ERRORS OF MEASUREMENTS AND MEASUREMENT INSTRUMENTS

The aim of any measurement is determination of the true value of PQ. But this aim is unattainable neither theoretically (see the definition of the term "true value of a PQ" ), non practically. A result of a measurement can be only approximate to the true value of a PQ. Unfortunately the difference always exists between a measurement result and the true value of the PQ and it is called “ the error of measurement”.

Error of measurement is a deviation of a measurement result from the true value of a measurand. In practice, the error is considered as a deviation of the measurement result from the actual value of the measurand (i.e. from the conventional true value).

 It is always necessary to take measures to reduce the errors influence on a measurement result or at least to estimate their influence numerically. As far as those measures are too manifold for different kinds of errors, it is necessary to develop a classification of errors. For this purpose we shall divide the total measurement error into the components, each of them vitiates the result to some degree.

3.1. According to the components of measurement the errors may be classified as:

- the unit reproduction error (the material measure error);

- the transformation error;

- the comparison error;

- the measurement result fixation error.

A material measure takes part in any measurement, either during a measurement experiment or before, when the direct evaluation MI was calibrated. Error of the material measure, i.e., deviation of the reproduced by one PQ from the true ("ideal") value, makes its own contribution to the total error. The error is also increased by the transformations that are occured to it as well as to the measurand at their transition through the elements of the MI block-diagram. Imperfection of the comparison and the result fixation increase the error as well.

3.2. Depending on the source of the origin the errors are classified as:

- the method errors (the methodical errors);

- the instrumental errors;

- the errors from interaction;

- the external errors;

- the personal errors.

The methodical error (of measurement) is a component of the measurement error caused by inadequacy of the object of measurement to its model, adopted for the measurement.

For example, in an accepted model of measurement we suppose that the ideal sinusoidal current, having, as it is known from electrical engineering, form factor K_f = 1.11, flows through the object. Its effective, i.e. R.M.S.(root mean square) value is measured with a rectifier-type ammeter (a part of a tester) that responds to the average rectified value of current, but is gauged in the effective values of a sinusoidal current. If in practice the form of the current curve is not the ideal sinusoid, we get the methodical error, appeared because of imperfection of the adopted model (it would be more rational to make the measurement with an instrument responding directly to the effective value of the quantity, of the electrodynamic system, for example).

The instrumental error (of measurement) is a component of a measurement error caused by the instruments properties. The instrumental error consists of the measurement instruments error and the error due to interaction of the MI with an object under measurement.

When manufacturing any MI, for example, electromechanical ammeter, some tolerances are unavoidable: deviations from the ideal technology, the moving parts backlashes, the inaccuracy of gauging, etc. These factors cause the instrumental error, which together with other errors vitiates the measurement results.

The interaction error is a component of the instrumental error, arising as a result of a measurement instrument influence to the status of the object under measurement.

Let us consider the example, that illustraes the influence of MI on the object. A voltage source with E.M.F. of 100 V, is connected to the 100 Ohm resistor. According to the Ohm’s law, the current of 1A flows through the resistor. In order to measure this current, we have to connect an ammiter, having the proper resistance, for instance, 1Ohm, with the resistor in series. Of course, the ammeter will indicate a little bit less current than the computed one. The reason is the connection of the MI, which changed the object regime – the total resistance of the circuit became 101 Ohm, not 100 Ohm as it was without the ammeter. 

How can we avoid this error? Theoretically, it is necessary to use an ammeter with zero internal resistance (not existing in reality). Practically, to diminish this error we should use an ammeter, the resistance of which has to be vastly less (e.g. in hundreds, thousands times) than the resistance of the object where the current of which is measured.

 From the same consideration, the input resistance of a voltmeter, or other instruments, that are connected in parallel to the object, has to be many times greater than the object resistance.

The external errors are caused by external conditions, which affect the MI operation, i.e., the conditions in which a measurement is realised.

For example, the metrological characteristics of an MI are affected by changes of temperature, humidity, external magnetic and electric fields, vibration, etc.

The personal errors are caused by the personal features of an operator.

For example, acuity of vision, responsiveness during the instrument indication changes, operator’s experience and others, influence the measurement results, introducing more or less errors.

3.3. According to the correspondence of usage conditions to those specified by a normative-technical documentation of a MI, the MI errors are divided into:

- the intrinsic error of a measurement instrument;

- the complementary error of a measurement instrument.

The intrinsic error (of a measurement instrument) is an error of MI under the normal conditions of its operation.

Any MI has its own intrinsic error, if it is used under so-called normal conditions, specified by its normative-technical documentation. For example, for a laboratory instrument the temperature range from 10 to 35^o C may be specified, for an airborne instrument – from minus 60 to 50⁰ C, etc.

