Protection and health care, life, habitat, material, and intellectual property of a person is an essential task at the present stage of development of society. To solve this problem, integrated security systems consist of a video surveillance system, security and fire alarms, access control, and management systems. In the early stages of development, these components were mainly used as independent protection elements. To date, they are used in one complex to solve the problem of technical protection of the facility. One of the important hardware and software means of protection is the elements and devices of electronic technology, including touch devices. Their functioning is based on the achievements of solid-state physics, optics, electrooptics, electroacoustics, etc. Modern electronic technologies make it possible to create effective microelectronic sensor devices for security and protection systems, the operation of which consists of the use of optical, mechanical, magnetic, piezoelectric, tensometric, capacitive, and other types of signal converters. In the process of building modern security and protection systems, it is necessary, on the one hand, to have information about the capabilities and features of the functioning of individual constituent elements that ensure the fulfillment of tasks for the protection of an object. On the other hand, it is necessary to evaluate the effectiveness of the developed system, which should include both the reliability indicators of all elements and information transmission channels and the performance indicators of the functional task. The developed mathematical model of the effectiveness of the application of the security system will make it possible to make the right choice of the constituent elements of the system, the parameters of which most fully ensure the fulfillment of the security task. This approach ensures the organization of interaction between security alarm systems, fire alarms, access control systems, video surveillance systems, and centralized security consoles. a complex of technical means, a security system sensor, a centralized security control panel, ORCID: 0000-0001-6825-4697 (T. Vakaliuk); 0000-0003-3448-6072 (O. Dubyna); 0000-0002-9068-931X (T. Nikitchuk); 0000-0002-2601-
the effectiveness of the security system
At present, the object protection system is an integral part of any enterprise, private house, etc. [
2023 Copyright for this paper by its authors.
the state of the object and its further processing. This information can be sent both to the security control
panel and the owner's computer or mobile phone, both via wired and wireless communication channels
[
Today, as primary sensors, devices that have a fairly powerful functionality with the formation of an extended format of data about the object can be used. The issue can be resolved not only by detection but also by its classification. This, firstly, affects the complication of the hardware implementation of the tools, secondly, it imposes restrictions related to the evaluation of the effectiveness of security systems taking into account their reliability.
This approach requires the use of private, generalized, and complex indicators when applying complex technical tools (CTT) in security systems by the assigned tasks. An analysis of the literature has shown that to date there is no mathematical model of CCT that would allow for an optimized choice of the structure and composition of the facility security system, taking into account the quality indicators of the system elements. Therefore, there is a problem in choosing a function model for evaluating the effectiveness of automated systems for the protection of objects of this type.
The purpose of the article is to build a mathematical model for evaluating the effectiveness of the security system, taking into account the reliability of its elements.
In [
In [
In the general case, indicators of efficiency with ISS, as an information system [
To determine the effectiveness of the security system, we will use the approach in which the process
of evaluating the effectiveness of the object's security systems as an information system consists of
several stages, which include, first, the step-by-step transformation of the structures of the systems of
private generalized indicators, and second, their presentation in an indicator containing models of the
lower level of association, namely a complex (integral) indicator of efficiency. This makes it possible
to visualize the indicators of complex-type protection systems in the form of a hierarchy of indicators
of the efficiency and reliability of CTT [
When considering the "tree" of efficiency and reliability indicators (Fig. 1), it is assumed that the
CTT consists (third level) of n sensors (primary elements) and m communication channels. Each of
these elements is characterized by the efficiency index Kefs, Kefch (left branch) and reliability Krs,
Krch (right branch). The second level is characterized, on the one hand, by efficiency indicators, namely
Kefs, Kefch, which have the meaning of generalizing efficiency indicators both due to the use of
security sensors and due to the use of communication lines (wired or radio communication),
respectively, on the other hand on the other hand, efficiency indicators, namely Krs, Krch, which have
the meaning of generalizing efficiency indicators that characterize the reliable characteristics of sensors
and communication lines, respectively. The first level of the hierarchy of CTT efficiency and reliability
indicators is characterized by higher-level indicators, which are presented in the form of Kectt, Krctt,
which have the meaning of complex indicators of the effectiveness of the CTT structure and the
reliability of the CTT structure, respectively. The higher level (zero) of the "tree" of indicators includes
indicators of the lower level and is represented by a comprehensive indicator of the effectiveness and
reliability of the CTT structure (Kef). At the same time, the analysis of the construction of object
protection systems makes it possible to conclude that this structure is an information-automated system
[
Next, IE will be understood as the simplest element of object protection, reflecting sources (channels) of information. Therefore, two classes of indicators that characterize, on the one hand, the detected and recognizable properties, and, on the other hand, the reliable capabilities of the security system, can act as indicators of the quality of the security system, in general, reflecting the efficiency and reliability of the third level of the hierarchy (Fig. 1).
