=Paper= {{Paper |id=Vol-3156/paper42 |storemode=property |title=Computer System for Evaluation the Reliability of Technological Systems |pdfUrl=https://ceur-ws.org/Vol-3156/paper42.pdf |volume=Vol-3156 |authors=Kateryna Yalova,Kseniia Yashyna,Leonid Dranishnikov,Abdel-Badeeh M. Salem |dblpUrl=https://dblp.org/rec/conf/intelitsis/YalovaYDS22 }} ==Computer System for Evaluation the Reliability of Technological Systems== https://ceur-ws.org/Vol-3156/paper42.pdf

Computer System for Evaluation the Reliability of Technological
Systems
Kateryna Yalovaa , Kseniia Yashynaa , Leonid Dranishnikova and Abdel-Badeeh M. Salemb
a
Dniprovsky State Technical University, Dniprobydivska str.2, Kamyanske, 51918, Ukraine
b
Ain Shams University, El-Khalyfa El-Mamoun Street Abbasya, Cairo , Egypt

Abstract
The paper presents the results of developing a computer system for evaluation of reliability of
technological systems, which uses the logical-graphic method Fault Tree Analysis.
Automation of the Fault Tree construction process is aimed at accelerating and improving the
accuracy of graphical representation process of the technological system model to assess the
level of its reliability and identify the components that most affect the risk of accidents. The
paper substantiates the feasibility of using the Fault Tree and describes the algorithm for
qualitative and quantitative analysis of Fault Tree data. The architecture of the developed
computer system is multi-layered, divided into data layer, user interface layer, and business
logic layer. The input for a computer system is a description of a technological system – the
object of study – which is defined by a set of interrelated events with a given intensity of
occurrence, the combination of which can result in a particular major undesirable event.
Based on the entered input data, the Fault Tree is automatically constructed, the probability
polynomial is formed, the probabilities of occurrence of intermediate events and the top event
are calculated, the list of the minimum emergency combinations and trajectories is
developed. The relational database proposes storing data on technological systems, events,
types of connections, and graphic notations to implement information actions of inserting,
deleting, editing, committing, and exporting data. The adequacy of the implemented design
solutions was proved by testing the computer system on the Fault Tree of different
complexity from different domain. The results of its application to analyze the reliability of
the technological design of brown smoke suppression of metallurgical production in the
framework of research work “System analysis and computer modeling of technological
processes and information technologies” are presented.

Keywords 1
System reliability analysis, fault tree analysis, computer system

1. Introduction
It is impossible to achieve absolute safety for systems that use energy. All measures for the safe
operation of technological systems must consider the possibility of dangerous, undesirable situations
and focus on the relevant risk [1]. Analyzing the reliability of technological equipment has recently
become increasingly important. The concept of manufactured risk management emerged when, given
the growing number of potentially dangerous facilities and the associated increase in accidents and
catastrophes, the question arose as to which strategy to choose to ensure the safety of manufacturing
facilities. The tasks of systems reliability evaluation in engineering practice are faced by specialists
who perform design and engineering work, developers of plans for localization and elimination of

