The rules for minimizing systematic errors influence to the measurement result.

The determinated character, i.e. the systematic errors distinctness, gives us the possibilities to diminish their influence to the measurement results or even to their complete exclusion. It can be made before measurement experiment, in the time the experiment and when processing the results.

Here are the common ways of systematic errors elimination:

1. Elimination of systematic errors causes–is the most important, the most radical method one should start with.

 For example, it is known in a room where measurements are held, the temperature varies and the power supply voltage is unstable during a working time.

Previous analysis of the used MI characteristics and the trial researches showed that it causes the systematic errors appearance.   

The most effective way to avoid them is to make the temperature stable, using, for example, an air-conditioner, and in the power upply voltage–with a voltage stabilizer or replacement domestic independent stable voltage power units.

   2. Applying of the corrections into results of measurements.

Unfortunately previous the most effective way may be used not every time. For example, it is necessary to use a voltmeter under field conditions, where in daytime the temperature can vary by several tens of degrees. It is actually impossible to stabilize the temperature, therefore the systematic errors are unavoidable.

 Redusing of their influence on the measurements results is possible by applying at the corrections. In order to find the corrections it is necessary previously to calibrate the instrument in the foreseeable usage conditions. For this purpose it may be put inside a thermostat, and by varying the temperature compare its indications against the indications of the reference instrument, situated outside the thermostat in the normal laboratory conditions. Difference between the indications may be used for the formation of a corrections table under the different temperatures.

 In further work outside the laboratory we need the above mentioned voltmeter, the thermometer (an auxiliary measurement instrument) and the corrections table. Having measured a temperature we add every result of the made beofre voltage measurement to a correction from the table. The systematic component of the temperature influence error to the voltmeter indications is excluded, in the results of the voltage measurement gained in this way.

   3. Substitution of the measuring instruments with those to which the systematic errors from the given reasons are not inherent.

For example, an experiment is held in the conditions of intense external magnetic fields that causes the considerable systematic errors of the electrodynamic type instruments. Let us substitute them by the electrostatic type instruments are not influenced practically by magnetic fields, and the problem of those errors will be liquidated.

4. Choice of the measurement methods, which give the  possibility to reduce the systematic errors influence.

For example, applying the substitution method at a measurement of a resistor resistance by a d.c. bridge gives the possibility to avoid a considerable part of the systematic errors. At first, having connected to the bridge the resistor examined, we balance the bridge. Then, instead of the above-mentioned resistor, we connect a regulble resistance material measure. Making no changes in the positions of the bridge controls, we balance it again by varying the regulble resistance material measure. Its resistance at the moment of balance equates the resistance of resistor being exemined.In this case the measurement error depends on the material measure error (as a rule, very little) and a random error of the bridge.The constant systematic errors in this case are excluded.

5.The sign reversal method of error compensation allows to exclude known on the reasons but unknown on the values systematic errors from the reasons of a directional action.For example, it’s known, that in a measurement instrument location place there is a constant magnetic field influencing its indications.

To exclude the systematic errors from this stimulus, every measurement is effected with this instrument twice, changing its orientation for 180°.Herewith, if the first indication of the instrument due to action of the constant field is increased, the second one is decreased for the same value. As a measurement result the arithmetic mean of those two indications of the instrument is taken.

Method of symmetrical observations (Fig.11) may be used for exclusion of systematic errors that vary linearly.

       For example, we make an indirect measurement of the resistor R_X resistance, having connected it in series with the resistance material measure R₀ to a power supply and by measurment with the voltmeter the voltage drops across those resistors U_X and U₀.

If currenti remains changeless , then it is very simple.

Actually:

                     i=;  Hence   R_x=R₀.

 Fig. 11. The method of symmetrical observations

Let us complicated the task. Let current i ≠ const, but

decreases in a linear way in time, e.g., on account of the discharged battery electromotive force decrease.

For exclusion of a systematic error, appearing herewith, we make not two measurements as before, but at least three. First time we measure a voltage drop U₀₁ from current i across the resistance material measure( resistor R₀):

U₀₁ = iR₀

The we measure the voltage drop U_X across the resistor R_X from the already decreased by Δi₁ current at regular intervals:

U_x = (i – Δi₁) R_x ,

      The, again the voltage drop U₀₂ - from the current decreased on Δi_2:

 U₀₂ = (i – Δi₂) R₀ .

If the current varies in time in a linear way, then:

                                  Di₁=Di₂.

Then:                    i-Di₁=,

                                 U_x=.

Hence:                     R_x=

     Method of periodical observations is used when the systematic error varies with a periodical regularity. To exclude the error we have to hold two observations through a half of the period in moments, when this error gets equal values of the opposite sign. As a result of averaging these observations data, the systematic error is excluded.

Method of standard signals is often used for the automatic correction of indications of the modern automatic measurement instruments and systems. In this case a material measure, value of which is known precisely, is periodically connected to the measuring input of the instrument, instead of the unknown quontaty. The difference between the material measure value and the instrument indication is used as a correction.

Method of auxiliary measurements may be used to execude the systematic errors from the known influencing quantities. If the systematic error dependence upon, for example, temperature, humidity, power supply voltage and other influencing quantities is known, then it is possible, having measured these quantities with the auxiliary measuring instruments, to calculate the error and to apply a correction to the result.

Some less widely used methods of systematic errors exclusion may be suggested as well. But unfortunately under almost all the measurements it is impossible to avoid completely the systematic errors influence, on account of that some remainder of the unexcluded systematic error always remains in their results.

Effectiveness of the measures on systematic errors exclusion from the measurement results is characterized by the so called correctness of measurements.

The correctness of measurements is quality of measurements displaying the systematic errors proximity to zero in their results.

            Questions for self-verifications: