=Paper=
{{Paper
|id=Vol-3288/paper4
|storemode=property
|title=Method of Estimating the Values of Reliability Indicators of Objects with Variable Structure
|pdfUrl=https://ceur-ws.org/Vol-3288/paper4.pdf
|volume=Vol-3288
|authors=Sergii Gnatiuk,Lev Sakovich,Yana Kuryata,Roman Odarchenko,Viktor Gnatyuk
|dblpUrl=https://dblp.org/rec/conf/cpits/GnatiukSKOG22
}}
==Method of Estimating the Values of Reliability Indicators of Objects with Variable Structure==
https://ceur-ws.org/Vol-3288/paper4.pdf
Method of Estimating the Values of Reliability Indicators
of Objects with Variable Structure
Sergii Gnatiuk1, Lev Sakovich2, Yana Kuryata2, Roman Odarchenko3, and Viktor Gnatyuk3
1
Administration of the State Service for Special Communications and Information Protection of Ukraine,
13 Solomianska str., Kyiv, 03110, Ukraine
2
Institute of Special Communication and Information Protection of the National Technical University of Ukraine
“Kyiv Polytechnic Institute named after Igor Sikorsky,” 37 Peremohy ave., Kyiv, 03056, Ukraine
3
National Aviation University, 1 Liubomyra Huzara ave., Kyiv, 03058, Ukraine
Abstract
The article proposes to improve the method of estimating the values of operating time on failure,
the average recovery time and the coefficient of readiness of radio equipment with variable
structure. The essence of improvement is to take into account the operating time of the
individual components of the product in the possible modes of use for its intended purpose. In
known works, this fact is not taken into account, so the results of calculations give an
underestimation of the values of reliability indicators, which, in turn, leads to an overestimation
of the cost of the product. An example of using the method is given and the effect of its
application is shown.
Keywords 1
Reliability indicators, multi-mode objects, variable structure, operating time on failure, average
recovery time.
1. Introduction time, the requirements for the value of failure time
and the average recovery time of these products
have not changed.
Modern research in the field of reliability
Modern foreign sources consider various
theory of complex technical systems is aimed at
aspects of ensuring the reliability of electronic
creating objects with specified values of
means - from improving the quality of the element
reliability indicators through the introduction of
base to predicting changes in the values of
redundancy of the least reliable structural
reliability over time, but methods for assessing the
elements, and the production of so-called
reliability of objects with variable structure are
“absolutely reliable systems” in which the
also not considered [9–15].
readiness factor A ≥ 0.997 [1–5] (in some cases,
Thus, the task arises to ensure the required
for example, for interplanetary spacecraft, robots
level of reliability of products while minimizing
to study other planets). In addition, special
their cost. To solve it, it is necessary to improve
attention is paid to the development of software-
the existing methods of calculating the values of
controlled radio equipment and systems, which
reliability of complex technical objects, taking
also affects their reliability [4–7]. However, the
into account their properties: multi-mode,
complexity of modern radio equipment and the
multifunctionality, the presence of redundancy,
density of installation is constantly increasing:
which leads to changes in the structure of the
only in the radio stations of the tactical level of
object during its intended use. Currently, there are
control over the past thirty years, the number of
not only practical but also theoretical methods for
elements and the density of installation has
calculating the efficiency of systems with a
increased more than six times [8]. At the same
variable structure, which can change randomly at
CPITS-2022: Cybersecurity Providing in Information and Telecommunication Systems, October 13, 2022, Kyiv, Ukraine
EMAIL: sgnatuk30@gmail.com (S. Gnatiuk); lev@sakovich.com.ua (L. Sakovich); ganaga@ukr.net (Y. Kuryata);
roman.odarchenko@npp.nau.edu.ua (R. Odarchenko); viktor.hnatiuk@npp.nau.edu.ua (V. Gnatyuk)
ORCID: 0000-0002-1541-7058 (S. Gnatiuk); 0000-0002-8257-7086 (L. Sakovich); 0000-0002-8625-6693 (Y. Kuryata); 0000-0002-7130-
1375 (R. Odarchenko); 0000-0002-4916-7149 (V. Gnatyuk)
©️ 2022 Copyright for this paper by its authors.