IntelITSIS’2022: 3rd International Workshop on Intelligent Information Technologies and Systems of Information Security, March 23–25,
2022, Khmelnytskyi, Ukraine
EMAIL: yalovakateryna@gmail.com (K. Yalova); yashinaksenia85@gmail.com (K. Yashyna); dr-leon@ukr.net (L. Dranyshnykov);
abmsalem@yahoo.com (A.-B. M. Salem)
ORCID: 0000-0002-2687-5863 (K. Yalova); 0000-0002-8817-8609 (K. Yashyna); 0000-0002-9291-4074 (L. Dranyshnykov); 0000-0003-
0268-6539 (A.-B. M. Salem)
©️ 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)
emergencies and accidents, developers of safety declarations for high-risk facilities. Risk should be
understood as the expected frequency or probability of specific hazards class or the amount of
possible damage (loss, damage) from an undesired event or some combination of these values. The
application of the concept of risk, thus, allows to translate the danger into the category of measurable
categories, where risk is a measure of danger and includes the following quantitative indicators:
• probability of occurrence (frequency of occurrence) of the dangerous factor under
consideration;
• the amount of damage from the influence of a dangerous factor;
• uncertainty of losses and probabilities.
The term “risk” is used to analyze the reliability of technological systems, determine the level of
hazards and form a set of actions to reduce the risk of an adverse event [2]. Suppose the concept of
“risk” is applied to the technosphere. In that case, it should describe the probability of an accident
when using the mechanisms or machines of a technological system particular process. The
manufactured risk analysis is used to assess the reliability of technological systems, which aims to
determine the frequency of adverse events and calculate the probabilities of their occurrence.
In general, the main tasks of risk assessment are related to:
1. Identification of hazards.
2. Analysis of the frequency or probability of adverse events.
3. Assessing the consequences of adverse events.
The generalized assessment of the reliability of technological systems should reflect the state of
industrial safety, taking into account the risk indicators of all adverse events that may occur at the
hazardous production facility, and based on the results:
• integration of risk indicators of all adverse events (accident scenarios), taking into account
their mutual influence;
• analysis of uncertainty and accuracy of the obtained results;
• analysis of operating conditions compliance with industrial safety requirements and
acceptable risk criteria.
In modern accidents researching, causation and effect diagrams with a branching structure and
called a “tree” (fault tree, event tree), each of which is a branched, finite and connected graph that
does not have loops or cycles, have become widespread.
To solve the problems of a quantitative evaluation of reliability and safety of complex
technological systems, logical-probabilistic methods, logical-graphic methods [3]: event trees, Fault
Tree Analysis (FTA), topological methods have become the most widespread. The first analysis of the
reliability of complex technological systems, implemented by FTA, was conducted in the ’60s [4].
Today, FTA is effectively used in the aerospace, nuclear energy, chemical and processing industries,
pharmaceuticals, petrochemicals, and other high-risk industries [5-7].
Despite the extensive coverage in the scientific and technical literature, experts make some
methodological and logical errors in practice, which leads to incorrect results of the technological
systems reliability analysis [8]. The urgency of automating the process of technological systems
reliability evaluation is associated with the ever-increasing structural complexity and dimensionality
of modern technical systems and the need to increase the level of reliability and safety of such
systems. Computer systems development and software applications with the function of automatic
construction and calculation of the events occurrence probability allows to increase the speed of
technological system model construction, simplify the Fault Tree (FT) design process, reduce errors
in calculations, get a mechanism for modeling various system states occurrence of adverse events.
Currently, there are a lot of commercial and non-commercial software and platforms that allow
building the FT and performing analysis of the technological systems reliability in automated mode,
such as [9]: OpenFTA, OpenAltaRica platform, ALD Fault Tree Analyzer, DFTCalc, CAFTA, RAM
Commander FTA. In addition to opening and advertising software products, scientists Y. Hiraoka, M.
Takahashi, A. Majdara, T. Wakabayashi [10,11] describe corporate software development to assess
the reliability of specific technological systems. The main disadvantage of commercial software is
paying for the purchased license. Free software has some limitations for building a FT, such as
restrictions on the number of initiating events or logical operators, the inability to save or reuse the
created FT, customization for a specific data domain.
The primary purpose of this work is to present the results of modeling, development, and practical
application of non-profit computer system, which provides the ability to design a FT for quantitative
and qualitative analysis of a wide range of technological systems reliability.

2. Models, methods and technology
System analysis, including the formulation and decomposition of the problem’s solution, is used to
formalize the process of technological system research, the reliability of which must be evaluated.
FTA is used to evaluate the system’s reliability, which is one of the main methods of quantifying
the probabilistic component of risk – the frequency of accidents. When constructing a FT, it is
necessary to define the conditions for the appearance of the top event; decompose complex
prerequisites; identify co-operating factors; exclude feedback between elements specify the reasons
for their occurrence; check the validity of all accepted assumptions and initial data. Using the trace-
back algorithm allows calculating the probability of events occurrence included in the FT, starting
from the bottom level of the tree. The significance of the events leading to the main undesirable event
is assessed using the Fussell-Vesely algorithm.
During the computer system design and implementation, the principles of system analysis,
function-oriented method of data domain analysis, data normalization rules, principles of relational
database design are used. The user interface development was carried out, taking into account the
interface’s usability.
The methods, principles, and algorithms used in the course of the work make it possible to state
that the study results are reasonable and reproducible.

