Lecture 11
Theme: Single measurement on an order scale. Indicator theory.
Single measurement on the graduated scales.
Direct single measurements.
Plan:
Single measurement on an order scale
Indicator theory
Single measurement on the graduated scales.
Direct single measurements.
Single measurement on an order scale. Indicator theory
Sequence of performance of single measurement on an order scale. Features of comparison with the size equal to zero. Indicator theory: optimum filtration; idea of the theory of statistical decisions.
Single measurement on the graduated scales
Sequence of performance of single measurement on the graduated scales of intervals and the relations. Options of use of aprioristic information. Amending.
The majority of technical measurements are straight lines single. Direct single measurements carry out in cases, if: there is no possibility of repeated measurements, at measurements there can be a destruction of object of measurement, economic feasibility takes place.
At direct single measurements use a unique value of counting of instrument readings. Being casual, single counting x includes tool, methodical and personal making errors of measurement, in each of which systematic and casual components can be allocated. Therefore before measurement the aprioristic assessment making errors with use of all available data should be defined. At definition of confidential borders of an error of result of measurements the confidential probability is accepted, as a rule, equal 0,95. The standard regulated the following form of record of result of direct single measurement of size
Repeated ravnotochny measurements
Need for repeated supervision of some physical size arises at existence in the course of measurements of considerable casual errors.
The technique of statistical processing of results of supervision consists of the following operations:
1. Carry out supervision and fix results of supervision of the same value of physical size:;
2. Exclude known systematic errors;
3. Find average arithmetic value of the corrected results of supervision:
4. Calculate an assessment of an average quadratic deviation of results of supervision:
5. Calculate an assessment of an average quadratic deviation of result of measurement:
6. Calculate confidential borders of a casual component of an error of measurements which without a sign is determined by a formula:
where – factor Styyudenta.
For symmetric confidential borders of an error the result of measurement of size is represented in shape:
Control questions
1. In what cases carry out repeated measurements?
2. List algorithms of processing of results of repeated supervision. 3. What criteria use for detection of rough errors?
Lecture 12
Theme: Repeated measurement on an order scale. Bases of the theory of selective statistical control.
Repeated measurement on the graduated scales. Repeated measurement with ravnotochny values of counting. Repeated measurement with neravnotochny values of counting. Processing of several series of measurements.
Plan:
Repeated measurement on an order scale
Bases of the theory of selective statistical control
Repeated measurement on the graduated scales
Repeated measurement with ravnotochny values of counting
Repeated measurement with neravnotochny values of counting
Processing of several series of measurements
Repeated measurement with ravnotochny values of counting
Fundamental idea of repeated measurement. Sequence of performance of repeated measurement on the graduated scales of intervals and the relations. Formation of the massif of experimental data. Amending. Exception of mistakes. Promotion and check of hypotheses about the law of distribution of probability of result of measurement. The solution of a return task at various laws of distribution of probability of result of measurement. Ensuring demanded accuracy of measurements.
Repeated measurement with neravnotochny values of counting
Average weighed. Dispersion of an average weighed. Solution of a return task.
Processing of results of several series of measurements
Homogeneous and non-uniform series of measurements. Check of a normality of results of measurements in each series. Check of the importance of distinction between average arithmetic values of result of measurement in two series. Check of a ravnorasseyannost of results of measurements in two series. Processing of results of homogeneous and non-uniform series of measurements.
Repeated ravnotochny measurements
Need for repeated supervision of some physical size arises at existence in the course of measurements of considerable casual errors.
Direct repeated measurements share on ravnotochny and neravnotochny measurements. Measurements which are led by gages of identical accuracy by the same technique under invariable external conditions are called as Ravnotochnymi. At ravnotochny measurements of SKO of results of all ranks of measurements are equal among themselves.