Use permitted under Creative Commons License Attribution 4.0 International (CC BY 4.0).
CEUR Workshop Proceedings (CEUR-WS.org)
33
short intervals. The change in structure always directions of automation of calculations of
occurs depending on the change in the functions reliability indicators of electronic means and their
performed by the system [1, 2]. changes over time also investigated.
A promising direction in the development of
2. Forming the Purpose radio-electronic means of the communication
industry is the introduction of software-controlled
means, the quality of which also affects the
The purpose of the article is to improve the reliability of individual products and the
method of estimating the values of reliability communication system as a whole.
indicators of objects with a variable structure, The value of the complex indicator of the
taking into account the operating time of reliability of radio-electronic means—their
individual sets of elements in possible modes of availability factor—is significantly affected not
use for their intended purpose. only by the MTBF, but also by the average
recovery time, so in special technical literature,
3. Mathematical Model research, and dissertation work, attention is paid
to improving the quality of diagnostic support for
Approximate calculation of the reliability of repair. During the quantitative assessment of the
radio-electronic means (REM) without taking into values of reliability indicators of electronic
account the property of their multi-mode is means, which are determined by design tasks, do
performed under the following assumptions: not take into account the property of multi-mode,
Failures of elements are independent. which leads to changes in the structure of objects
Failure of at least one element entails the during their intended use.
failure of the equipment. At present, there are not only engineering
methods but also theoretical developments of
Intensity of element failures does not depend
reliability analysis of technical systems with
on time, i.e. λі = const. changing structure, which is due to its multi-
Elements operate in typical (nominal) modes. functionality and multimode, when in separate
Elements of the same type are equally reliable. modes of operation the corresponding sets of
The second condition practically means that elements are used. Multi-mode properties used in
redundancy is not applied in the equipment, and the development of diagnostic software, but when
elements that perform auxiliary functions should assessing reliability, it is traditionally believed
be excluded from the calculations. In other words, that all elements of the object operate
in the approximate calculation, it is assumed that simultaneously, and this significantly
all elements of the equipment are connected in underestimates the MTBF.
series, with both complete and partial failure of Today, in modern domestic and foreign
any element leading to equipment failure. publications on topical issues of the reliability of
Means of various purposes are continuously complex technical objects and systems, some
developing and improving in the direction of directions for increasing the values of their
improving quality indicators by consumer reliability indicators considered. However, these
requirements through the introduction of new publications do not consider the issues of complex
schematic and design solutions, as well as the use consideration of the reliability of individual
of modern element base. This causes a components of software-controlled multi-mode
corresponding complication for products, which communication facilities with changing structures
does not lead to an improvement in the values of during the assessment of their performance in
their reliability indicators. Therefore, the issue of both the design process and refinement during
ensuring the required level of reliability of trial operation.
modern electronic means is very important for There is a problem with increasing the
both manufacturers and consumers. accuracy of a quantitative assessment of the
There are known methods of ensuring the reliability of radio-electronic means with a change
required values of reliability indicators of radio- in structure by using a new model that takes into
electronic means by reserving the least reliable account the operating time of individual elements
structural units, which increases their cost and of the object in various modes of operation and
weight, and dimensions, as well as the volume of increases the accuracy of calculations taking into
spare tools and accessories for the implementation account the peculiarities of construction and
of current repairs by the aggregate method. The intended use of these objects.
34
The development task standardizes the mean elements and a core consisting of elements 7 and
time between failures and the average recovery 8, which are used in all modes of operation.
time of existing, modernized, and prospective In the traditional approximate calculation of
multimode radio electronic devices. Therefore, reliability, the minimum and maximum values of
during the design, it is mandatory to perform a the parameter of the flow of failures of individual
reliability calculation with a quantitative elements in (Zi) are summed up, after which the
assessment of all reliability indicators, which are limits of change and the average values of the
then checked during trial operation. MTBF are determined
Communication equipment belongs to the T 1 L . (1)
Zi
class of objects with changing structures, which
can be single and multifunctional, multimode with
і 1
a fixed or arbitrary change of operating modes.