2.1. Features of the Fault Tree construction
FTA is a logical-graphical method, which is to build and analyze a model of reliability (safety),
that is a model of causal relationships of studied system failures with failures of its elements and other
influences, which allows elaborating visually and in detail related elements of infrastructure and
events that affect reliability. The advantages of the FT are [12]:
• analysis focuses on finding failures, which allows showing the existing unreliable places
of the system;
• provides graphics and presents visual material for those professionals who participate in
the maintenance of the system;
• provides an opportunity to perform qualitative or quantitative analysis of system
reliability.
The graphical representation of the model uses a highly branched tree data structure, the elements
of which reflect the structure of the causal relationships of hazardous situations in reverse so that the
root of the tree is the main undesirable event in the technological system probability of which must be
established.
The main advantage of the FTA (compared to other methods) is that the analysis is limited to
finding only those elements of the system and events that lead to a particular system failure or
accident. The main disadvantage of FTA is that the tree has the form of a Boolean algebra diagram,
which shows only two states: working and non-working, which makes it impossible to consider the
state of partial failure of elements.
The generalized FT construction algorithm can be represented as a set of the following steps:
1. Determining the content of analysis, which establishes the system’s boundaries, determines
the data for the analysis of its reliability, sets the top adverse event, the risk of which will be
analyzed. This fact considers that FT can build both for the whole system and its part.
2. Identify the set of initiating events and states that can lead to the top event. Also, many
additional conditions are formed, which in the presence of particular type initiating events can
contribute to the development of accidents in an undesirable direction.
3. Establishing logical relationships between established events.
4. Determining the frequency of adverse events.
5. Graphical representation of the failure tree and calculation of intermediate events and top one
probabilities.
The main reasons for errors when building a FT are:
• errors of system analysis when describing the composition of the technological system and
the set of process events to be analyzed;
• incorrect use of logical symbols;
• incorrect use of statistics on the initiating events probabilities.
The following steps of working with the graphic model data of FT are aimed to conduct a
qualitative and quantitative analysis of system reliability.

2.1.1. Fault tree elements
The FT elements can be divided into three groups: primary failures or initiating, or basic events
(conditions in which the technical system usually operates); secondary failures (deviations from
process regulations); control failures (equipment does not receive control signals for any reason). A
FT includes one top event connected by logical conditions with those intermediate and initial
prerequisites, the occurrence of some of which can lead to a specific incident.
The graphical display of the FT uses standardized graphic notations, which makes it possible to
clearly define events, logical elements, and types of transmission [4,11]. Event symbols allow setting
such events as: “Top Event”, “Intermediate Event”, “Initiating Basic Event”, undeveloped event,
external event. The initiating events do not develop further, and the intermediate events are at the
output of the elements. The logical gates symbols describe the relationship between input and output
events and correspond to classical Boolean logic. Transmission elements are used to connect the
inputs and outputs of the corresponding FT, such as the FT of the subsystem in its system. Table 1
shows the basic graphic notations used to build the FT.

Table 1
Basic graphic notations of the failure tree
Graphic notation Description
The main element of the FT. It describes the main and
intermediate events that can be broken down into components.
Describes initiating events that are at the lowest level of the
hierarchy and have no underlying connections.
AND gate - sets the logical connection “AND”. Used to describe a
situation where an output event occurs if all input events occur
simultaneously.
OR gate - displays the OR connection used to describe the
situation when the output Event occurs if any of the input
events occur.

The most commonly used logical elements are AND and OR, but some trees may also use logical
operators such as XOR or NAND. For any event to be further analyzed, first look at all possible
events that are inputs of operation OR, then that are inputs of operation AND. This scheme is applied
to the basic event and all other events whose analysis makes sense to continue.