The problem of processing of results of measurements consists in finding of an assessment of the measured size and a confidential interval in which there is its true value. Processing should be carried out according to GOST 8.207-76 «GSI. Direct measurements with repeated supervision. Methods of processing of results of supervision. General provisions».
Initial information is a row from n (n> 4) results of measurements
X1, the X-th 2, x1 x2 from which known systematic errors - sample are excluded. The number of "n" depends on requirements to accuracy of received result and from real possibility to carry out repeated measurements.
The sequence of processing of results of direct repeated measurements consists of a number of stages:
I stage: Definition of dot estimates of the law of distribution of results of measurements.
Are defined:
- average arithmetic value x of the measured size;
SKO of result of measurement of Sx;
SKO of average arithmetic value S.
According to criteria misses are excluded, then repeated calculation of estimates of average arithmetic and its SKO is carried out. For more reliable calculation can other dot estimates will be defined: factor of an assimetriya of v, эксцесc ε and its counterexcess To;
П stage: Definition of the law of distribution of results of measurements or casual errors of measurements.
From sample of results of measurements х1.х2 хз..., x„ pass to sample of deviations from average arithmetic Akh1, Akh2, Akh3.... Akhp where Ah, = x, - x.
At identification of the law of distribution determine construction by the corrected results of measurements х1, where by i=I, 2..., n, a variation row (the ordered sample), and also Vi where y1=min (x1 and yn=max (In a variation row results of measurements or their deviation have x1 in ascending order; a row break into optimum number of t of identical intervals of grouping in length of h = (y1 + unitary enterprise)/t. Leah of practical application it is expedient to use mmin expression = 0,55п04 and ттах = 1,25п ° received for often meeting distributions with an excess in limits from 1,8 to 6, those from uniform Laplas before distribution. Required value of t in an interval ттin and ттах should be odd as at even value of t the middle of a curve of distribution it is artificial уплощается.
Define
intervals of grouping of experimental data in a look
also
count up number of hits
of
n, (frequency) of results of measurements in each interval of
grouping. The
sum of these numbers should equal to number of measurements. On the
received values
count
probabilities of hit of results of measurement to frequency in each
of grouping intervals on a formula:
рk = n) / п, where к=1,2 … t.
These calculations allow to construct the histogram, the range and a cumulative curve.
Drawing 7.1 - the Histogram, the range (and) and a cumulative curve
For creation of the histogram on an axis of results of supervision x ∆t intervals in ascending order numbers are postponed and on each interval is under construction in p1 rectangle in height. The area concluded under the schedule, is proportional to number of supervision of "n" Sometimes height of a rectangle postpone equal empirical density of probability р1 = pt/∆k = n k/(∆n k) which is an assessment of average density of n “n” interval In this case the area under the histogram is equal 1. At increase in number of intervals and respectively reduction of their length the histogram more and more comes nearer to a smooth curve - to graphics of density of distribution of probability.
The range represents the broken curve connecting the middle of the top bases of each column of the histogram; it reflects a form of a curve of distribution. Outside of the histogram on the right and at the left there are empty intervals in which the points corresponding to their middle, lie on an axis of abscissae. These points at creation of the range connect among themselves pieces; as a result together with an axis x the closed figure, which area according to rationing rules is formed, should be equal to 1 (unit) (or to number of supervision when using by frequency).
The
cumulative curve is a schedule of statistical function of
distribution.
For its construction on an axis of results of supervision x
postpone
intervals
Д4
in
ascending order numbers and on each interval build a rectangle
Fk value is called as a cumulative particular, and n sum - cumulative frequency. By the form constructed dependences the law of distribution of results of measurements can be estimated.
III stage: An assessment of the law of distribution by statistical criteria. At number of supervision of n> 50 for identification of the law of distribution Pearson is used criteria!' - х2 (хи - a square) or Mizesa-Smirnov's criterion (ω2). At 50> п> 15 the compound criterion is applied to check of a normality of the law of distribution (by d - criterion), given in Gost8.207-76. At п <the 15th belonging of experimental distribution to the normal is not checked.
IV stage: Definition of confidential borders of a casual error.
If it was possible to define the law of distribution of results of measurements, with its use find a kvantilny multiplier of Zp at a preset value of confidential probability of R; in this case confidential borders of a casual error д = ± z p Sk
V stage: Delimitation of not excluded systematic error in results of measurements.
Borders of not excluded systematic error are accepted equal to limits of allowed main and additional errors of measuring instruments if their casual components are negligible. The confidential probability at delimitation 0 is accepted the equal confidential probability used at finding of borders of a casual error.
Control questions:
According to what state standard specification processing of results of measurements is carried out?
Ravnotochnye and neravnotochny measurements.
Call sequence of stages of processing of results of measurements.
What dot estimates are applied to more reliable calculation?
How intervals of grouping of experimental data are defined?
How the probability of hit of results of measurements (frequency) in grouping intervals pays off?
How the histogram, the range and a cumulative curve on the basis of the carried-out calculations is under construction?
How confidential borders of a casual error are defined?
Delimitation of not excluded systematic error.
Lecture 13
Metrological Supervision and state testing of measuring instruments. Metrological control the measurements, condition and use of measuring instruments. Organization, procedure and methods of verification of measuring instruments. The concept of verification, calibration, adjustment and calibration of measuring instruments. Calibration scheme. Public acceptance and routine tests measuring tools
Plan:
Quality of measurements on an order scale
Quality of measurements on the graduated scales
Quality of measurements on an order scale
Quality of decisions. Bases of the theory of statistical decisions.
Quality of measurements on the graduated scales
Quality of single measurement
Uncertainty of the amendment. Uncertainty of value of the measured size. Indicators of quality of single measurement - accuracy and correctness.
Quality of repeated measurement
Uncertainty of counting. Uncertainty of the indication. Uncertainty of the amendment. Uncertainty of value of the measured size. Indicators of quality of repeated measurement - accuracy and correctness - at ravnotochny and neravnotochny values of counting.
Quality of measuring information
Reliability of measuring information at measurements on an order scale. Reliability of measuring information at measurements on the graduated scales.
In a serial scale of number are used not only for distinction of objects, but also for order establishment between objects. The elementary example are estimates of knowledge of pupils. It is symbolical that at high school estimates 2, 3, 4, 5 are applied, and at the higher school exactly the same sense is expressed verbally - unsatisfactory, satisfactorily, well, excellent. It emphasizes "non-numerical" character of estimates of knowledge of pupils. In a serial scale all strictly increasing transformations are admissible.
Establishment such as a scale, i.e. tasks of group of admissible transformations of a scale of measurement - business of experts of the corresponding applied area. So, an assessment of appeal of professions we in the monograph [2], representing itself as sociologists, considered measured in a serial scale. However certain sociologists disagreed with us, believing that graduates of schools use a scale with narrower group of admissible transformations, for example, an interval scale. Obviously, this problem belongs not to mathematics, and to sciences about the person. For its decision rather labor-consuming experiment can be put. While it is not put, it is expedient to accept a serial scale as it guarantees against possible mistakes.
Estimates of experts as it was already noted, often it is necessary to consider measured in a serial scale. A typical example are problems of ranging and classification of the industrial facilities which are Theme to ecological insurance.
Why it is natural to express opinions of experts in a serial scale? As showed numerous experiments, the person more correctly (and with smaller difficulties) answers questions qualitative, for example, comparative, character, than quantitative. So, it is easier to it to tell, what of two weights is heavier, than to specify their approximate weight in grams.
In various areas of human activity many other types of serial scales are applied. So, for example, in mineralogy the scale Moosa on which minerals are classified according to criterion of hardness is used. Namely: talc has a point 1, plaster - 2, calcium - 3, fluorite - 4, apatite - 5, ортоклаз - 6, quartz - 7, topaz - 8, corundum - 9, diamond - 10. The mineral with big number is firmer, than a mineral with smaller number, by pressing scratches it.
