncertainty can be multiplied by a coverage factor (s: coverage factor) are multiplied k> 1, in order to increase the confidence interval. This product is referred to as expanded uncertainty U at a given expansion factor:

In the technique expanded uncertainties are usually indicated with k = 2. The region thus defined ( the interval ) is about the width of a 95% probability of occurrence.

Another notation is the trailing indication of the uncertainty of measurement in parentheses. In doing so the standing in the brackets digits to the uncertainty of the last digits of the measured value.

Example: 0.8543 ( 24) corresponds to 0.8543 ± 0.0024

Metrological importance

The measurement uncertainties in science and technology should fulfill three tasks.

• They should objectively measuring results by setting the interval in which the true value of the measurand can be expected. According to classical diction, the confidence intervals whose lengths depended on the level of trust levels were. The classical error analysis must be extended to so-called unknown systematic measurement error. Therefore, the measurement uncertainty can not be assigned in the same way a chance as it is possible in purely statistical errors.

• The thus created network of physical constants must be internally consistent, that is, was calculated on the basis of a given logic function from a subset of constants another, numerically already known constant, so the company resulting from the uncertainty propagation measurement uncertainty must turn to the true value of this constants locate. Measurement uncertainties must therefore satisfy the requirement for " traceability of the true values."

• Measurement uncertainties are to make theory and experiment objectively comparable. They are used as a means to reject a new theory under discussion either or to confirm it.

Questioning of the error calculation

The "classical" Gaussian error calculation deals only with random measurement error. However, Gauss had already referred to the existence and importance of so-called unknown systematic error. These are time-constant, unknown in terms of magnitude and sign of disturbances, which are usually in a way comparable to the random errors of magnitude. Unknown systematic measurement errors must be limited by means of intervals.

Today's mainstream metrology interprets the process of estimating the measurement uncertainty as a " technical regulation ", which is uniform to practice. In the field of legal metrology and calibration service in Germany, it is recommended to determine measurement uncertainties to DIN. This Guide to the Expression of Uncertainty in Measurement conforms to the European pre-standard ENV 13005, which accepts the recommendation of the ISO; He has become well known under the acronym " GUM".

Exact values

Values ​​( not rounding up) do not wear measurement uncertainty are referred to in metrology as exact. For example, the mass of the international prototype kilogram is exactly 1 kg a Troy pound contains exactly 12 troy ounces.