# Measurement deviation

Measurement deviation is a term from measurement technology or metrology . The measurement deviation is defined as the difference between the measured value and the reference value. (The term measurement error is no longer used in the current standard because it is not clearly defined whether it refers to the measurement deviation, measurement uncertainty or even a gross error , see measurement error ). The following can be used as a reference value:

• A value with negligible uncertainty or an agreed value ,
which is designated as the correct value in DIN 1319-1 and DIN 55350-13 .

Measurement errors always have a systematic and a random component. The systematic component can become zero, the random component cannot.

## Preliminary remark

When specifying a measured value, one should always ask:

• How far can I rely on the displayed (determined) value as a correct statement about the size to be measured?
Example: An electrical current is exactly 5 A, is exactly 5 A displayed?
• How far can I rely on the determined numerical value?
Example: Does the specification "5" mean: estimated between 0 and 10, maybe also 6, or does the specification "5" mean exactly up to a deviation of ± 0.1 that is possible due to the estimation uncertainty? In the second case, 5.0 should be written. It is mathematically the same, but of a different quality in terms of measurement technology.
Example: What is the meaning of the specification “4.8376” with a deviation of ± 0.1 due to error limits ? The specification pretends a non-existent quality and is to be replaced by 4.8. Without information on the reliability of a measurement statement, the statement is of dubious value.

## Definitions

### basis

In measurement technology, a distinction is made between

• ${\ displaystyle x_ {w}}$= true value of the measured variable as the target of the evaluations of measurements of the measured variable; this is an “ideal value” that is usually not exactly known.
• ${\ displaystyle x_ {r}}$ = correct value of the measured variable as “known value” for comparison purposes, the deviation from the true value of which is considered to be negligible for the purpose of comparison.
Between and there is a difference in principle, but quantitatively insignificant.${\ displaystyle x_ {w}}$${\ displaystyle x_ {r}}$

• ${\ displaystyle x_ {a}}$ = displayed (output) value

together from the true value and the measurement error in the form ${\ displaystyle x_ {w}}$${\ displaystyle e}$

${\ displaystyle x_ {a} = x_ {w} + e}$ .

The measurement deviation results from this

${\ displaystyle e = x_ {a} -x_ {w}}$ .

It is not exactly known because the true value of the measurand is not precisely known.

### Quantitative information

In practice, there are two types of information for quantitative information:

#### Absolute measurement error

To determine a measurement error, the unknown true value is replaced by the known correct value, and the difference between the two values ​​is neglected for this purpose. The deviation thus determined instead of by calculation is also referred to as measurement deviation or often as absolute measurement deviation (also absolute measurement error) ${\ displaystyle e}$ ${\ displaystyle F}$

${\ displaystyle F = x_ {a} -x_ {r}}$ .

This variable has a magnitude, a sign and a unit , namely always the same as the measured variable.

#### Relative measurement error

In the conversion

${\ displaystyle x_ {a} = x_ {r} + F = x_ {r} \ cdot \ left (1 + {\ frac {F} {x_ {r}}} \ right)}$

the fraction as a relative error (and relative measurement error) is referred ${\ displaystyle f}$

${\ displaystyle f = {\ frac {F} {x_ {r}}} = {\ frac {x_ {a} -x_ {r}} {x_ {r}}} \ cdot 100 \ \% = \ left ( {\ frac {x_ {a}} {x_ {r}}} - 1 \ right) \ cdot 100 \ \%}$.

This quantity has the unit one ; it can be positive or negative.

• Note 1: A value does not give rise to a measurement. The relative error cannot be calculated for this either.${\ displaystyle x_ {r} = 0}$
• Note 2: It applies   to everyone . Furthermore: 100% = 1.${\ displaystyle x \ cdot 1 = x}$${\ displaystyle x}$

Example :${\ displaystyle x_ {a} = 3 {,} 80 \ \ mathrm {A}; \ x_ {r} = 3 {,} 85 \ \ mathrm {A}}$

${\ displaystyle F = -0 {,} 05 \ \ mathrm {A}}$
${\ displaystyle f \, = - 1 {,} 3 \ \%}$

Risk of confusion : In connection with class symbols , the upper limit of the measuring range is mainly used as a reference value (i.e. in the denominator) instead of the correct value . Then the related quantity (i.e. in the numerator) is not an error, but an error limit, which has nothing to do with definitions of the term error or deviation.

## causes

• Measuring device deviations as a result of the imperfection of the design, manufacture, adjustment (e.g. due to materials, manufacturing tolerances)
• Influences caused by the measuring method as a result of the effect of the measuring device on the measured variable (e.g. feedback deviation [circuit influence error] due to internal consumption of the measuring device)
• Environmental influences as a result of changes in the effects of the environment (e.g. temperature, refraction anomalies , external electric or magnetic fields, influence of the spatial position , vibrations)
• Instabilities in the value of the measured variable or the carrier of the measured variable (e.g. statistical processes, noise)
• Observer influences as a result of different human characteristics and abilities (e.g. attention, exercise, visual acuity , estimation ability , parallax , timing and target errors )

Stand here outside the discussion

• Falsifications due to errors of the observer ( gross errors ),
• Falsifications due to the choice of unsuitable measurement and evaluation methods,
• Falsifications due to non-observance of known disturbance variables.

## species

The measurement deviation of an unadjusted measurement result is made up of the systematic measurement deviation and the random measurement deviation.

