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POINT ESTIMATION OF THE TRUE VALUE AND MEAN
SQUARE DEVIATION OF THE MEASUREMENT
1
Melibaev Makhmudjon
,
2
Negmutullaev Sadiqjon Ergashevich,
3
Jumaeva Makhliyo,
4
Akbarov Saydullahon Askarkhan
1
NamMQI "Metrology and standardization" department professor, Ph.D.
2
NamMQI "Metrology and standardization" department senior teacher
3
NamMQI "Metrology and standardization" department Teacher
4
NamMQI "Metrology and standardization" department 25-MSMSM-21 group student
https://doi.org/10.5281/zenodo.7558337
Abstract.
This article covers in detail the issues of ensuring metrological dimensions at
the required level in the process of production and repair of mechanical engineering parts,
information about the types of measurements, means and rules for their use.
Keywords:
Measurement, device, machine, deviation, deviation, metrology, object,
function, distribution, interval.
It is known in metrological practice that when estimating the true (searched) value of a
measured quantity or finding a measurement result and finding its error according to a group of
results of a series of measurements, the point (point) estimation method of the values of the
distribution function of a random quantity is used. This method is based on solving a statistical
problem, that is, a series of values from the results of n independent experiments based on a
selection.
If the value is represented by a single number, it is called a point estimate. Any point
estimate calculated on the basis of the data obtained from the experiment is a function of it, and
therefore it depends on the distribution of the initial value of the random variable and the results of
the experiment.
It must satisfy the three requirements of point evaluation: perfect, stable and efficient
(effective)
.
Perfect estimation means that the estimable values correspond to the characteristics of the
estimator in terms of probability.
The measurement process and, of course, the measurement results are affected by many
factors, which in some cases are difficult to take into account.Бу омилларни кўриб чиқишни It is
necessary to start by understanding the concept of "measurement process" itself. "Measurement
process" means the total amount of measurement data, devices and operations. In this case, the
"element of the measurement process" should be understood as any individual factor affecting the
measurement result (Fig. 1). Such factors include:
measuring object;
- measurement subject (operator);
- measurement method;
- measuring tool;
- measurement conditions.
The object of measurement has been sufficiently studied, and the formation of its model,
its level of detail (in-depth study of the object of measurement) should be adequate for the
intended purpose of measurement.
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Figure 1.
Measurement of groove dimensions
For example, if "thread size should be measured". First, the object model is created and the
shaft diameter is measured once so that the cross section of the shaft can be circular.
The operator also affects the measurement process, causing subjective error. Subjectivity
of the operator depends on his qualification, psychophysiological condition, sanitary and hygienic
conditions of work (measurement) and others.
Among the factors affecting the measurement result, the measurement method and
measurement tools are also of great importance. It is necessary to choose both the measurement
method and the measurement tool in accordance with the purpose of the measurement process and
the conditions of its implementation.
It should be remembered that measuring instruments have only a specific error
(instrumental component of measurement error) and can change the value of the object of
measurement, that is, it can affect the measured quantity itself.
The measurement conditions affect all other elements of the measurement process - the
measurement object, the measurement tool, and the operator himself.
Often, measurements of a quantity in different ways and using different measuring
instruments give completely different results. Each of these options has its advantages and
disadvantages, and the choice of the most optimal option (for a particular measurement problem)
depends on the skill of the experimenter. Of course, in this case, there cannot be a specific ready-
made solution and recommendation. However, there are some error reduction methods that can
significantly reduce the individual components of the regular error.
Correlation function of random process and their properties.
The following laws are used to study the distribution of random quantities in metrology:
normal (Gauss), uniform distribution law, Student, triangular (Simpson), xi-
(Pearson), Fisher's law, exponential law, etc.
The normal distribution of random variables is often used in measurement techniques. The
law of normal distribution of random errors, based on the theory of probability, is used when the
results of measurements are affected by random factors. Random effects cause measurement
results and errors to be distributed according to (almost) normal law.
The distribution curves according to the normal law for different values of the mean square
changes are presented in Figure 2.
Triangular and uniform even distribution of random quantities are also found in
metrological practice.
Figure 2.
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Uniform (flat) (a) and triangular (b) distribution of random variable
If the random variable X assumes values in the interval from a to b with a constant
probability density, such a distribution is called a uniform (flat) distribution, and this is
characteristic of the display of most digital instruments (Fig. 2a).
