Processing of the results of direct measurements. Measurement accuracy

Introduction ……………………………………………………………………………3

Measurement error……………………………………………………….. 4

Accuracy and reliability of measurement results ……………………………8

Conclusion ………………………………………………………………………….9

List of used literature …………………………………………..11

Introduction

Metrology as a science and a field of human practical activity originated in ancient times. Throughout the development of human society, measurements have been the basis of people's relationships with each other, with surrounding objects, and with nature. At the same time, certain ideas were developed about the sizes, shapes, properties of objects and phenomena, as well as rules and methods for comparing them.

With the passage of time and the development of production, the requirements for the quality of metrological information have become more stringent, which ultimately led to the creation of a system for metrological support of human activity.
In this paper, we will consider one of the areas of metrological support - metrological support for certification and standardization of products in the Russian Federation.

Measurement error

Metrology is the science of measurements, methods, means of ensuring their unity and ways to achieve the required accuracy.

Measurement - finding the value of a physical quantity empirically using special tools.

The value of a physical quantity is a quantitative assessment, i.e. a number expressed in certain units accepted for a given quantity. The deviation of the measurement result from the true value of a physical quantity is called the measurement error:

where A is the measured value, A0 is the true value.

Since the true value is unknown, the measurement error is estimated based on the properties of the device, the conditions of the experiment, and the analysis of the results obtained.

Usually objects of study have an infinite set of properties. Such properties are called essential or basic. The selection of essential properties is called the choice of the object model. To choose a model means to set the measured quantities, which are taken as the parameters of the model.

The idealization present in the construction of the model causes a discrepancy between the model parameter and the real property of the object. This leads to error. For measurements, it is necessary that the error be less than the permissible norms.

Types, methods and methods of measurements.

Depending on the method of processing experimental data, direct, indirect, cumulative and joint measurements are distinguished.

Straight lines - a measurement in which the desired value of a quantity is found directly from experimental data (voltage measurement with a voltmeter).

Indirect - a measurement in which the desired value of a quantity is calculated from the results of direct measurements of other quantities (the gain of the amplifier is calculated from the measured values of the input and output voltages).

The result obtained in the process of measuring a physical quantity at a certain time interval is an observation. Depending on the properties of the object under study, the properties of the medium, the measuring device and other reasons, measurements are performed with single or multiple observations. In the latter case, statistical processing of observations is required to obtain the measurement result, and the measurements are called statistical.

Depending on the accuracy of the error estimate, measurements are distinguished with exact or approximate error estimates. In the latter case, the normalized data on the means are taken into account and the measurement conditions are approximately estimated. Most of these measurements. Method of measurement - a set of means and methods of their application.

The numerical value of the measured value is determined by comparing it with a known value - a measure.

Measurement technique - an established set of operations and rules, the implementation of which ensures that the measurement result is obtained in accordance with the selected method.

Measurement is the only source of information about the properties of physical objects and phenomena. Preparation for measurements includes:

analysis of the task;

creation of conditions for measurements;

Choice of means and methods of measurements;

operator training;

testing of measuring instruments.

The reliability of the measurement results depends on the conditions under which the measurements were performed.

Conditions are a set of values that affect the meaning of the measurement results. The influencing quantities are divided into the following groups: climatic, electrical and magnetic (fluctuations in electric current, voltage in the network), external loads (vibrations, shock loads, external contacts of devices). For specific measurement areas, uniform normal conditions are established. The value of a physical quantity corresponding to the normal value is called nominal. When performing accurate measurements, special protective equipment is used to ensure normal conditions.

The organization of measurements is of great importance for obtaining a reliable result. This largely depends on the qualifications of the operator, his technical and practical training, testing of measuring instruments before the start of the measurement process, as well as the chosen measurement technique. During measurements, the operator must:

Observe safety rules when working with measuring instruments;

monitor the measurement conditions and maintain them in a given mode;

carefully record readings in the form in which they are received;

Keep a record of readings with the number of digits after the decimal point two more than required in the final result;

Determine the possible source of systematic errors.

It is generally accepted that the rounding error when taking a reading by the operator should not change the last significant digit of the error of the final measurement result. Usually it is taken equal to 10% of the permissible error of the final measurement result. Otherwise, the number of measurements is increased so that the rounding error satisfies the specified condition. The unity of the same measurements is ensured by uniform rules and methods for their implementation.

Taking measurements.

The terms are divided into the error of the measure, the error of the conversion, the error of comparison, the error of fixing the result. Depending on the source of occurrence, there may be:

Method errors (due to incomplete correspondence of the adopted algorithm to the mathematical definition of the parameter);

instrumental errors (due to the fact that the adopted algorithm cannot be accurately implemented in practice);

external errors - due to the conditions in which measurements are carried out;

· subjective errors - introduced by the operator (incorrect choice of model, reading errors, interpolation, etc.).