The revealed and recognition properties of the CTT of the security system can be represented by the
probabilities of correct detection of the signal by the sensors, erroneous or correct classification of
objects, and timeliness of information processing in the path of signal recognition [
The reliable capabilities of CTT are associated with sudden failures that occur during the operation of security systems and are characterized by a set of several indicators, among which can be highlighted, for example, the probability of error-free operation, the timely release of information through communication channels, the effectiveness of the task performed in communication channels. 3.2.
The above allows you to imagine the quality of the functioning of the security system of the object protection system based on the hierarchy of indicators (Fig. 1) and introduce a vector indicator that determines the effectiveness and reliability of CTT in the following form:
е = ‖ 1, 2, 3, 4, 5‖ (1)
In expression (1), components 1, 2, 3, 4, 5 are performance indicators characterizing the detection of an object by sensors, the correctness of object classification, timeliness and correctness of information processing in the processing unit, reliable characteristics of sensors and communication lines, and timeliness of information delivery through communication channels, respectively. 0 level 1 level 2 level 3 level
Кеf Кеfcct
Кrcct s f e К h c f e К s r К h c r К 1 s f e K n s f e К 1 h c f е К m h c f е К 1 s r К n s r К 1 h c r К m h c r К
In general, the work of any security system consists in performing the following basic operations: detection of a conditional violator, his recognition or identification as a result of processing the primary information received from the sensor, making an appropriate decision based on the purpose of this system (formation of control signals) and data transmission by communication channels to the technical means of displaying information (computer, mobile phone, remote control) to the operator (owner).
It should be noted that a certain class of modern sensors (for example, video cameras) are capable of performing several of the main operations: detection, recognition, and identification, while for others only detection is performed, and the rest of the operations take place in the processing unit (video recorder, reception and control device, controller, etc.).
In the general case, when building protection systems taking into account the works to evaluate the constituent components 1, 2, and 3 included in expression (1), probabilistic indicators can be considered:
Ppr is a probability that characterizes the timeliness of information processing in the signal recognition path.
It should be noted that two factors must be taken into account when analyzing security systems, namely: firstly, the elemental base when creating sensors and communication channels is characterized by sudden failures, that is, the above-mentioned IE during operation has a finite failure time, and secondly, it is necessary to ensure the release of information within a time that does not exceed the established regulatory requirement. In this case, when evaluating the elements of the structures of the object protection system, it is advisable to present the components of the vector indicator with probabilistic indicators and supplement them with the following reliability characteristics: the probability of failure-free operation of the sensor Prd, the probability of failure-free operation of the communication channel Prch and the probability of execution, which characterizes timeliness issuing information via the communication channel Ptch. Taking into account the above, the vector indicator represented by expression (1) is reduced to the form е = ‖ , , , , ℎ, ℎ‖ (2)
Taking into account the fact that currently the latest advances in microelectronics, namely integrated
technologies, are used in the protection systems in the manufacture of IEs, the presented types of IEs
are approximately equally reliable. In this case, from a practical point of view, in expression (2), along
with the values ℎ, , it is possible to operate with the value of the average failure intensity [
111 110 … 000
Taking into account the multiplicative approach to combining generalizing indicators, the indicator of
efficiency and reliability of the CTT of the security system can be written analytically as
е = , , , , ℎ
(3)
At the initial stage of the security system, the detection process takes place with
- the probability
of object detection by tools of detection (TD). This practically determines the next stages of processing
and execution of the task by the security system as a whole [
The following schemes of logical processing of alarm signals from individual emergency shelters have become the most widespread for CTD: M with N, in particular: 1 with 2 (N=2, M=1); 1 of 3 (N = 3, M = 1); 2 of 3 (N=3, M=2). Processing of such signals, as a rule, is carried out based on AND and
According to the first scheme, all TDs must have the same probability of detection (when fixing the probability of false alarms). When processing signals according to the second scheme, it is advisable to equalize the values of the false alarm probabilities of all TDs, when fixing the probability of detection.
At present, the following algorithms for processing binary signals from TD are the most widely used: - based on theoretically possible combinations of TD that worked; - as a result of the assignment of weighting coefficients to TD. probabilities and ̅̅1̅,̅̅̅2̅̅,̅̅3̅ - false alarm probabilities.