The integral function F(t) of the normalized normal distribution is related to the
Laplace function (probability integral) by the following expression.
dV
е
t
L
p
t
v
p
0
2
1
2
2
1
)
(
)
(
5
,
0
)
(
p
t
L
t
F
.
This function does not differ from 1 for large values of t1 in the range outside the limit of
values of t from -3.5 to +3.5.
XI is the squared X2 distribution - the sum of squares of the standard normal
distribution of a random variable.
2
2
2
1
2
1
x
x
n
i
x
x
i
k
S
n
m
x
Х
,
in this
К=н-1
- number of degrees of freedom;
н
- number of random variables. If
х
and
У
are independent quantities, in this
х
- standard normally distributed quantity,
У
while -
К
- with degrees of freedom
2
x
- is a normally distributed random variable,
then the random variable
К
У
x
Т
/
For different values, the Student's distribution is defined as the Student's fraction and is
given in Table 1 (True value of K-size)
n
S
Q
x
S
Q
x
S
m
x
t
x
x
x
x
p
of the magnitude measured using the Student's distribution or from Table B.1
x
p
p
S
t
true value can be determined if its deviation (deviation) from the average arithmetic value
does not exceed.
Fisher distribution.
If
Х
and
У
– independent (unrelated) random variables
1/(
b
-
a
)
2/(
b
-
a
)
p
(
x
)
p
(
x
)
0
a b x
0
a
(
a+b
)/2
b x а)б)
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к
1
and
к
2
– with degrees of freedom
Х
2
if distributed according to, then a random variable
2
1
/
/
k
y
k
x
F
,
ie
F
Fisher distribution
к
1
and
к
2
distributed by degrees of freedom.
The main characteristics of the laws of distribution of random numbers (variables), integral
and differential functions of distribution are given in Table 1.
Table 1.
Characteristics of distribution laws of random variables
Distribution law
Distribution function
Differential
Integral
Normal (Gaussian)
dt
e
t
F
p
t
t
p
2
2
1
2
1
)
(
dx
e
x
F
x
m
x
x
x
x
0
2
2
2
)
(
2
1
)
(
Equally distributed
(Uniform)
x
b
b
x
a
a
b
a
x
x
p
;
0
;
1
;
0
)
(
x
b
b
x
a
a
b
a
x
a
x
x
F
;
1
;
;
0
)
(
Triangle (The Simpsons)
x
b
b
x
b
a
a
b
x
b
b
a
x
a
a
b
a
x
a
x
x
p
;
0
2
;
)
(
)
(
4
2
;
)
(
)
(
4
;
0
)
(
2
2
x
b
b
x
b
a
a
b
x
b
b
a
x
a
a
b
a
x
a
x
x
F
;
1
2
;
)
(
)
(
2
2
;
)
(
)
(
2
;
0
)
(
2
2
2
2
Standardized (normal)
2
2
1
2
1
t
e
t
p
бунда т = (х – м
х
)/σ
dt
e
t
F
p
t
t
2
2
1
2
1
Exponential one-way
(exponential)
x
e
x
P
)
(
x
e
x
F
1
)
(
Example: The distribution of measured sizes of tractor wheel tires can be represented
graphically (Figure 3). On the abscissa axis, the size intervals are plotted according to Table 2, and
on the ordinate axis, the corresponding frequencies m or m/n are plotted. As a result of graphing, a
step line 1 is obtained, which is called a distribution histogram. If we successively connect the
points corresponding to the middle of each interval, a broken curve is formed, which is called the
curve of the empirical distribution or the polygon of the distribution. With a large number of
measured tire treads and a large number of size intervals, the broken empirical curve approximates
a smooth curve in the form of a so-called distribution curve. It is recommended to divide the
measured sizes into at least six intervals with a total number of measured tires of at least 50 units
to construct a histogram distribution.
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183
Under different conditions, the tire tread, the distribution of its actual dimensions, obeys
different mathematical laws. Taking into account that the following laws are of great practical
importance in the work of MTA, normal distribution (Gauss's law), equilateral triangle (Simpson's
law), eccentricity (Rayleigh's law), probability laws and distribution functions that are part of
these laws were taken as a basis.
Table 2.
Distribution of deflection dimensions of tire tread pattern (9.5-42 Ya-183). MMTP
"Kokumboy" and "Hudayberdiyev" in Kosonsoy district
T/r
Interval, mm
Frequency m
Frequency m/n
1
30,00…30,05
2
0,02
2
30,05…30,10
11
0,11
3
30,10…30,15
19
0,19
4
30,15…30,20
28
0,28
5
30,20…30,25
22
0,22
6
30,25…30,30
15
0,15
7
30,30…30,35
3
0,03
Itogo
n = Ʃ m=100
Ʃ m/n = 1
Figure 3.
Distribution of deflection dimensions of tire tread pattern (9.5-42 Ya-183)
"Kokumboy" and "Hudayberdiyev" MMTP of Kosonsoy district
Conclusion
Using the laws of probability allows you to find optimal options for the size of research
results.
REFERENCES
1.
Melibayev M., Dadakhodjaev A., Mamadjonov M. FEATURES OF THE NATURAL-
INDUSTRIAL CONDITIONS OF THE ZONE AND OPERATION JF MACHINE-
TRACTOR UNITS. //ACADEMICIA An International Multidis ciplinary Research Journal.
ISSN 2249-7137. Vol 9 Issue 3, March 2019.
Impact Factor SJIF
2018=6.152.
India
. 2019.
– p. 37-41. (10.5958/2249-7137.2019.00033.8). 6 ieaf.
0
5
10
15
20
25
30
30,00…30,05 30,05…30,10 30,10…30,15 30,15…30,20 30,20…30,25 30,25…30,30 30,30…30,35
1
2
3
4
5
6
7
SCIENCE AND INNOVATION
INTERNATIONAL SCIENTIFIC JOURNAL VOLUME 2 ISSUE 1 JANUARY 2023
UIF-2022: 8.2 | ISSN: 2181-3337 | SCIENTISTS.UZ
184
2.
Melibayev M. Indicator of average resource of pneumatic tires. // International journal of
advanced Research in science, engineering and technology. Journal. ISSN 2350-0328. Vol.6
Issue 10, october 2019.
India
. –p. 11216-11218. 6 ieaf.
3.
М.Мелибаев. Capacity of universal-well-towed-wheel tires. Универсал чопиқ трактори юк
кўтариш қобилияти. //Scientific-technical journal of FerPi. ISSN 2181-7200. Vol.2. 2019.
Fergana. - p. 144-146.
4.
M. Melibayev., A. Dadakhozhozhaev., M.M.Mamadzhonov., Sh.E.Khaydarov. Experimental
methods for determining deformations and stresses of tractor wheel tires.
Scopus ASCC:
2200.
Impact Factor
: Sol 1.1/TAS DOL: 10.15863/TAS International Scientific Journal.
Theoretical & Applied Science.p-ISSN: 2308-4944 (print). e-ISSN: 2409-0085 (online). Year:
2020. Issue: 03. Volume: 83/ Published: 30.03/2020. http://T--Science.org. 7 ieaf.
5.
Мелибаев М., Нишонов Ф., Содиков М.А. Показатели надежности пропашных
тракторных шин. //
UNIVERSUV
: Технические науки. Выпуск: 2(83). Февраль 2021.
Часть 1. М., 2021. –с. 91-94. (http: 7universum.com/ru/tech/archive/category/283).
6.
Melibayev M., Yigitaliyev J. Characteristics of the parameters of tractor tires on a non-
horizontal support surface //International journal for Innovative Engineering and
Management Research. ELSEVIER SSRN.
IJIEMR
Transactions, online available on 26 th,
Feb. 2021. Link: http: //ijiemr.org/downloads/Volume-10/Speciel. Iesse 0,3 Pages: 239-246.
7.
Melibayev M., Dadakhozhozhaev A. Rules for the characteristics of tractor tire parameters on
a non-horizontal support surface.SJIF
Impact Factor
: 2021: 8/013| ISI I.F. Volue:1.241|
Journal DOL: 10.36713/ISSN:2455-7838 (Online).EPRA International jounal of Research
and Developmet (IJRD)|Volime:6|Issue:5| May 2021. Pades: 124-136.
8.
Tolibzhon S. Khudayberdiyev, Makhmudzhon Melibayev, Anvar Dedokhodzhayev,
Ma’rufzhon M. Mamadjonov. (2021). The Dynamic Characteristics of the Tires of the Wheels
of the Tractor.
Annals of the Romanian Society for Cell Biology
,
25
(6), 6758–6772. Retrieved
from https://www.annalsofrscb.ro/index.php/journal/article/view/6767 (Scopus)
9.
Худайбердиев Т.С., Мелибаев М., Дадаходжаев А. Экономическая эффективность
результатов исследований ресурса шин трактора.Gospodarka I innowacje.Laboratorium
WIEDZY Artur Borcuch. ISSN: 2445-0573. Volume: 23/2022.p 464-470/
10.
Мелибаев М., Нишонов Ф., Кидиров А. Требования к эксплуатационным качествам
шин. SCIENCE TIME. Общество Науки и творчества. // Международный научный
журнал.
Казань
Выпуск. № 1/2017 г. -с 287-291.
11.
Мелибаев М., Нишонов Ф. Определение площади контакта шины с почвой в
зависимости от сцепной нагрузки и размера шин и внутреннего давления. //SCIENCE
TIME. Общество Науки и творчества. //Международный научный журнал. Выпуск. № 3
–
Казань
, 2017 г. – с 227-235.
12.
Мелибаев М., Нишонов Ф., Кидиров А. Тягово-сцепные показатели машинно-
тракторного агрегата. //SCIENCE TIME. Общество Науки и творчества.
//Международный научный журнал. –
Казань
. Выпуск. № 1/2017 г. – с 292-296.
13.
Мелибаев М., Дедаходжаев А. Методология системного подхода при выборе
рациональных параметров тракторных шин. Научные традиции и инновации в
прикладных исследованиях. Материалы международной научно-практической
конференции студентов, аспирантов и молодых ученых высших учебных заведений. 26-
SCIENCE AND INNOVATION
INTERNATIONAL SCIENTIFIC JOURNAL VOLUME 2 ISSUE 1 JANUARY 2023
UIF-2022: 8.2 | ISSN: 2181-3337 | SCIENTISTS.UZ
185
апреля 2018 г. ФГБОУ ВО «Российский государственный аграрный заочный
университет». –
Балашиха
: Изд-во ФГБОУ ВО РГАЗУ, 2018 г. – с. 198-202.
14.
Мелибаев М., Дедаходжаев А., Кидиров А. Агротехнические показатели машинно-
тракторных агрегатов.
«Инновационное
научно-образовательное обеспечение
агропромышленного комплекса» 69-ой Международной научно-практической
конференция. ФГБОУ ВО РГАТУ.
Рязань
. 2018 г. - с 261-265.
15.
Мелибаев М., Нишонов Ф., Кидиров А., Акбаров. Буксование ведущих колес
пропашных трехколѐсных тракторов. //Журнал «Научное знание современности».
Материалы Международных научно-практических мероприятий Общества Науки и
Творчества (г. Казань). Выпуск № 4 (16).
Казань
. 2018 г. – с 98-100.
16.
Мелибаев М. Эксплуатационные показатели пропашных агрегатов в тяговых и
агротехнических показателях ведущих колес. Инновационное научно-образовательное
обеспечение агропромышленного комплекса» 69-ой Международной научно-
практической конференция. ФГБОУ ВО РГАТУ.–
Рязань.
2018 г. - с 253-257.
17.
Мелибаев М., Акбаров Ш., Дадаходжаев А. Определение деформации шины в
зависимости от внутреннего давления и размеров шин ведущего колеса. /Федеральное
государственное бюджетное образовательное учреждение высшего образования
“Рязанский государственный агротехнологический университет имени П.А.
Костычева” “Научно-практические аспекты инновационного развития транспортных
систем и инженерных сооружений”. Материалы Международной студенческой научно-
практической конферен. 20 февраля 2020 г.
Рязань
, 2020. –С 164-169.
18.
Мелибаев М., Дедаходжаев А., Лаптев И. Зависимость эксплуатационного ресурса шин
от внутреннего давления. Вестник науки и образования. Электронный научно-
методический журнал. Издательство «Проблемы науки» №10 (22) май. 2019 г. –
Иванова
. 2.06.2019 г.