Depending on the conditions for the use of funds, there are:

· the main error of the tool, which occurs under normal conditions (temperature, humidity, atmospheric pressure, supply voltage, etc.), specified by GOST;

additional error that occurs when conditions deviate from normal.

Depending on the nature of the behavior of the measured quantity, there are:

static error - the error of the tool when measuring a constant value;

· measurement instrument error in dynamic mode. It occurs when measuring a time-variable quantity, due to the fact that the settling time of transient processes in the device is greater than the measurement interval of the measured quantity. Dynamic error is defined as the difference between the measurement error in dynamic mode and the static error.

According to the patterns of manifestation, they distinguish:

· systematic error - constant in magnitude and sign, which manifests itself in repeated measurements (scale error, temperature error, etc.);

random error - changing according to a random law with repeated measurements of the same value;

Gross errors (misses) are the result of negligence or low qualification of the operator, unexpected external influences.

According to the way of expression they distinguish:

The absolute measurement error, defined in units of the measured quantity, as the difference between the measurement result A and the true value A 0:

Relative error - as the ratio of the absolute measurement error to the true value:

Since A 0 \u003d A n, in practice, instead of A 0, A p is substituted.

Absolute error of the measuring device

Δ n \u003d A n -A 0,

where A p - instrument readings;

Relative error of the device:

The reduced error of the measuring device

where L is a normalizing value equal to the final value of the working part of the scale, if the zero mark is on the edge of the scale; the arithmetic sum of the end values of the scale (ignoring the sign), if the zero mark is inside the working part of the scale; the entire length of the logarithmic or hyperbolic scale.

Accuracy and reliability of measurement results

Measurement accuracy - the degree of approximation of the measurement to the actual value of the quantity.

Reliability is a characteristic of knowledge as justified, proven, true. In experimental natural science, reliable knowledge is considered to be that which has been documented in the course of observations and experiments. The most complete and profound criterion for the reliability of knowledge is socio-historical practice. Reliable knowledge should be distinguished from probabilistic knowledge, the correspondence of which to reality is asserted only as a possible characteristic.

The reliability of measurements is an indicator of the degree of confidence in the results of a measurement, that is, the probability of measurement deviations from the actual values. The accuracy and reliability of measurements are determined by the error due to the imperfection of methods and measuring instruments, the thoroughness of the experiment, subjective characteristics and qualifications of experimenters and other factors.

State system of devices.

Increasing requirements for the quantity and quality of measuring instruments for the needs of the national economy led to the creation of the State System of Industrial Instruments and Automation Equipment (GSP). GSP is a set of products intended for use in industry as technical means of automatic and automated systems for monitoring, measuring, regulating and controlling technological processes (APCS). With the help of GSP means, quantities are measured and regulated: space and time, mechanical, electrical, magnetic, thermal and light.

The development of science and technology causes an increase in the role of measurements. The number of means and methods of measurement is constantly increasing, while it is important that the quantitative and qualitative development of metrology takes place within the framework of the unity of measurement, which is understood as the presentation of results in legal units, indicating the value and characteristics of errors.

Conclusion

Not only metrologists are involved in metrological support activities, i.e. persons or organizations responsible for the uniformity of measurements, but also every specialist: either as a consumer of quantitative information, in the reliability of which he is interested, or as a participant in the process of obtaining it and providing measurements.

The current state of the system of metrological support requires highly qualified specialists. It is impossible to mechanically transfer foreign experience to domestic conditions, and specialists need to have a sufficiently broad outlook in order to creatively approach the development and adoption of creative decisions based on measurement information. This applies not only to workers in the manufacturing sector. Knowledge in the field of metrology is also important for sales specialists, managers, economists who must use reliable measurement information in their activities.

In the general case, the procedure for processing the results of direct measurements is as follows (it is assumed that there are no systematic errors).

Case 1 The number of measurements is less than five.

1) According to formula (6), the average result is found x, defined as the arithmetic mean of the results of all measurements, i.e.

2) According to the formula (12), the absolute errors of individual measurements are calculated

3) According to the formula (14), the average absolute error is determined

4) According to formula (15), the average relative error of the measurement result is calculated

5) Record the final result in the following form:

, at
.

Case 2. The number of measurements is over five.

1) According to formula (6), the average result is found

2) According to the formula (12), the absolute errors of individual measurements are determined

3) According to the formula (7), the mean square error of a single measurement is calculated

4) Calculate the standard deviation for the average value of the measured value by the formula (9).

5) The final result is recorded in the following form

Sometimes random measurement errors may turn out to be less than the value that the measuring device (instrument) is able to register. In this case, for any number of measurements, the same result is obtained. In such cases, as the average absolute error
take half the scale division of the instrument (tool). This value is sometimes called the limiting or instrumental error and denoted
(for vernier instruments and stopwatch
equal to the accuracy of the instrument).