We will give an example of the algorithm for processing binary signals from three TDs based on theoretically possible combinations of TDs. For each of the TD, let's take 1, 2, 3 - their detection ∆ passes and in the presence of interference ⃑∆⃑⃑⃑⃑ (j- number of the combination). Theoretically possible combinations of three TD
∆ 1 2 3 1 2(1 − 3)
… 2/3 = ∑ ∆ ̅̅2̅/̅3̅ = ∑ ⃑∆⃑⃑⃑⃑
4 4 =1 =1 8 ∑ ∆ = ∑ ⃑∆⃑⃑⃑⃑ = 1 ⃑∆⃑⃑⃑⃑
… ̅̅1̅̅̅̅̅̅3̅
2 ̅̅1̅̅̅2̅(1 − ̅̅3̅) (4) (5) (6) (1 − 1)(1 − 2)(1 − 3) (1 − ̅̅1̅)(1 − ̅̅2̅)(1 − ̅̅3̅)
To find the probability of detection for the logic processing scheme 2 out of 3, it is necessary to add
up the probabilities of those combinations in which there are two or three units [
given probability of detection.
The optimal scheme for the logical processing of the CTD will be the one that, with the provision of a given probability of detection, has the lowest probability of a false alarm, and, accordingly, the synthesis of such an algorithm will be as follows: arrange the combinations in Table 1 in descending order of the ratio
and select from this table the number of first combinations that provide a
At present, approaches to evaluating the effectiveness of ISS practically do not take into account the fact that any object protection system operates under the conditions of significant uncertainty of both internal and external environments and is described by mathematical models based on information that is of an undefined or incomplete nature.
Existing approaches are based either on the exclusion of uncertainty from their mathematical models or on simplifications and formal descriptions. Therefore, the question arises in the development of new, additional analytical approaches to solving problems regarding the assessment of the effectiveness of
Based on the analysis of existing methods, it can be concluded that ISS should be considered a
complex information system and its effectiveness should be characterized by several partial indicators
and a general criterion should be formed based on them [
As the analysis [
[
programming is solved: maximize ∑ =1
If =1 ∑ ≤ , = 1, ; ∈ {0,1}; = 1, ;
categories.
privacy levels and a set of privacy
Balash's methods for integer variables, branches, and limits, exclusion of groups of unknowns, elements of duality theory, linear, convex, and parametric programming
tools. 1. Finding parameters. 2. Formation of a threedimensional matrix of
relations and its transformation into a two
dimensional table. 3. Finding qualitative and quantitative values of
indicators 1. To carry out risk fixing. 2. Determine the risk index. into account - total probable losses without treatment of identified risks; total probable losses after risk processing M; total actual losses from exposure to risks ; total actual costs for processing identified risks (
= ); total actual losses from exposure to risks ; total actual costs for processing risks = ( ∑ − ∑ ) − ( ∑ + ∑ ) + =1 =1 − ( + ( ∑ =1
=1 =1 + ∑ =1 ) )
approach (multicriteria evaluation) Fuzzy indicators of protection of the object in the form of linguistic variables, such as: "completely unprotected", "insufficiently protected", "protected", "sufficiently protected", "fully protected" = ∑ =1 ( )
( , ) = 1 level of action and degree of influence. 4. Determination of risk management methods.
characterizing risks.
of the economic effect of risk management.
Belonging to a certain level of
security is determined on the
interval [
An analytical calculation of the information entropy of the system is carried out using the concept of function convolution. With a linear dependence, the efficiency of the integration of subsystems in terms of information is considered satisfactory.
Otherwise, it is ineffective. parameters (i) that characterize ISO are determined. The values of the subjective coefficients of importance ( ) are given to each of the characteristics assigned by an expert. SR parameter values are
= ( , ) where - is the parameter of the frequency of the appearance of the threat;
2 = ∑ =1 2 ∑ =1 ( ⃗/ ⃗) ( ⃗) ( ⃗/ ⃗) + , ( ⃗/ ⃗) – the probability of
elimination; ( ⃗) – a priori probability of the state of the object of control; ( ⃗/ ⃗) – loss of decision-makings at the state of the object s m is the number of recognized threats.
average during the time Based on the analysis of statistical material, the value of S is set, the value of V is chosen to be equal from 1 to the maximum possible amount of damage, and the value of the indicator is calculated as a function of the parameters V and S.
fulfillment of tasks as intended by the object as a result of the implementation of threats is determined.
One of the ways to evaluate the effectiveness of ISS is an approach called optimization or
combinatorial. It solves the task of optimizing a species: maximizing a certain function under given
constraints. The type of objective function and the system of restrictions are built depending on the
nuances of the task [
To build a mathematical model, we enter the variable p(i,j) equal to 1 if the jth threat is detected by the ith - TD and 0 otherwise.