 If an instrument is used under the proper, “normal” for it, temperature interval it has an error and this error is called the “intrinsic” error.

The complementary error of MI is a measurement instrument error that additionally appears during the instrument usage under unproper conditions, i.e., when at least one of the influencing quantities deviates from the normal value or is outside the normal value range limits.

The complementary error appears when normal conditions are violated. It is added to the intrinsic error and, thus, increases the total error of a given MI.

     3.4. According to the behavior of a measurand during the measurement, the MI errors are divided into:

- the static error of MI;

- the MI error in dynamic regime;

- the dynamic error of MI.

This aspect of the MI errors classification is caused by the MI’s inertia, both mechanical and electrical, that becomes especially appreciable during a measurement of the fast varying quantities.

The matter is, that the instrument indications are set not immediately after changes of a measurand, but only after a certain transient process – electrical, caused by reactivity of instrument schemes and mechanical, for electromechanical instruments depending upon their moving parts masses. That indication lag is the MI error itself.

The static error of MI is an error of static measurement. The static error occurs at measurement of a time-invariant quantity.

For example, a measurement with a voltmeter of a direct current voltage or the effective value of alternating current voltage if those values stay costant during the whole time of a measurement experiment.

 The MI error in dynamic regime іs an error of MI used for measurement of a quantity that changes during a measurement experiment.

The dynamic error of MI is a component of the error, arising in addition to the static error during the dynamic measurements.

The MI dynamic error is a difference between the MI error in the dynamic regime and its static error that corresponds to the value of the measurand in the given moment of time.

This component of the error is caused by the fact that a measurand change rate prevails over the MI transient processes rate.

3.5. According to regularity of appearance the errors are divided into:

 -  the random errors;

- the systematic errors;

 - the gross errors (or crude errors).

The random error of measurement (MI) is a component of the total error that changes unpredictably in the series of measurements of the same quantity .

The random errors result from the occasional causes. As a rule, in the case of the random errors arising neither direct causes nor moreover the regularities connecting these errors with their causes can be distinguished

After the completion of the each measurement from the series of measurements of an unchangeable quantity, its result can not be foreseen. The result, that contains the random error can not be foreseen, in principle – will it be more than the previous one, or less, or, may be, the same.

 Of course, when a series of measurements is started without preliminary information about the object, the experiment conditions and the features of the MIs used, all the errors, arising at the first observations, will be random. By the way, the observation is a term used by metrologists to define a single-shot measurement.

However, in the course of the further work, analysing the observation results and connecting them with some causes based on the operator’s knowledge and experience, certain regularities may be revealed.

For example, during repeated measurements of the same value at a gradually increase of the temperature we can see a regular increase of the measurement results (for this purpose it could be useful to plot a diagram of their dependence on the temperature). Various regularities may be found after analysis of many other causes, for example, voltage value in a power supply system of electronic instruments, etc.

 After such analysis, some errors lose the occasionality, indefiniteness as soon as the causes and regularities become known. Such errors are called systematic, i.e., the foreseeable, predictable errors.

The systematic error of measurement (measurement instrument) is a component of the error that remains stable or changes predictably in series of measurements of the same quantity.

The example of a variable systematic error is mentioned above. Let us consider an example of a constant error. Before measurements a pointer of a voltmeter is not fixed on the zero scale mark, as it must be, but indicates one scale division.

For this reason, the result of any measurement will be overrated by one scale division (of course, besides other errors not mentioned here).

Unpredictability, uncertainty of the random errors gives us no possibility to avoid them by an experimental way.

The systematic errors, the causes and regularities of which appearance are well known, may be diminished or even avoided during the experiment preparation, during its performance or by statistical analysis of the measurement results.

The gross measurement error (gross error of MI) is a measurement error that greatly exceeds an expected error  (under given conditions).

The gross measurement errors arise mostly as a result of the MI damage or the mistakes caused by the poor qualification of an operator.

 For example, after dropping a tester an attempt to measure with it a power supply voltage that has to be close to 220 V gives us a result of 100V. Having examined carefully the instrument, we may notice that the pointer touches the scale and for this reason it cannot move further. When measuing the same voltage with serviceable instrument but with several scales, an unqualified operator may give an obviously incorrect result, having used the wrong scale or incorrectly counted the scale factor.

The gross measurement errors are too dangerous, so one has to be very accurate to prevent their appearance. As it will be shown below, when processing the frequentative observation results, all the errors, exceeding the value of 3s are qualified as gross errors and they are not taken into consideration in calculations (s is experimental standard deviation or, as it is called sometimes, the error).