Systematic error
It refers to "the difference between the average value of the results obtained from an infinite number of measurements of the same measured object and the measured true value under repeatability conditions". It is a component of measurement error that remains unchanged or changes in a predictable manner in repeated measurements. Because only a limited number of repeated measurements can be made, the true value can only be replaced by an agreed true value, so the systematic error that can be determined is only an estimate. The source of systematic error can be known or unknown, so how to find the systematic error?
1. Measure the same measured object multiple times under specified measurement conditions, and find and obtain an estimate of the constant systematic error from the difference between the measurement results and the measurement standard reproduction value.
2. When measurement conditions change, for example, when street conditions such as time and temperature change, they change according to a certain law, which may increase linearly or nonlinearly, but will decrease, so that variable systematic errors in measurement results can be found. In general, methods can eliminate or reduce systematic errors, as follows:
(1) Use modified methods: For the known part of the systematic error, use modified methods to reduce the systematic error. Systematic error correction methods include adding correction values to the measurement results; multiplying the measurement results by the correction coefficient; drawing correction curves; and making correction value tables. For example, if the measurement result is 20 and the measurement result is 20.1, the estimated value of the known systematic error is -0.1, that is, the corrected measurement result is equal to the uncorrected measurement result plus the correction value. That is, the corrected measurement result is 200.1=20.1.
(2) During the instrument calibration experiment, all factors that cause systematic errors should be reduced or eliminated as much as possible. For example, when using the instrument, do not center it, but adjust it to the ideal state of horizontal, vertical or parallel, which will cause systematic errors, so the operator should adjust it carefully to reduce the error.
(3) Select appropriate measurement value methods to offset systematic errors instead of incorporating them into the measurement results. For example, the constant systematic error elimination method can use the opposite sign method, that is, change some conditions in the measurement, such as measurement direction, voltage polarity, etc., so that the error signs in the measurement results under the two conditions are opposite, and take the average value to eliminate the systematic error. The exchange method is to appropriately exchange some conditions in the measurement, such as exchanging the position of the measured object, in an attempt to make the error sources in the two measurements have opposite effects on the measurement results, thereby offsetting the systematic error. The substitution method is to keep the measurement conditions unchanged and replace the measured part with a standard device of known value, so that the indication of the indicating instrument remains unchanged or points to zero. At this time, the measured value is equal to the known standard value to eliminate the systematic error.
In order to eliminate variable systematic errors, a reasonable design of the measurement procedure can eliminate the systematic errors caused by the linear drift or periodic changes of the measurement system.
Random error
Random error is "the difference between the average value and the measurement result of the same measurement result measured infinitely many times under repeated conditions". In fact, the conditions of multiple measurements cannot be absolutely the same. The fluctuations or small differences of various factors combine to cause the error of each measurement value to change in an unpredictable way. Therefore, random error may only determine its estimated value, because the measurement can only be carried out a limited number of times, and there is no definite regularity as far as a single random error is concerned; but in general, it follows certain statistical laws. Random errors are generally caused by random spatiotemporal changes in influencing variables, resulting in the dispersion of data in repeated measurements. The repeatability of measurement results is caused by the fact that all influencing factors affecting the measurement results cannot remain constant.
The statistical regularity of random errors can be summarized as symmetry, boundedness and unimodality. Symmetry refers to errors with equal absolute values and opposite signs, and the probability of occurrence is roughly equal. That is, the measured values are symmetrically distributed with their arithmetic mean as the center. Because the algebraic sum of all errors is close to zero, random errors are compensated. Boundedness means that the absolute value of the measurement value error will not exceed an irregular limit, that is, there will be no errors with large absolute values. Single peak means that the errors with smaller absolute values are more than the errors with larger absolute values, that is, the measured values are relatively concentrated with their arithmetic mean as the center.
Random error is a component of measurement error, which changes in an unpredictable way in repeated measurements. The size of the random error is reflected in the discreteness of the measured value, that is, the repeatability of the measurement. The repeatability of the measurement is characterized by the experimental standard deviation. When the arithmetic mean of multiple measurements is used as the measurement result, the experimental standard deviation of the measurement result is 1/3 times the experimental standard deviation of the measured value (n is the number of measurements). Therefore, when the repeatability is poor, increasing the number of measurements can reduce the random error of the measurement. However, as the number of measurements increases further, the degree of reduction of the experimental standard deviation of the arithmetic mean decreases, which will increase problems such as manpower, time, and instrument wear. Generally, 3 to 20 times can be taken.