2.1.2. Fault tree analysis
FT can be used for qualitative and quantitative analysis of system reliability. At the qualitative
level, it is used to identify possible causes and ways of failure (final event); at the quantitative level –
to calculate the probability of a final event based on data on the probabilities of causal events.
Qualitative analysis requires an understanding of the system and the reasons for the failure and a
technical understanding of how the system may fail. When conducting the analysis, it is advisable to
draw up detailed schemes. It is necessary to set basic events BE={BE1,…BEn} and a set of
intermediate events IE={IE1,…IEn}, each of which occurs when a single initiating event or set of
initiating events. Boolean algebra is used to describe the relationships between intermediate and
initiating events. A complex tree has different sets of initiating events, in which an event is reached at
the top; they are called emergency combinations (sections). The minimal cut set is the minor set of
initiating events in which an event occurs at the top. The complete set of minimum emergency
combinations of a tree represents all variants of combinations of events at which there can be an
accident. The minimum trajectory is the smallest group of events in which an accident occurs.
Qualitative analysis of the tree is carried out using the selected minimum emergency combinations
and trajectories; it compares different routes and initial events to the final and identifies critical (most
dangerous) pathways leading to the accident.
Quantitative analysis of the FT calculates the probability of an accident during a given time on all
possible routes. The calculation of the probabilities of the intermediate and main events, which are
part of the constructed FT, is based on the input statistics of the frequency of occurrence of the
initiating events. The following data are used to determine the frequency of occurrence of initiating
events:
• statistical data on accidents and reliability of the technological system, the specifics of the
hazardous production facility;
• expert assessments by taking into account the opinion of experts in this field;
• analysis of accidents in order to determine the required probability.
The probability of occurrence of events is associated with the intensity of the event by exponential
law [13]:
𝑃 = 1 − exp⁡(−𝑡), (1)
where  – the intensity of the failure event in the technological system, t – the operating time of the
technological system, which determines the intensity of the failure event in the technological system.
In the case of⁡𝑡 < 0,1 equation (1) turns into:
𝑃  𝑡. (2)
FT quantitative analysis can be carried out in various ways:
• using structural functions (calculated probability polynomials);
• step-by-step reduction of the FT using trace-back algorithm;
• quantitative assessment of the top event probability using minimal combinations of initial
prerequisites.
Using structural functions. In this case the problem is to simplify the relations according to the
rules of event algebra in order to obtain calculated probability polynomials. The prediction of the
probability of a top event is carried out in the following sequence [3]:
1. The analytical model of the process is decompressed into separate blocks;
2. In selected blocks, those subsets of events that are interconnected by conditions AND, OR
and have known probabilities are distinguished;
3. For the selected units the probability calculation at the event vertices is performed;
4. The structural function is simplified by replacing each subset of the property with one
member having an equivalent probability;
5. The probability of the occurrence of the FT top event is calculated in a similar way.
Using trace-back algorithm. If the probabilities of all initiating events are known, the trace-back
algorithm to calculate the probabilities of intermediate events and the main undesirable event can be
used. The probability of intermediate events depends on the relationship between the events that lead
to them. The trace-back algorithm calculates the probability of events that are part of the generated FT
by levels, starting from the lowest. N failure tree prerequisites combined by logical condition AND
are replaced by one event with equivalent probability of occurrence 𝑃∩ [14]:
𝑁 (3)
𝑃∩ = 𝑃1 ∙ 𝑃2⁡ ∙∙∙ 𝑃𝑛 = ∏ 𝑃𝑖 .
𝑖=1
M of the FT initial prerequisites, connected by a logical gate OR, are also replaced by one event,
and its equivalent probability 𝑃∪ is calculated using a formula that estimates the probability of
realizing at least one initial event:
𝑚

𝑃∪ = 1 − (1 − 𝑃1 )(1 − 𝑃2⁡ ) ∙∙∙ (1 − 𝑃𝑚 ) = 1 − ∏(1 − 𝑃𝑖 ),
𝑖=1 (4)
where Pi – the probability of i-th event occurrence.
Also, the probability of a basic event can be determined based on the minimum cut sets as [5]:
𝑁𝑐 (5)
𝑃(𝑇) = 1 − ∏(1 − 𝑃(𝐶𝑖 )).
𝑖=1
where Ci(i=1,..,Nc) – is the minimum cut set combination at which a top event occurs.
Using minimal combinations of initial prerequisites. This method consists of constructing another
tree equivalent to the analyzed FT and including all minimal combinations of one type [15]. The new
diagram is also a FT and has only one logical condition: AND if only minimum cut set combinations
are used, and OR – when only minimum throughput combinations are used. To calculate the
probability Q of incidents, the following expressions are used:
𝑎 𝑚𝑖 (6)
𝑄 = 1 − ∏ (1 − ∏ 𝑃𝑖𝑗 .) .
𝑖=1 𝑗=1
𝑏 𝑛𝑘

𝑄 = 1 − ∏ [1 − ∏(1 − 𝑃𝑙𝑘 ).]
𝑘=1 𝑙=1
where a ,b – the amount of minimum cut set and minimum throughput combination of the FT, mi, nk,
the number of initial prerequisites in each of its i-th throughput and k-th cut set minimum
combinations of initial events prerequisites.
Importance indicators are used to determine the contribution of each event or their combination to
the occurrence of a system failure. The assessment of the importance of an event is based on the logic
of its association with other FT events. It is advisable to use the Fussell-Vesely algorithm to assess the
importance of the occurrence of a particular event on the occurrence of the main adverse event.
Fussell-Vesely Importance is defined as [16]:
𝑃min 𝑐𝑢𝑡 (Х𝑖 ) (7)
𝐼𝑖𝐹𝑉 =
𝑄
where Pmin cut (Xi) – is the probability of the i-th minimum cut sets leading to the basic event, Q is the
probability of the main undesirable event.

3. Experiment, Results and Discussions
The analysis of software used to build a FT of complex technological systems made it possible to
form functional and non-functional requirements for system software, main of which are:
1. Client-server data processing, with the ability to save data in a database.
2. Implementation of mechanisms for forming a description of the technological process or system
in the form of events set with the probabilities of their occurrence.
3. Implementation of probabilistic modeling software mechanisms with automatic calculation of
events occurrence probabilities in the system and creation of probability function polynomial.
4. Graphical construction of the FT.
5. Qualitative and quantitative analysis realizing on FT data.

3.1. Computing system for automated FTA construction
The computer system is designed as a desktop application in C # as Windows Form Application,
does not require an Internet connection, interacts with the user through a standardized interface. The
primary functional purpose is the automated design of FT to conduct qualitative and quantitative
analysis of the reliability of technological systems.
The system architecture is multi-layered, consisting of a data representation layer, a business logic
layer, and a data layer. The scheme of the architecture of the developed computer system is presented
in the Figure 1.

Figure 1: Architecture of the developed computer system

The data layer of the system was designed based on the approach described in [17], which
implements the division of the data layer into three components: normative, operation, and resulting
information. Normative information of the system is conditionally unchanged data, repeatedly used in
data entry and the resulting samples formation. Operation information entered by the user is the
primary source of data describing changes in the state of the data domain. Obtaining the resulting
information is the purpose of the system; it is formed based on the results of queries to the database.
The data storage in this system is a relational database, which stores descriptions of technological
systems, sets of graphic notations, and types of relationships between events to build a FT, sets of
accidents, and the intensity of their occurrence over time.
The business logic layer is designed as a set of software modules:
1. Module for data and descriptions of the technological system input.
2. Module of the FT graphic model construction.
3. Module for calculating and analyzing the data obtained.
Data processing mechanisms were implemented through stored procedures and representations of
the database level and software application.
The data representation layer is a user interface developed on the base of the Window – Image –
Menu – Pointer (WIMP) graphics standard as a set of screen forms. All graphic forms meet the
requirements of unification and standardization and implement the same algorithms to build a
dialogue between the user and the software application.

3.2. Roles and functions analysis
The developed computer system is user-dependent, i.e., the reliability of input data describing
basic and intermediate events sets, the establishment of the main undesirable event, the choice of the
logical relationships types of between events, the correctness of initiating events intensity or
probability input is the responsibility of system users. The system validates the input data.
During the data domain analysis, two roles of computer system users were identified: the operator
and the administrator. The available functions are determined, and the schemes of interaction and
support of work with the system are formed considering each user’s rights to access information. The
system operator is a user-analyst who has sufficient knowledge of the technological system, the
reliability analysis of which will be carried out. Table 2 lists the main functions and available
operations for the system operator.
Table 2
Functions and available actions of the computer system users
Function Action