Assessment of the reliability of measurement results

In any experiment, the number of measurements of a physical quantity is always limited for one reason or another. Due with this may be the task of assessing the reliability of the result. In other words, determine with what probability it can be argued that the error made in this case does not exceed the predetermined value ε. This probability is called the confidence probability. Let's denote it with a letter.

An inverse problem can also be posed: to determine the boundaries of the interval
so that with a given probability it could be argued that the true value of the measurements of the quantity will not go beyond the specified, so-called confidence interval.

The confidence interval characterizes the accuracy of the result obtained, and the confidence interval characterizes its reliability. Methods for solving these two groups of problems are available and have been developed in particular detail for the case when the measurement errors are distributed according to the normal law. Probability theory also provides methods for determining the number of experiments (repeated measurements) that provide a given accuracy and reliability of the expected result. In this work, these methods are not considered (we restrict ourselves to mentioning them), since such tasks are usually not posed when performing laboratory work.

Of particular interest, however, is the case of assessing the reliability of the result of measurements of physical quantities with a very small number of repeated measurements. For example,
. This is exactly the case with which we often meet in the performance of laboratory work in physics. When solving this kind of problems, it is recommended to use the method based on Student's distribution (law).

For the convenience of the practical application of the method under consideration, there are tables with which you can determine the confidence interval
corresponding to a given confidence level or solve the inverse problem.

Below are those parts of the mentioned tables that may be required when evaluating the results of measurements in laboratory exercises.

Let, for example, produced equal (under the same conditions) measurements of some physical quantity and calculated its average value . It is required to find the confidence interval corresponding to the given confidence level . The problem is generally solved in the following way.

According to the formula, taking into account (7), calculate

Then for given values n and find according to the table (Table 2) the value . The value you are looking for is calculated based on the formula

(16)

When solving the inverse problem, the parameter is first calculated using formula (16). The desired value of the confidence probability is taken from the table (Table 3) for a given number and calculated parameter .

Table 2. Parameter value for a given number of experiments

and confidence level

Table 3 Confidence probability value for a given number of experiments n and parameter ε

The main properties that determine the quality of measurements. Unity, accuracy and reliability of measurements

Accuracy of measurements- the quality of measurements, reflecting the proximity of their results to the true value of the measured quantity (close to zero error of the measurement result). High measurement accuracy corresponds to small errors of all kinds, both systematic and random. Quantitatively, the accuracy can be expressed by the reciprocal of the modulus of the relative error.

Unity of measurements- the state of measurements, in which their results are expressed in legal units and measurement errors are known with a given probability. One of the necessary conditions for ensuring the uniformity of measurements is the uniformity of measuring instruments.

Under uniformity of measuring instruments understand the state of measuring instruments, characterized by the fact that they are graduated in legal units and their metrological properties comply with the standards. The uniformity of measuring instruments is a necessary but not sufficient condition for maintaining the uniformity of measurements.

Measurement- finding the value of a physical quantity empirically using special technical means (GOST 16263 -70).

The measurement result is obtained with some error. For a preliminary (qualitative) assessment of the value and nature of the error, such most general properties of measurements as accuracy, correctness, convergence and reproducibility of measurements are used.

Accuracy of measurements- the quality of measurements, reflecting the proximity of their results to the true value of the measured quantity. High measurement accuracy corresponds to small errors of all kinds, both systematic and random. Quantitatively, the accuracy can be expressed by the reciprocal of the modulus of the relative error.

Correctness of measurements is the quality of measurements, reflecting the closeness to zero of systematic errors in their results.

Convergence of measurements- the quality of measurements, reflecting the proximity to each other of the results of measurements performed under the same conditions. A high level of measurement convergence corresponds to small values of random errors in multiple measurements of the same physical quantity using the same measurement technique. As a simplified estimate of convergence, such a parameter as the range of measurement results in a certain series can be used. R = Xmax – Xmin.

Measurement reproducibility- the quality of measurements, reflecting the proximity to each other of the results of measurements performed under different conditions (at different times, in different places, by different methods and means).

The reproducibility of measurements can be assessed, for example, after performing several series of repeated measurements of the same physical quantity using different measurement techniques.

Geometric representations of the range R of the measurement results can be obtained using scatter plot the results of multiple measurements of the same physical quantity, which is built in the coordinate system "measured values X - measurement number N" in any convenient scale. The scatter plot in certain cases allows you to make some judgments about the correctness of measurements

SAINT PETERSBURG STATE ACADEMY OF SERVICE AND ECONOMICS

discipline: "Metrology, standardization, certification"

on the topic: “Measurement error. Accuracy and reliability of measurement results»

Performed:

Course: 3, correspondence department

Specialty: Economics and management at the enterprise (health)

St. Petersburg, 2008

Introduction 3

Measurement uncertainty 4

Accuracy and reliability of measurement results 9

Conclusion 11

References 12