19.
Мелибаев М., Дедаходжаев А., Мамадалиев Ш. Общие и инерционные характеристики
тракторных шины. //Omega science. Традиционная и инновационная наука: история,
современное состояние, песпективы. Сборник статей. Международной научно-
практической конференции.
Тюмень.
14 марта 2020 г. с. 51-53.
20.
Melibayev M., Yigitaliyev Jaloliddin Adkham ugli. Results of operational tests of tractor tires
with increased service life and their technical and economic efficiency. Euro Asia
Conferences. Euro Science: International Conference on Social and Humanitarian Research,
Hosted from Cologne,
Germany
. April 25
rd
-26
th
2021. http://euroasiaconference.com. Pages:
113-118.
21.
Melibayev M., Yigitaliyev Jaloliddin Adkham ugli. Determination of parameters affecting the
performance of tracto tires. International Journal of Academic pedagogical Reseerch (IJAPR)
ISSN:
2643-9123.
Vol.5
Issue
5,
May
–
2021,
Washgton
DC,USA
.
http://WWW.ijeais.org/ijapr ijaprchiefeditor@gmail.com. Pages: 131-135.
22.
Акбаров, С., Жавохир, Қ., & Мелибаев, М. (2022). ШИНАЛАРНИНГ ҚОЛДИҚ
РЕСУРСИНИ
БАШОРАТ
(ПРОГНОЗ)
ҚИЛИШ.
Journal
of
new
century
innovations
,
18
(1), 60-63.
23.
Askarjon, A. S., Qizi, A. M. K., & Makhmujon, M. (2022). Analysis of the Structure and
Classification of Airless Tires.
Eurasian Journal of Learning and Academic Teaching
,
8
, 78-
81.
SCIENCE AND INNOVATION
INTERNATIONAL SCIENTIFIC JOURNAL VOLUME 2 ISSUE 1 JANUARY 2023
UIF-2022: 8.2 | ISSN: 2181-3337 | SCIENTISTS.UZ
186
24.
Saydullo, A. va Mahmujon, M. (2022, aprel). PAXTA G'ildirakli TRAKTORLAR
SHINALARINI O'RTA RESURSINI ANIQLASH. Konferentsiya
zonasida
(112-115-betlar).
25.
Saydullo, A. va Mahmujon, M. (2022, aprel). PAXTA G'ildirakli TRAKTORLAR
SHINALARINI O'RTA RESURSINI ANIQLASH. Konferentsiya
zonasida
(112-115-betlar).
26.
Melibaev, M., Negmatullaev, S. E., Farkhodkhon, N., & Behzod, A. (2022, May).
TECHNOLOGY OF REPAIR OF PARTS OF AGRICULTURAL MACHINES,
EQUIPMENT WITH COMPOSITE MATERIALS. In
Conference Zone
(pp. 204-209).
27.
Кенжабоев, Ш. Ш., & Негматуллаев, С. Э. (2020). Обучение материаловедения как
специальных предметов для бакалавров транспортных направлений. In
Современные
автомобильные материалы и технологии (САМИТ-2020)
(pp. 162-166).
28.
Негматуллаев, С. Э., & Кенжабоев, Ш. Ш. (2021). ОСОБЕННОСТИ ТЕСТОВОГО
КОНТРОЛЯ ПРИ ИЗУЧЕНИИ ОБЩЕПРОФЕССИОНАЛЬНЫХ ДИСЦИПЛИН
ТРАНСПОРТНЫХ НАПРАВЛЕНИЙ. In
Современные автомобильные материалы и
технологии (САМИТ-2021)
(pp. 224-227).
29.
НЕГМАТУЛЛАЕВ, С., & КЕНЖАБОЕВ, Ш. МЕТРОЛОГИЯ, СТАНДАРТИЗАЦИЯ И
ВЗАИМОЗАМЕНЯЕМОСТЬ. - fmmp.bntu.by
30.
НЕГМАТУЛЛАЕВ, С. Э., КЕНЖАБОЕВ, Ш. Ш., & БЕКМИРЗАЕВ, Ш. Б. У. (2020).
Особенности межпредметных связей при изучении общепрофессиональных дисциплин.
In
Российские регионы как центры развития в современном социокультурном
пространстве
(pp. 71-75).