Serial scales in geography are - бофортова a scale of winds ("calm", "light breeze", "a moderate wind" etc.), a scale of force of earthquakes. Obviously, it is impossible to argue that earthquake in 2 points (the lamp shook under a ceiling - such happens and in Moscow) exactly in 5 times is weaker, than earthquake in 10 points (final fracture of all on an earth surface).
In medicine serial scales are - a scale of stages of a hypertensive illness (according to Myasnikov), a scale of degrees of warm insufficiency (on Strazhesko-Vasilenko-Langu), a scale of degree of expressiveness of coronary insufficiency (according to Fogelson), etc. All these scales are constructed according to the scheme: the disease is not revealed; first stage of a disease; second stage; third stage … Sometimes allocate stages 1а, 1б, etc. Each stage has the medical characteristic peculiar only to it. At the description of groups of disability of number are used in an opposite order: the heaviest - the first group of disability, then - the second, the easiest - the third.
Numbers of houses are also measured in a serial scale - they show, in what order the street house stand along. Numbers of volumes in collected works of the writer or number of affairs in archive of the enterprise are usually connected with chronological order of their creation.
At an assessment of quality of production and services, in a so-called kvalimetriya (a literal translation: quality measurement) serial scales are popular. Namely, the unit of production is estimated as suitable or not the suitable. In more careful analysis the scale with three gradation is used: there are major defects - there are only insignificant defects - there are no defects. Sometimes apply four gradation: there are critical defects (doing impossible use) - there are major defects - there are only insignificant defects - there are no defects. The similar sense has production rating - the premium, the first grade, the second grade, …
At an assessment of ecological influences the first, most generalized assessment - usually serial, for example: environment is stable - environment is oppressed (degrades). Similarly in an ekologo-medical scale: there is no expressed impact on human health - negative impact on health is noted.
The serial scale is used and in many other areas. In эконометрике it first of all various methods of expert estimates. (see the material devoted to them regarding 3).
All scales of measurement divide into two groups - scales of qualitative signs and a scale of quantitative signs.
Serial scale and scale of names - the main scales of qualitative signs. Therefore in many concrete areas results of the qualitative analysis can be considered as measurement on these scales.
Control questions:
Quality of measurements on an order scale
Lecture 14
Metrological examination (ME) and the study of metrology (MP) technical documentation. The concept of metrological examination and metrological elaboration of technical documentation. Design documentation for the measuring instruments to be ME and MP
Plan:
Quality of measurements on the graduated scales
Quality of single measurement
Quality of measurements on the graduated scales
Quality of single measurement
Uncertainty of the amendment. Uncertainty of value of the measured size. Indicators of quality of single measurement - accuracy and correctness.
Quality of repeated measurement
Uncertainty of counting. Uncertainty of the indication. Uncertainty of the amendment. Uncertainty of value of the measured size. Indicators of quality of repeated measurement - accuracy and correctness - at ravnotochny and neravnotochny values of counting.
the raduirovka of measuring instruments (German graduiren — to graduate, lat. gradus — a step, a step, degree) — metrological operation by means of which a gage (a measure or the measuring device) supply with a scale or the calibration table (curve). Marks of a scale should to correspond with demanded accuracy to values of the measured size, and the table (curve) with demanded accuracy to reflect effect communication in a device exit with the size brought to an entrance (for example, dependence of EDS of the thermocouple of a pyrometer on temperature of her worker spy).
Graduation is made by means of more exact, than graduated, measuring instruments according to which indications establish the valid values of the measured size. Exact measuring instruments are graduated individually, less exact are supplied with the standard scale printed in advance, or the standard table (curve) graduation. Application of standard scales or the standard graduated tables demands sometimes adjustment of measuring instruments for the purpose of finishing of their errors to established by norms.