Access to the projects Create a new one
stored in the database Open an existing one
Top event, intermediate and initiating events insert
Overview of the technological system model current content
Working with a new Deleting, editing the top event, intermediate and initiating
project events
Transactions committing
Inserting data on the intensity of the initiating events occurrence
Designing a technological Selection of the intermediate i-th event
system model Identification of the events set that cause the i-th event to occur
Establishing of the relation type between the events that lead to
the i-th event
Updating, deleting, committing data on relations between events
Graphic representation of Choice of technological system for FT construction
a FT Getting a graphic display
Image saving and importing
Reliability analysis Obtaining a probability polynomial
Obtaining the values of the intermediate events and the top
event probabilities
Obtaining a list of minimum emergency combinations and
minimum emergency trajectories
Obtaining an array of the significance of the initiating and
intermediate events estimates

A system administrator is a user who has access rights to the information stored in a database. In
addition to the actions described in Table 2, the administrator has the functions of database
management and administration: backup, recovery, data archiving, determination of server connection
characteristics, etc.
The functions and actions of users are distributed between screen forms to simplify the dialogue of
users with the system, the general scheme of transition between which corresponds to the following
logical sequence:
1. Entering data on the technological system, determining the main adverse event.
2. Form a list of initiating events with data entry on the intensity of their occurrence over time
and entering data of intermediate events that may affect the technological system reliability and
contribute to emergencies.
3. Forming relations between events.
4. Request for automatic construction of the FT and obtaining its graphical model.
5. Request for qualitative and quantitative analysis of the generated FT data.
In addition to the mainline of dialogue with the computer system to implement all the actions
described in Table 2, child modal forms are used. The results of confirmed data transactions are
displayed in a single relational database.

3.3. Data storage
Data and system logic are shared between the database, user interface, and business rule
algorithms for implementing information operations with data. According to the proposed system
architecture (Figure 1), the normative and operation data are subject to storage in the data storage,
implemented in a relational database. The normative information of the system includes:
• set of graphic notations;
• list of developed projects;
• description of technological systems and a set of events.
The input information of the system, which has the properties of dynamism and is entered by
operators, is the relationship between events, the intensity of events, the timing of the system, for
which it is necessary to calculate the probabilities. The resulting information is a graphical
representation of the FT, the formed probability polynomial, the set of calculated probabilities of the
base, intermediate and main event, the set of minimum emergency combinations and trajectories. The
resulting information is generated by the system automatically according to the input parameters of
the calculation.
Database modeling was performed based on the data domain object model with the application of
data normalization rules. The specification of the main objects characteristics stored in the database is
presented in Table 3.

Table 3
Basic entities stored in the database
Entity Entity description Properties Links to Relation
external plurality
entities
Tree A dynamic entity describing The entity is characterized by: Event 1:1
event the data of each event name, serial number in the tree, Type 1:1
included in the tree intensity/probability of Graphic
occurrence, graphical notation. notation
Project Static entity describing the Entity, characterized by the Tree 1:N
main characteristics of a name of the technological
given data domain system, a description of the
main characteristics of the
system.
Relation A dynamic entity describing The entity is characterized by: Event 1:N
data about the type of name, graphic notation, Graphic 1:1
relationship between tree calculation algorithm. notation
events
Tree Dynamic entity describing The entity is characterized by Event 1:N
data for system reliability the name, the name of the top
analysis event, the date, time of
creation.
Event Static entity The entity is used to determine Tree 1:1
type the type of event: base, event
intermediate, main
Graphic Static entity The entity is used to store and
notation display the type of the project
object

Inserting data on the “event” entity, the user is given the opportunity to choose which numerical
characteristic will be included in the list of initiating events properties of a particular system: the
intensity of occurrence or probability. If the user enters the intensity, the system automatically
calculates the probabilities of occurrence for the initiating events for (1) – (2). The obtained
probability values are then used to calculate the probabilities of intermediate events and top event
probabilities using (3) – (5).
The default calculating period is a calendar year. The user can change this value. If necessary, the
user can specify n time calculation periods for which the system will give the results of the probability
calculation. Based on the introduced characteristics and calculated probabilities, the system generates
minimal cut sets and calculates their contribution to the occurrence of the top event according to (7).
Accuracy of probability calculations is 10-5.

