Random deviation

In technology , the natural sciences and other sciences it is known that measured values often result differently in repeated measurements despite the same conditions. As random deviations or random errors , the deviations of the measured values from their mean value referred to (strictly according to DIN 1319 -1, the deviations from the expected value as the limit value of the average value to an infinite number of measured values). Random deviations vary in amount and sign.

The alternative are measurement deviations, which always result in the same way with repeated measurements. They are called systematic deviations .

The deviation of a measured value from the true value is made up of a systematic and a random component.

In principle, the systematic component can be identified by exploring its causes and their (constant) influences (e.g. temperature influence, circuit influence ).
The random component can be calculated from a sufficiently large number of individual measured values using statistical methods (preferably error calculation ).

With an increasing number of measured values, their mean value approaches the expected value; the random deviation or uncertainty of the mean value also approaches zero. Mathematically, the convergence results from the law of large numbers .

By correcting the expected value for the systematic deviations, the true value is obtained.

According to DIN 1319-1, the causes of random measurement errors are usually:

Unmanageable influences of the measuring devices ,
Influences from the environment that cannot be controlled,
Changes in the value of the measured variable that can not be controlled ,
Influences of the observer that are not one-sided (e.g. when reading a scale ).

If the mean value and its uncertainty are determined from the measured values , then in the absence of systematic deviations the true value is assumed with a certain statistical certainty in ${\ displaystyle {\ bar {x}}}$ ${\ displaystyle \, u}$ ${\ displaystyle \, x_ {w}}$

{\ displaystyle {\ bar {x}} - u \ \ leq x_ {w} \ \ leq {\ bar {x}} + u}

abbreviated to

{\ displaystyle x_ {w} = {\ bar {x}} \ pm u.}

This notation with ± must not lead to confusion with unknown systematic measuring device deviations, for which an error limit G is given in practical measurement technology , so that the same notation applies to a read value ${\ displaystyle \, x_ {a}}$

{\ displaystyle x_ {a} -G \ leq x_ {w} \ leq x_ {a} + G}

abbreviated to

{\ displaystyle \! \, x_ {w} = x_ {a} \ pm G.}

In the case of measuring device deviations, according to DIN 1319-1, it can be assumed that the amount of the random deviation is significantly smaller than the error limit (otherwise the random deviation must also be taken into account when determining the error limit). In the case of measured values, the quality of which is determined by the error limits of the measuring devices, the investigation of random deviations is therefore not useful.