In this case, the real operating time of
To model these objects, the well-known individual elements is not taken into account.
mathematical apparatus of set theory was used,
If the value of the parameter ZRi of failures of
but only during the development of diagnostic individual elements of the product is known, then
software. Set-theoretic models allow us to for each mode of operation we obtain:
estimate the power of sets of elements used in
separate modes of operation, as well as their Z R1 Z1 Z 4 Z 5 Z 7 Z 8 ; (2)
interconnection. Z R2 Z 2 Z 4 Z 6 Z 7 Z8 ; (3)
For example, with a fixed change of modes, it
Z R3 Z 3 Z 5 Z 6 Z 7 Z8 . (4)
is advisable to use a model of the "garland" type,
when with each step the number of elements of the In this case, the MTBF of the product in each
object increases. This leads to a decrease in operating mode is equal:
MTBF and an increase in the average recovery 1 1 1
T1 ; T2 ; T3 . (5)
time, which worsens the value of the complex Z R1 ZR2 Z R3
reliability indicator - the facility availability
If there is additional data on the time of
factor.
operation of the product in individual modes (Трі),
When arbitrarily changing the operating
it is possible to calculate the value of the relative
modes of a radio receiver or radio station, it is
utilization factor of each element accordingly:
advisable to use a set-theoretic model with
intersections of subsets of elements that have a T p1 Tp 2 Tp3
u1 ; u2 ; u3 ; (6)
core (for example, amplifiers, power supply or Tp Tp Tp
generator equipment). In this case, the reliability T p1 T p 2 T p1 T p 3 T p 2 T p 3 ; (7)
of individual subsets of elements is significantly u4 ; u5 ; u6
Tp Tp Tp
affected by the time of their operation in a given
mode (for example, the operating time of the radio u7 1; u8 1; Tp Tp1 Tp 2 Tp3 ; (8)
station in the "receive" mode is many times longer where Тр is the total operating time of the product
than in the "transmit" mode), that is, the technical in all possible modes.
resource of the elements is calculated unevenly. This allows, taking into account the specific
To take into account this circumstance, it is operating time of each element of the product, to
proposed to apply the coefficient of use for each quantify the predicted number of their failures and
subset of elements in possible modes of operation the product as a whole:
of the product, which is calculated as the ratio of 8 8 8 Tpi
the operating time of a subset of elements to the N Tp U i Z i Z iTpi . (9)
total operating time of the product in all possible i 1 i 1 i 1 Ti
modes. Its value can be quantified from the Then the failure rate of the product as a whole
analysis of the use of communication means, is equal:
which is reflected in the hardware logs of N 8
communication nodes. Z U i Z i , (10)
Consider the use of these proposals on the T p i 1
example of a multi-mode object, the scheme of where T pi / Ti N i is MTBF of individual
which shown in Fig. 1. The object operates in
three modes, each of which uses five of the eight subsets of elements, and MTBF taking into
total subsets of elements. This is a set-theoretic account the operating time of subsets of elements
model with strong intersections of a subset of in separate modes, respectively T T p / N .
35
Figure 1: An example of a multi-mode technical object with a core and a strong intersection of a subset
of elements
Suppose that all subsets of elements in the product, taking into account its multi-mode
example under consideration are equally reliable properties, has increased several T / T 1,6
(Zi=Z) and in each mode of operation the product times, or by (T T ) / T 100% 37,5% .
operates for the same time ( T pi T p / 3 ), then we Obviously, the greater the number of possible
obtain modes of operation of the product, the more
u1 u2 u3 1/ 3; accurate is the estimate of the MTBF value taking
into account the multi-mode property. But, this
u4 u5 u6 2 / 3; (11)
requires additional initial data for the predicted
u7 u8 1. time of operation of the product in each mode.