We believe that informational threats are not related to each other. The task is to find the maximum effect from the detection of threats U with the help of the declared in the system of TD A, subject to restrictions on the total amount of expenses C.
Taking into account the obtained analytical expressions, the optimization problem of determining the best structure of the integrated security system is presented in the form of the following ratio: with restrictions
=1 =1 ∑ ∗ ∑ ∑ е ( , ) ( , ) → ∈ ( , ) ∈ (1,0) ∑ ( , ) ≤ (7) (8)
Modern object protection systems can use several information transmission channels to increase
reliability. It can be a wired or Wi-Fi channel, or one or more mobile communication channels using
different operators [
To investigate the effectiveness of the proposed approach and mathematical model, we will use the modern equipment of the Ajax security system. It represents the basic security alarm kits on the market, which are necessary for the technical protection of the object. The main components of the kit are a control panel, wireless motion, and opening detectors, and a key fob. Based on this set, by adding the necessary elements, depending on the complexity of the object, you can form the required integrated security system. These sets differ in various parameters and characteristics of the devices included in the composition. In addition, video cameras from most modern manufacturers can be added to the system. Thus, we get a modern integrated security system (ISS).
By the proposed mathematical model, the probability of detecting an object is determined by motion sensors and partially by video cameras, the probability of correct classification is determined by video cameras, the operator, and the capabilities of special software, the probability characterizing the timeliness of information processing in the signal recognition path is determined by the operator and the capabilities of special software, the probability of execution characterizing the timeliness of information output via the communication channel ℎ is determined by the state and number of channels In addition, each element is characterized by a failure probability, which is approximately equal to .
Table 1 shows the main characteristics of the elements of the basic set of the integrated security system (ISS). By the proposed mathematical model, the probability of detecting an object is determined by motion sensors and partially by video cameras, the probability of correct classification is determined by video cameras, the operator, and the capabilities of special software, the probability characterizing the timeliness of information processing in the signal recognition path is determined by the operator and the capabilities of special software, the probability of execution characterizing the timeliness of information output via the communication channel ℎ is determined by the state and number of channels In addition, each element is characterized by a failure probability, which is approximately equal to .
Table 3 shows the main characteristics of the elements of the basic set of the integrated security system (ISS).
To obtain realistic values, it is necessary to conduct a study of each specific device (which is partially done in production) and use expert groups. The price of each set is presented in conventional units.
A graph of the dependence of the allowable costs of protection C on the efficiency of a given ISS is shown in Fig. 2.
The analysis of the data in Table 4 and the graph in Fig. 2 shows the value and nature of changes in the components of the security system depending on the probability indicators and, accordingly, the costs. Thus, when using a motion detector without photo verification, the values of , will be the lowest, and with only two communication channels in the central unit, the value of ℎ will also be minimal, which determines the lowest efficiency indicator and, accordingly, the lowest costs. The use of security system elements with better performance leads to an increase in costs, but also an improvement in efficiency. At the same time, the proposed mathematical model makes it possible to determine the weight of the improvement of the efficiency indicator when selecting the necessary elements. For example, increasing the resolution of the video camera to 4 and 8MP in variants 4 and 5 (Table 4) leads to a slower improvement in the efficiency indicator than in the first three variants.
Paper [
In contrast, the proposed mathematical model makes it possible to find the best set of components of an integrated security system at limited costs based on quantitative indicators characterizing the quality of the main functions of the devices. This, in turn, more accurately takes into account the specifics of each device and its contribution to the overall optimization process.
Thus, the considered approach to assessing the quality of the functioning of the technical component in automated security systems, based on the use of the proposed probabilistic indicators, allows for the analysis of devices of CTT from the position of an element of an automated information system. The proposed analytical expressions make it possible to evaluate the effectiveness of the work of the CTT within the framework of the implementation of the assigned tasks, taking into account the reliability of their structures and probability indicators of information elements.
As an efficiency indicator, it is proposed to use a complex parameter determined by the probabilities of correct detection and classification of the object, timeliness of information processing, and fault-free operation of both primary sensors and information transmission channels.
To evaluate the effectiveness of the security system, it is suggested to use an optimization approach. It allows you to determine the optimal ISS structure with the necessary restrictions that are characteristic of this enterprise (cost, reliability, number of security lines, etc.). The optimization problem can be solved by the methods of Balash or parametric programming.
It is known that the probability of correct detection and classification is affected by a large number of factors (time of day, weather conditions, distance to the object, etc.). One of the solutions to this issue can be the application of the theory of fuzzy sets.