3.4. Adequacy substantiation
The adequacy of the implemented design solutions was carried out by checking the manually
constructed FTs for different technological systems and the results obtained in the developed system.
The data of technological systems were used as a test set:
1. Conveyor system bulk cargo overload in assessing the main undesirable event, “Destruction
of the conveyor belt”, data on the intensity of the initiating events, and the results of calculating
the probabilities described in the works of A. A. Tverigin.
2. Computer System in estimating the top adverse event “Computer is not functioning” based on
A. Saxena and T. Manglani.
3. Filling system in an automotive production line in assessing the main adverse event “Failure
in the fluid filling system” based on data from H. Soltanali, M. Khojastehpour, J. T. Farinha, J. E.
Pais [5].
Testing the developed software on actual data showed the adequacy of the applied methods,
correctness of calculations, and indicators of system reliability. The result of test checks was the
conclusion that the implemented design solutions are universal and can be used to calculate the
reliability of other technological systems.

4. Practical application
After substantiating the adequacy of the implemented software solutions, the developed computer
system was used to assess the reliability of the brown smoke suppression system during the release of
steel from the blast furnace in the research work “System analysis and computer modeling of
technological processes and information technologies” conducted by the team of the Department of
Software Systems at Dniprovsky State Technical University. Input data on the technological chain,
equipment composition, the intensity of accidents are taken from actual industrial data of
technological process logs.
The top event for the analysis and construction of the FT is the emission of brown smoke during
the release of steel from the blast furnace.
This event is undesirable because, during the interaction of steel with oxygen, iron oxidizes and
partially evaporates, turning into dust, the particles of which rise into the air and form orange (brown)
smoke. Emissions of brown smoke reduce the volume of fused steel by 0.0025-0.0075%, significantly
pollute the environment, and threaten employees.
The technological system is supplemented by various devices controlled through an automated
control system to minimize the formation of brown smoke – the type of automated workplace shown
in Figure 2.
The input parameters for building a FT in a given data domain are technological processes set,
technological events, and technological equipment, presented in a hierarchical dependence of system
states and transitions between them.
The array of input data describing the baseline events was set with the values of the intensity of
occurrence and the period t = 1 year. The set of initiating events BE={BE1,…BE11}, their description
and intensity are given in Table 4.
The set of intermediate events IE={IE1,…IE8}, the occurrence of which contributes to the
development of the emergency situation consists of 8 events described in Table 5.
Figure 2: The main screen of the automated brown smoke suppression system

Table 4
List of initiating events of the brown smoke suppression system
Event Event name Intensity of occurrence, 1/year
number
BE1 Power plant №1 failed 0,00500
BE2 Power plant №2 failed 0,00500
BE3 Lack of nitrogen in the tanks 0,01000
BE4 Engine failure 0,02000
BE5 No engine power 0,03200
BE6 No connection to controller 0,02800
BE7 Network switch failure 0,02800
BE8 The controller power supply burned out 0,03100
BE9 The limit switch has failed 0,03300
BE10 Damage of electrical power wires 0,03700
BE11 Voltage surge 0,02400

Table 5
List of intermediate events of the brown smoke suppression system
Event Event name
number
IE1 There is no electricity
IE2 There is no nitrogen pressure
IE3 The dome of the tap hole does not fall
IE4 The dome of the ladle does not fall
IE5 There is no pressure in the network
IE6 Closed valve
IE7 Pressure sensor failure
IE8 Lack of power to the pressure sensor

After entering the input data, the user is allowed to view the results of the automatic FT design and
analyze the results of automatic calculations. The screen form of the system with the generated tree is
shown in Figure 3. The events B9-B14 on Figure 3 are the same as BE3-BE8 respectively. The events
B15 B16, B17 are the same as BE9, BE10, BE11 respectively.
Figure 3: Screen form with constructed FT

The screen form of the resulting information is divided into three parts:
1. The area of the FT graphical representation.
2. The area of the output descriptions of the events entering into the FT;
3. The area of calculated data presentation.
Standardized graphical elements for events and logical elements are used to increase the visibility
of the displayed FT.
Each event graphic element contains its sequence number in the event list, displayed in an
additional area of the screen form.
The top event has the sequence number 0, the base and intermediate events are marked with the
sequence number of their set. There are no restrictions on the number of basic, intermediate events
and logical elements.
As the size of the FT increases, horizontal and vertical scrolls appear on the screen. The graphic
representation of the tree can be exported as a graphic element.
The data generated by the system allows for qualitative and quantitative analysis of the generated
FT. The result of the qualitative analysis is the formed set of minimal emergency combinations.
For the case under consideration, C={C1,..,C6} and is described as:
𝐶1 = 𝐵𝐸1 ∩ 𝐵𝐸2 , (8)
𝐶2 = 𝐵𝐸3 ,
𝐶3 = 𝐵𝐸10 ∪ 𝐵𝐸11 ,
𝐶4 = 𝐶5 = 𝐵𝐸4 ∪ 𝐵𝐸5 ∪ 𝐵𝐸6 ∪ 𝐵𝐸7 ∪ 𝐵𝐸8 ∪ 𝐵𝐸9 ,
𝐶6 = 𝐵𝐸3 ∪ 𝐵𝐸10 ∪ 𝐵𝐸11 .
The probability РТ of the top event occurrence event can be calculated as follow:
𝑃𝑇 = 1 − [(1 − 𝑃𝐶1 )(1 − 𝑃𝐶2 )(1 − 𝑃𝐶3 )(1 − 𝑃𝐶4 )(1 − 𝑃𝐶5 )(1 − 𝑃𝐶6 )]. (9)
where PС1,..,PС6 is the probability of the i-th minimum emergency combination leading to the top
event. Quantitative analysis of the tree is performed by the system automatically based on (8) - (9).
The results of calculating the probabilities of occurrence of all intermediate events are presented in
Table 6. The probabilities of occurrence of the minimum cut sets, and their weight in the occurrence
of the main event are shown in table 7.
The estimated probability of occurrence of the main event is 0.40757. Obtained data can be used to
identify potential causes of failure, understand co-occurrence events that lead to system failure,
establish a list of measures to reduce the probabilities of a “brown smoke emission” event, and
increase the reliability of the process as a whole.
Table 6
Automatically calculated probabilities of intermediate events
Event Calculated probability of event occurrence
Event name for t=1 year
number
IE1 There is no electricity 0,00002
IE2 There is no nitrogen pressure 0,06854
IE3 The dome of the tap hole does not fall 0,16950
IE4 The dome of the ladle does not fall 0,16950
IE5 There is no pressure in the network 0,00995
IE6 Closed valve 0,05918
IE7 Pressure sensor failure 0,02371
IE8 Lack of power to the pressure sensor 0,03632

Table 7
Automatically calculated probability of cut sets

Event number Probability of occurrence Contribution to the top event

С1 0,00002 0,00006
С2 0,00995 0,02469
С3 0,06004 0,14895
С4 0,16950 0,42053
С5 0,16950 0,42053
С6 0,06999 0,17364

5. Сonclusions
Determining the reliability of technological systems is an important task. It allows identifying
hazardous parts of the technological system and developing measures to minimize adverse events.
One of the ways to quantitatively and qualitatively assess the system’s reliability and the probability
of occurrence of a particular event is FTA, which allows to visually and mathematically describe a
given technological system.
The developed computer system is a unified software tool for creating FTs and risk analysis of
technological systems. It is not adapted to a specific data domain or a specific process, expertly
dependent at the stage of process description and entering of input parameters of the frequency of
occurrence of events included in the FT.
The primary purpose of creating a computer system for FT design is to increase the speed of FT
construction, automatic polynomial construction to calculate the probabilities of the intermediate and
main event, increase the accuracy of calculation, minimize the impact of skills and accuracy of
analysts’ calculations. Otherwise, the calculation is performed automatically under the rules for
constructing a probabilistic polynomial, changing the incoming system parameters to analyze risks
and identify the most vulnerable points in the system. Using trace-back algorithm makes it possible to
calculate the probability of FT events occurrence starting from the lowest level. Application of the
Fussell-Vesely algorithm allows evaluating the contribution of each event to the probability of the
main undesirable event occurrence.
The paper describes main functional requirements for the system, defines the target audience,
functions, and available actions depending on the level of data access rights. The system architecture
is multi-layered, which ensures the logical and functional independence of the layers. The system data
storage is implemented in the form of a relational database that allows storing data on the results of
design and analysis of the FT. Testing of the developed system on real industrial data showed the
adequacy of the applied methods, correctness of calculations and indicators of system reliability. The
practical value of the proposed system is applicability to various data domains, no restrictions on the
size of the studied system, the ability to save and export data.

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