The total number of product failures during The MTBF of electronic equipment as a whole
8 (T) depends on the operating time of individual
operation T p is N ZT p U 5ZT , and
i 1
i p parts of the product used in various operating
modes (Ti), which in turn is determined by the
MTBF is T 1/ 5Z . failure rate of this subset of elements (Zi)
Under the same conditions with the traditional Ti 1 / Z i .
conditional calculation of reliability we obtain The multi-mode property of radio electronic
T 1/ 8Z , that is, the real value of MTBF of the equipment is taken into account by introducing
36
the coefficient of use of individual sets of The probability of product failure due to a
elements depending on the relative time of their defect among the elements Li is
operation ui T pi / T p ; i 1, n ; where n is the Tpi uiT p
Ni uZ
number of subsets of radio electronic equipment i i , (15)
N TiTp i1 ui Z i
n 1
Tp Z Z
elements used in different modes;
Zi
T p is total operating time of radio electronic
while T i 1 ui Z i 1 .
n
means.
In this case, the total number of product The average recovery time of the product is a
failures over time T p is discrete random variable, the mathematical
expectation of which is the sum of products of its
n T pi n
N T p U i Z i , (12) possible values (Ki) by the probability of their
i 1 Ti i 1 occurrence (uizi/z). Then the estimated recovery
and the failure rate parameter of the radio time of radio electronic means (without taking
electronic means as a whole is equal to into account the metrological reliability of
measuring instruments) is equal to
Tp 1
T 1 n ; (13) t n
N
u Z i i
Z Т ВР t y ui Z i og 2 Li .
Z i1
(16)
i 1
In this case, the complex indicator of product
where Z is parameter of the product failure rate.
reliability is availability factor, is equal to
Another indicator of the reliability of radio
T
electronic means, which is standardized and set by A
the guiding documents, is the average recovery Т TВР
time TB. It depends on the qualification of the . (17)
1
performers (t is average time of parameter n n
checking, and ty is average time of fault 1 t ui Z i og 2 Li t y ui Z i
elimination), quality of metrological and i 1 i 1
diagnostic support, power of subsets of elements The readiness factor U 1 A .
used in separate modes of the product operation, This expression does not take into account the
and probability of their failure. probability of correct diagnosis P = pk, where р is
When searching for defects during the current the probability of correct assessment of the result
repair by programs based on the use of conditional of the test of the parameter of radio electronic
algorithms of the minimum form, the average means, as well as the metrological reliability of
number of checks measuring instruments P(τ), where τ is the period
K i og 2 Li ; i 1, n ; (14) of testing of measuring instruments.
Thus, the objective function of the research is
where Ki is the average number of inspections to minimization of the value of the complex
find defects in a subset of elements Li, among indicator of product reliability is availability
which it is necessary to determine the faulty one. factor with restrictions on the permissible values
Average number of inspections during the of MTBF (Td) and mean time to failure (Tvd),
current repair of the product, in general determined by the guidelines, at a given mode of
1 n operation ( Т pi , ui ), takes the form:
Ki og 2 Li .
n i 1 U ( x) min U ( x* );
In this case, the total number of elements of x* ; (18)
n
x ( Li , ui , Tpi , Z i , n, t , t y , P( ), T , Т В ),
radio electronic means L L provided that
i 1
i
where x is parameters affecting product
the elements of subsets are used only in certain reliability; x* is their importance in solving the
modes of operation, and the average number of problem; is the range of permissible limits for
1 n
checks K i og 2 Li .
changing parameter values.
n i 1
37
Groups of uncontrollable parameters: with the one obtained by the proposed model of
Li , n , Z i are depend on the product circuit and reliability of objects with a variable structure (U):
the reliability of the element base. 100(U U ) / U % . (19)
Groups of controlled parameters under
operating conditions: The results are summarize in table 1, which is
a mathematical model for estimating the values of
Tpi , ui are depend on the operating product mode;
reliability indicators of radio-electronic means
t, t y are depend on the qualification of the with a variable structure.
performers and the conditions for restoring The proposed model differs from the known
performance; ones by taking into account the operating time of
К is depend on the quality of diagnostic the product in individual modes, the probability of
software and the form of conditional algorithms failure in each mode of operation and the
for finding defects; metrological reliability of measuring instruments.