Control questions:
1. Quality of single measurement
Lecture 15
Metrological control of technical documentation. Organization and procedure. Metrological control design documentation. Metrological control process documentation. Documenting the results of monitoring. Duties and rights of persons conducting metrological control.
Plan:
Measuring information.
Obtaining measuring information
Obtaining measuring information is connected with definition of a delay of distribution of probing impulses. The momentum transfer in the form of the packages filled with fluctuations of bearing frequency, gives a power prize and provides a high noise stability and an informativnost of the measuring channel.
Obtaining necessary measuring information with minimum (or limited) material and temporary inputs demands an attentive approach to preparation and carrying out experiment at measurement of physical sizes. It gains the special importance at statement of difficult expensive experiments. In understanding of a place of measuring experiment that circumstance is important that measurements carry out not for the sake of measurements, and for achievement of the purpose put in this or that research or test. In this regard by preparation of measuring experiment the question first of all is solved: for what to measure. The solution of this question makes essential impact on all procedure of measurement including preparation, carrying out and processing of results of measurements. Depending on the purpose of measurement such problems as what to measure are solved, with what accuracy to measure how to measure and than to measure. Answers to these questions define the content of preparation of experiment at measurement of physical sizes.
Obtaining exact and full measuring information on behavior of object of regulation is most complicated at management of indicators of structure and properties of substances., As a rule, it is impossible to measure parameter interesting us in these cases directly and indirect measurements are used. So, for determination of concentration of solution measure its density and use known dependence of concentration on solution density. If solution multicomponent, for determination of concentration of separate components it is necessary to measure except solution density additional parameters, such, as an elektroprovodnost and viscosity. Accuracy of such indirect measurements can appear insufficient for the purposes of management of technological process.
For obtaining measuring information from many objects or about a large number of parameters of some object, and in some cases and for processing of this information, the special measuring devices which have received the name of information and measuring systems are created. They represent set of measuring instruments, cybernetic and auxiliary devices.
On a way of obtaining measuring information deep devices are subdivided two groups: 1) independent, which results of measurement can be received only after extraction them from a well, IT 2) remote, providing a signal transmission of measuring information on a cable on an earth surface.
On a way of obtaining measuring information the deep - Ttrybora are subdivided into two groups: 1) independent, which results of measurement can be received only after extraction them from a well, and 2) remote, providing a signal transmission of measuring information on a cable on an earth surface.
In some cases obtaining measuring information on controllable process is connected with need of performance of arithmetic operations with frequencies of compared signals. More often measuring information contains in the sum, a difference or the relation of frequencies of target signals of sensors.
The measuring system provides obtaining complex measuring information on properties of breeds directly on a face, its transfer for registration in an analog or discrete form. Continuous record of the signals arriving from primary converters of a probe (in scales 1: 50 and 1: 100 on depth), it is provided with the corresponding ratios of speeds of a protyazhka of a tape of a recorder and probe movement in soil.
Scanning IS are intended for obtaining measuring information on a condition of a field of physical sizes.
Existing practice provides generally obtaining measuring information in field and trade conditions, and its processing - in stationary geophysical laboratories.
The choice of this or that way of obtaining measuring information essentially depends on the nomenclature of measured parameters, dynamic properties of controllable parameter, reliability (non-failure operation and maintainability) analyzers and their metoologichesky providing.
Striking example of modern possibilities of telemeasurements is obtaining measuring information from spaceships when, besides measurement of parameters of the ship, the physiological condition of cosmonauts with transfer of these data to Earth is supervised.
As all gages are intended for obtaining measuring information, it is necessary to stop especially on their information characteristics.
For obtaining measuring information, and also the scientific questions arising thus, the branch of science and the technicians, called by measuring equipment is engaged in production and application of measuring instruments. Thus, the measuring equipment is considered as the sphere of activity of people including scientific activity, production and operation of measuring instruments. The part of scientific bases of measuring equipment is made by metrology as a science about measurements, methods and means of ensuring of their unity and ways of achievement of demanded accuracy.