### Systematic error

A unidirectional deviation that is caused by identifiable causes in principle is a systematic deviation .

• If a measurement is repeated under the same conditions, the same systematic measurement error is present; it cannot be seen from the measured values.
• A systematic measurement deviation has a magnitude and sign.
• A systematic measurement deviation is made up of a known and an unknown systematic measurement deviation.
• To calculate a measurement result, the measured value is corrected by the known systematic measurement deviation.

### Random measurement error

A non-controllable, non-one-sided deviation is a random deviation .

• With repetitions - even under exactly the same conditions - the measured values ​​will differ from one another; they scatter.
• Random measurement deviations vary according to their amount and sign.

A distinction must be made between:

• A measurement result is always incorrect due to systematic measurement deviations.
• A measurement result is always uncertain due to random measurement deviations.

## special cases

### Dynamic measurement error

In the case of non- stationary processes, a dynamic measurement error occurs. The value supplied by a measuring device generally follows the change in the input signal over time with a delay. The delay can often be described by a low-pass behavior. For the case of the proportional relationship, which is common in the steady (steady) state${\ displaystyle x_ {a}}$${\ displaystyle x_ {e}}$

Relative dynamic deviation after a jump with a first-order low pass
${\ displaystyle x_ {a} = k \; x_ {e}}$

the delay creates a dynamic measurement deviation (also dynamic error)

${\ displaystyle F _ {\ mathrm {dyn}} (t) = x_ {a} (t) -k \; x_ {e} (t)}$.

In the event of a sudden change in the input signal, this deviation fades away again with a delay element . In the case of vibratory systems, damping is required for this.

In the case of sinusoidal alternating quantities with a variable frequency, a frequency response is created that influences the amplitude and phase angle.

### Quantization measurement deviation

In the case of a measuring device with an analog-to-digital converter , a measurement deviation arises as a result of the digitization , which is treated under quantization deviation .

### Meter deviation

Every meter has had a meter deviation since it was manufactured. This can be determined by comparison with a much better measuring device; it is therefore of a systematic nature and in principle correctable. However, the effort involved is high. There are two ways of dealing with the deviation, one of which should be provided by the manufacturer of the measuring device:

1. The error curve of a measuring device is the graphic representation of the deviation, plotted as a function of the display; sometimes a table is given instead of the curve. The error curve can be used to read the amount and sign of the deviation from a measured value; it is possible to make corrections.
2. Since the error curve only documents the deviation at a certain point in time and under specified influencing conditions, it is usually dispensed with and the manufacturer only guarantees error limits under certain conditions. In some cases, error limits are described across the board using class symbols.

## Margin of error

The margin of error is to distinguish conceptually strictly on the error. It states how large the error in magnitude maximum may be. There is an upper and a lower error limit, preferably the same size, described by the unsigned variable . The true value is (in the absence of a random deviation) in a range  . ${\ displaystyle G}$${\ displaystyle [x_ {a} -G, x_ {a} + G]}$

Occasionally it is possible to improve a measurement method and thus reduce the error limits; The question remains whether the increased (cost) effort is worthwhile.

In many areas, the MPEs are the subject of regulations; then calibration offices and industrial specialist laboratories have to deal with it.

## Individual evidence

1. JCGM 200: 2012 International vocabulary of metrology - Basic and general concepts and associated terms (VIM) , Definition 2.16. (PDF; 3.8 MB; accessed January 19, 2015).
2. Burghart Brinkmann: International Dictionary of Metrology: Basic and General Terms and Associated Terms (VIM) German-English version ISO / IEC Guide 99: 2007 . 4th edition. Beuth, Berlin 2012, ISBN 978-3-410-22472-3 , pp. 36 ( limited preview in Google Book search).
3. DIN 55350-13: 1987, Terms of Quality Assurance and Statistics - Part 13: Terms for the accuracy of investigation procedures and investigation results , No. 1.4. - Withdrawn; As of May 12, 2019
4. ^ VIM, definition 2.17.
5. ^ VIM, definition 2.19
6. a b c DIN 1319-1, Fundamentals of measurement technology - Part 1: Basic concepts , 1995.
7. German Academy of Metrology (DAM): Glossary of Metrology , 2007.
8. ^ A b Elmar Schrüfer, Leonhard Reindl, Bernhard Zagar: Electrical measurement technology . Hanser 2014
9. a b Rainer Parthier: Fundamentals and applications of electrical measurement technology for all technical fields and industrial engineers . 5th edition. Vieweg + Teubner, Wiesbaden 2010, ISBN 978-3-8348-0811-0 , p. 51 f . ( limited preview in Google Book search).
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11. Wilfried Plaßmann: Basics and basic concepts of measurement technology . In: Detlef Schulz (Ed.): Handbook of electrical engineering. Basics and applications for electrical engineers . 6th edition. Vieweg, Wiesbaden 2007, ISBN 978-3-8348-2071-6 , pp. 718 ( limited preview in Google Book search).
12. ^ Tilo Pfeifer, Robert Schmitt: Production metrology . Oldenbourg, 2010, p. 47 ( limited preview in Google book search).
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14. ^ Rudolf Busch: Electrical engineering and electronics for mechanical engineers and process engineers . Vieweg + Teubner, 6th ed. 2011, p. 358 restricted preview in the Google book search.
15. Hans-Rolf Tränkler: Pocket book of measuring technology. Oldenbourg 1990, p. 29.