р, P( ) are depend on the measuring The adequacy of the model is confirmed by the
fact that the formulas obtained in the right column
equipment used during the current repair to assess
the values of signals at the control points of the of Table. 1 with u i 1 and Р( ) 1 and without
product. taking into account the probability of failure of
In this case, as an indicator of efficiency, it is subsets of elements are transformed into known
advisable to use the relative reduction of the expressions, which are given in the left column of
unavailability coefficient, the value of which is Table 1. This model is the mathematical basis of
calculated using known methods ( U ), compared the method for estimating the values of reliability
indicators of objects with a variable structure.
Table 1
Mathematical model of estimation of values of reliability indicators of radio electronic means with
variable structure
Functional dependences
Indicator Without taking into account With taking into account
multimode multimode
n n
Failure rate parameter Z Zi Z ui Z i
i 1 i 1
MTBF (mean time to failure) T 1/ Z T 1/ Z
n n
Total number of failures N Tp Z i N Tp ui Z i
i 1 i 1
n
t t n
Estimated average recovery
time
ty
Т ВР og 2 Li
n i1
Т ВР t y ui Z i og 2 Li
Z i 1
1 n
Average number of checks Ki og 2 Li
n i 1
Probability of correct diagnosis Р рк
TВР TВР
Average recovery time TВ TВ
Р Р Р ( )
T T
Product availability factor A A
T TВ T TВ
Coefficient of unreadiness of TВ TВ
U U
the product T TВ T TВ
U U
Effect of using the model 100%
U
38
the values of which affect all other indicators of
4. Developed Method reliability.
The block diagram of the algorithm for the
implementation of the advanced method is shown
The purpose of the method, its essence, initial in Fig. 2, where it is additionally marked: Td is the
data, limitations and assumptions, as well as the allowable value of the product operating time to
result of use are shown in the block diagram of failure, Tvd is the allowable recovery time of the
Fig. 1. The proposed mathematical apparatus is product during maintenance. The values of these
summarized in Table 1, where for the first time indicators are in the guiding documents.
the coefficients of use of sets of product elements,
Figure 2: Block diagram of the algorithm for implementing the method of estimating the values of
reliability indicators of objects with variable structure
39
Other source data are obtained: L, n, Li are the operating time for failure is equal T' =1007
from the analysis of the product scheme; Zi is hours. During the current repair of the radio
calculation of the failure parameter of sets of station using measuring equipment with
elements according to known methods [1, 2, 5]; metrological characteristics p = 0.997 and
Tp, Tpi are from the analysis of the product P(τ) = 0.96 [16–19]. If conditional diagnostic
operation mode during operation; p, P(τ) are algorithms are used during the current repair, then
depending on the type of measuring equipment K 8,86 . Assuming that the qualification of
[16–19]; t, ty are on the analysis of work of experts specialists provides t = 3,5 min and ty = 8 min, we
of repair body depending on their qualification. obtain the average recovery time
Consider the use of the results on the example 𝑇в′ = 43 min. These indicators fully meet the
of estimating the values of the reliability of the requirements for the reliability of similar objects
fifth generation radio [8]. Td ≥ 1000 hours and Tvd ≤ 60 min, while
Theoretical is multiple model of the radio A' = 0.9993 (𝑈 ′ = 0,0007).
station is shown in Fig. 3, where M1 is the set of The results of calculations for the same initial
elements used in the “transmission” mode; M2 is data according to the algorithm of Fig. 2 using the
in the “reception” mode; M12 is core used in both mathematical model of reliability of Table 2
modes of operation (subsystems of power supply, taking into account the properties of the radio in
control and operation, generator equipment, two modes depending on the ratio of operating
antenna) [20, 21]. The total number of elements of time to “receive” (U2) or “transmit” are shown in
the radio station is L = 4096, of which L3 = 512 Fig. 5–8.