Definition of the main error pursues the purpose obtaining objective measuring information on real metrological characteristics calibrated in the SI and is one of the main operations by results of which carrying out suitability of SI to further operation is defined.
Let's allocate basic elements of systems without which obtaining measuring information is impossible, and on this element basis we will define possible structures of IS.
In brought to attention of the reader to the book theoretical bases of obtaining measuring information unite with their annex to an explanation of principles of action and design of the IIS main versions.
Showing devices of control of pressure apply to measurement of pressure and obtaining measuring information in a manometer or tyagonaporomer installation site. During the studying and the analysis of technical documentation it is necessary to pay attention to that the working pressure specified in the specification did not exceed 0 75 top limits of measurements of a manometer at relative stability of measured pressure and 0 66th scales of the device at pulsing or sharply changing at operation of the unit pressure.
Showing devices of control of pressure apply to measurement of pressure and obtaining measuring information in a manometer or tyagonaporomer installation site. During the studying and the analysis of technical documentation it is necessary to pay attention to that the working division specified in the specification did not exceed 0 75 top limits of measurements of a manometer at relative stability of measured pressure and 0 66th scales of the device at pulsing or sharply changing at operation of the unit pressure.
For determination of METs parameters the decision of system of the equations that demands obtaining measuring information on active or passive sizes is necessary.
Development of means of IIT is connected with reduction of the power expenses necessary for obtaining of measuring information. So, In electric equipment transition from devices with manual, management to electromechanical automatic devices, and then to the devices based on application of electronic, полупроводниковых1и of microminiature elements, was steadily connected with reduction of the energy spent for performance of process of measurement. This way of improvement of one of operational external characteristics of means of IIT depends mainly on the element base used for нх of construction.
The set of measured parameters, their spatial dispersal, need of automation of management by centralized obtaining measuring information, its processing and elaboration of operating influences predetermine primary use of electric methods of measurement of not electric sizes as electric signals are most convenient for transfer, measurement and processing.
The dosimeter - the device or installation for measurement of ionizing radiation - is intended for obtaining measuring information on an exposition dose and capacity of an exposition dose of photon radiation and (or) about the energy transferred by ionizing radiation or transferred to object, being in a radiation action field.
Radiometr - the device or installation for measurement of the ionizing radiation, intended for obtaining measuring information on activity of a radio nuclide in a source or the sample derivative of it of sizes, about density of a stream and (or) a stream and флюенсе (transfer) of ionizing particles.
The dosimeter - the device or installation for measurement of ionizing radiation - is intended for obtaining measuring information on an exposition dose and capacity of an exposition dose of photon radiation and (or) about the energy transferred by ionizing radiation or transferred to object, being in a radiation action field.
Radiometr - the device or installation for measurement of the ionizing radiation, intended for obtaining measuring information on activity of a radio nuclide in a source or the sample derivative of it of sizes, about density of a stream and (or) a stream and флюенсе (transfer) of ionizing particles.
Lack of test methods and methods of exemplary measures is that additional measurements of tests or exemplary measures are necessary for obtaining additional measuring information. More often additional measurements are carried out consistently in time that reduces speed of IIS as a whole. At fast change of the measured size it can lead to loss of considerable volumes of necessary measuring information.
Nevertheless there are also essential peculiar features without which obtaining qualitative measuring information on a chemical composition is impossible.
The system can be used as independently, and as a part of АСУТП, providing obtaining measuring information, its transformation and representation in a demanded look to the consumer - to the operator who has been directly connected with performance of technological operations, and for input in АСУТП.
In these (5.92) characteristics are designated uniformly: equality to zero of any physical characteristic excludes possibility of obtaining measuring information.
Control questions:
Obtaining measuring information
Radiometr
Dosimeter