Systematic error

As a systematic error (also systematic deviation or distortion; . Engl systematic error or bias) are used in the art, the natural and other sciences refers to measurement errors do not cancel with repeated measurement on the average. Measurement error, which (theoretically infinite number of times ) to offset repeated measurement on average, are, however, referred to as random error.

Systematic errors have thus " flip side ", they cause a trend towards high or low reading. A typical example of systematic errors are errors that arise due to incorrectly calibrated measuring instruments. The sign of the systematic error may depend on the true value ( for example, a wrong calibrated thermometer which has high temperatures above underestimated and low. )

Probability Theoretically, the random deviation of a measured value Δ x disassemble from the true value in a systematic and a random component. The systematic component is then defined as the expected value of the total error, the random component of the difference between the expected measurement error and the actual measurement error.

In practice, all measurements are subject to systematic, random and gross errors. In order to control systematic errors are measures such as the compensation bill after analysis or calibration with closer meter, or possibly used other methods or environment, or mathematical modeling.

Outside of the measurement technique, for example in connection with the IEC 61508, systematic errors in analogous application are considered error as " built-in" that are present in each product. In this sense, for example, the Pentium FDIV bug was one of the systematic errors, because the correct execution of a wrongly implemented function at every produced copy of the Pentium processor at exactly the same led, reproducible calculation errors.

For the nomenclature

Constant Systematic measurement errors are offset tray or similar, called ascending / descending measurement error, however, trend (English and bias) or drift (eg for slow changes in the display of very fine instruments). Trends and drifts are relatively easy to detect by repeated measurements and often go undetected back to temperature effects.

In accordance to the English the word bias is used for systematic error often, among which, however, in electronics, a deliberate and unilateral Vorbeaufschlagung or pre-distortion can be understood.

Causes of systematic errors

The causes of systematic errors can be varied and are usually classified as follows:

• Instrumental influences (eg inaccurate adjustment or calibration, loose parts on the meter, thermal expansion of metal parts, parallax, directional deviation or non-circularity of axes ... )
• Personal errors (eg unilateral small target error, cant read on thermometer scale ...); in surveys response bias
• Environmental influences ( eg, refraction, asymmetrical effects of temperature or wind, vibrations in the ground ... )
• "Other" ( unexplained, non- deterministic) effects
• Systematically usually also act gross errors (eg reading and meter error ), as they may happen due to carelessness, confusion or shock. Performing an adjustment but they can be usually seen if their residual exceeds the 2- 3-fold standard deviation.

Simple example: measuring with a ruler

Internal and external accuracy

The error measure "external accuracy " should be understood as included, while the " inner accuracy " most of the standard deviation (mean error ) at the mere repetition of the measurement corresponds to systematic errors in general. The difference between the two is revealed in part the change of the measuring instrument ( see Figure 1 ), the observer (2) or external circumstances ( 3), such as the weather.

Thus, an astronomical latitude determination with stars and a passage or a digital instrument astrolabe an (internal ) accuracy of ± 0.1 ", but can range from one night to the next by 0.5 " vary. The reason for such " Evening error " is in anomalies of the atmospheric layers ( Astronomical refraction, dome-shaped Saalrefraktion ) or in small temperature effects, such as the telescope flexure.

Countermeasures

As there are systematic errors unlikely to be reduced by repetition, one must either

• Accept and consider when to be specified tolerances,
• Considered in the evaluation model of the data processing (see reduction)
• Compensated by a symmetric measurement process (e.g., 2 circular layers on theodolite ), or
• Reduce or eliminate by calibration, calibration, etc..

Unknown systematic measurement error

Unknown systematic measurement errors are time- constant, unknown in magnitude and sign disturbances; they are in principle not be eliminated and be delimited only by intervals.

Example of a time- constant, unknown systematic error is realizable only with finite precision mechanical adjustment of an optical component: each repeat measurement is superimposed on the same unknown systematic errors. It should apply: -fs ≤ f ≤ fs with

Measured values ​​are superimposed generally both random and unknown systematic errors.

In general, the aim is to work with " drift-free " measurement instruments. Drift free, however, does not mean that the measuring apparatus would be free of systematic errors. Rather, the unknown systematic errors should be no temporal trend, that is temporally not seen change. Specifically, during the recording of repeat measurements observed the experimenter only random errors. The measured values ​​also superimposed unknown systematic error is prior to the start of the repeat measurements to determine not change any more after that and remains hidden from the experimenter. The fact that he is seen physically still present, can alone show the functional analysis of the apparatus. This situation illustrates how difficult it is to locate the true values ​​of measured variables.

To systematic errors change during the measurement, the experimenter records a time series. For the treatment of time series, such as stock quotes, statistics has developed its own, completely different method.

Random and unknown systematic errors are superimposed additively, the type of link sets the error model.