elements are used in both modes, in the “receive” Comparison of the results with the prototype
mode L2 = 3072 elements and in the “transmit” (calculation of similar indicators without taking
mode L1 = 1024 elements. With Z1 = 307 • 10-6 into account the multimode of the radio station)
hours-1, Z2 = 532 • 10-6 hours-2, Z3 = 154 • 10-6 shows that at 90% of the radio station operating
hours-1. time in the “reception” mode (u2 = 0,9), which
Without taking into account the properties of often occurs in practice, we have a refinement
multimode we obtain (n = 3): time of 33% (T = 1507 h), the average recovery
3
Z Z 993 10 hours ,
6 -1 time by 14% (TB=50 min) and a decrease in the
(20) coefficient of unpreparedness by 28% (U =
i 1 i
0.000548).
Table 2
Mathematical model for estimating the values of reliability indicators of objects with variable
structure
Indicator Functional dependencies
The utilization factor of the sets of elements і ui=Tpi/Tp; 𝑖 = ̅̅̅̅̅
1, 𝑛
𝑛
Product failure flow parameter 𝑍 = ∑ 𝑢𝑖 𝑍𝑖
𝑖=1
Product operating time to failure T=1/Z
𝑛
1
The average number of inspections during maintenance 𝐾 = ∑ log 2 𝐿𝑖
𝑛
𝑖=1
Probability of correct diagnosis 𝑃 = 𝑝𝐾
𝑡
𝑡𝑦 + 𝑍 ∑𝑛𝑖=1 𝑢𝑖 𝑍𝑖 log 2 𝐿𝑖
The average recovery time of the product 𝑇𝐵 =
𝑃 · 𝑃(𝜏)
Product readiness ratio 𝐴 = 𝑇⁄𝑇 + 𝑇𝐵 )
The coefficient of unpreparedness of the product 𝑈 = 𝑇𝐵 ⁄(𝑇 + 𝑇𝐵 )
40
Figure 3: Block diagram of using the method of quantitative assessment of the values of reliability
indicators of objects with variable structure
Figure 4: Theoretical-multiple model of a tactical radio station
That is, it was possible to use elements of The operating time for failure decreases,
lower cost to ensure the necessary requirements because in this mode most of the elements of
for the reliability of the radio station during its radio stations are used (Fig. 5).
design and production. The average recovery time also does not
Analysis of the obtained dependences shows
increase significantly as the probability of
that with increasing relative operating time of the
failure in the receiving part of the radio station
radio station in the “reception” mode:
increases, and this pattern is maintained at any
time during the test t (Fig. 6);
41
Figure 5: Dependence of operating time on the
failure of the radio station on the relative
operating time in the mode “reception” Figure 7: Dependence of the readiness factor of
the radio station on the relative operating time
in the "reception" mode
Figure 6: Dependence of the average recovery
time of radio stations on the relative operating
time in the "reception" mode
Figure 8: Dependence of the coefficient of
unpreparedness of the radio station on the
relative operating time in the “reception” mode
Due to the decrease in the value of operating 5. Conclusions
time to failure T and increase the average recovery
time Tv also decreases the complex reliability 1. The paper proposes the improvement of the
indicator is readiness factor A (Fig. 7) and, method of quantitative assessment of reliability
accordingly, increases the value of the indicators of objects with variable structure, the
unpreparedness factor U (Fig. 8). algorithm of realization is given and the
These trends are maintained at any values of advantages over the existing methods are shown.
the average time of the test t, moreover, its 2. It is established that the use of multi-mode
reduction by improving the skills of performers properties, which affects the structure of the
and improving diagnostic support (the choice of object, improves the value of reliability
tests with less labor) leads to an increase in the indicators: both the failure time and the average
coefficient of readiness (A). recovery time.
42
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