2.2.2. Formal IPI model

The formal model of the IPI process is proposed [7, 8, 11]. For the IPI object Obj there is a set of subject matters Subi, and a set of characteristics (Eq. (4)) is defined for each of them:

Figure 3. Scheme of IPI.

$$\text{Obj} = \{Sub\_1, \dots, Sub\_n\}, \quad Sub\_i = \{Char\_1, \dots,Char\_k\}. \tag{4}$$

ð Þ¼ Obj; <sup>S</sup> <sup>X</sup>

l

0

BBBBBBBB@

Operation « � » has the following properties:

.

(

0

BBB@

2.2.3. Mathematical model of information-psychological impact

Obj ¼

1 … Subnð Þ Char<sup>1</sup> ……… Sub1ð Þ Chark … Subnð Þ Chark 1 … 1 ……… 1 … 1

2. Subið Þ� Charm Sj ¼ Ef i,m,j ¼ 1—the property Subið Þ Charm has disappeared.

3. Subið Þ� Charm Sj ¼ Ef i,m,j ¼ 0—the property Subið Þ Charm has not changed.

Subs Charf

<sup>1</sup> � Sj <sup>¼</sup> <sup>1</sup>, if the property continues being absent,

The result of the malefactor's attack on the IPI object is a matrix of properties, which will take

1 Ef <sup>1</sup>, <sup>2</sup>,l … 1 Ef <sup>2</sup>,1,j 1 … Subnð Þ Char<sup>2</sup> … ……… 1 Sub2ð Þ Chark … Subnð Þ Chark

Some of the properties resulting from IPI may remain unchanged; others are replaced by

The change in the property which undergoes IPI can be described by equation or model [11,

where P is the characteristics of the IPI object, H is the characteristics of the IPI (means of impact), and K is the response (the level of change). As the characteristic of IPI, we will use H

as the effectiveness of implementing the means of influencing the property Ef i,m,j

� �, if the property has appeared:

1

Probabilistic Analysis of the Influence of Staff Qualification and Information-Psychological Conditions on…

CCCCCCCCA

� Sj, Obj ¼

0

BBBBBBBBB@

1 … Ef n,<sup>1</sup> …… … Ef <sup>1</sup>, <sup>k</sup> … Subnð Þ Chark 1 … Subnð Þ Charkþ<sup>1</sup> …… … Ef <sup>1</sup>,f … 1

http://dx.doi.org/10.5772/intechopen.75079

:

1

K ¼ f Hð Þ ; P , (12)

K ¼ f Obj ð Þ ð Þ ; S ; P : (13)

CCCA: (11)

. Thus, the

1

239

CCCCCCCCCA :

(9)

(10)

j¼1

1. Subið Þ� Charm Sj ¼ Ef i,m,j

the changed form (Eq. (11)):

Ef i,m,j .

16–19] (Eq. (12)):

equation takes the form (Eq. (13)):

Each object can have several characteristics. Dependence of objects and their characteristics is estimated in the matrix of properties. In the columns, the subject-matters of the IPI object are indicated; in the lines, characteristics are indicated; at the intersection, their correspondence is denoted (Eq. (5)):

$$\begin{array}{ccccc} \text{Cobj} = \begin{pmatrix} \text{Sub}\_1(\text{Char}\_1) & \text{Sub}\_2(\text{Char}\_1) & \dots & \text{Sub}\_n(\text{Char}\_1) \\ \text{Sub}\_1(\text{Char}\_2) & 1 & \dots & \text{Sub}\_n(\text{Char}\_2) \\ & \dots & \dots & \dots & \dots \\ & 1 & \text{Sub}\_2(\text{Char}\_k) & \dots & \text{Sub}\_n(\text{Char}\_k) \end{array} \tag{5}$$

The subject has many means of impact that do not always correspond with articles of the IPI object; this is proposed that the set of means of the subject's impact is defined as S ¼ f g S1;…; Sn .

Each of the means of impact Sj is applied for the purpose of changing the property Subið Þ Charm and affects different objects and their characteristics in different ways. The result of such a change will be denoted Ef i,m,j , which can be equal to zero or be negative (that means it has the opposite effect to the aims of IPI) and can be positive (it means it can have an effect corresponding with the goals of the IPI).

Realization of IPI for m-characteristics (Eq. (6)):

$$\left(\text{Sub}\_{i}(\mathsf{Char}\_{m}), \mathsf{S}\_{\dagger}\right) = \mathsf{E}f\_{i,m,\dagger}.\tag{6}$$

For the case when the IPI object possesses articles with characteristics, and the subject has means of impact, this is proposed to obtain the matrix of efficiency of IPI; in the columns, the articles of the IPI object are indicated; in the lines, characteristics are indicated; at the intersection, their correspondence is denoted (Eq. (7)):

$$S = \begin{pmatrix} Ef\_{1,1,1} & Ef\_{1,1,2} & \dots & Ef\_{1,1,l} \\ Ef\_{1,2,1} & Ef\_{1,2,2} & \dots & Ef\_{1,2,l} \\ \dots & \dots & \dots & \dots \\ Ef\_{n,1k1} & Ef\_{n,k2} & \dots & Ef\_{n,k,l} \end{pmatrix} \tag{7}$$

The sum of all impacts on the m-characteristic is described by Eq. (8):

$$\sum\_{j=1}^{l} \left( Sub\_i(\mathsf{Char}\_{\mathfrak{m}}), \mathcal{S}\_{\mathfrak{j}} \right) = Ef\_{i, \mathfrak{m}'} \tag{8}$$

where the efficiency is provided when the matrixes are added in stages, which means that several IPI tools can affect one characteristic. The formal model of IPI implementation can be written in the following form (Eq. (9)):

Probabilistic Analysis of the Influence of Staff Qualification and Information-Psychological Conditions on… http://dx.doi.org/10.5772/intechopen.75079 239

$$(Obj, S) = \sum\_{j=1}^{l} \begin{pmatrix} 1 & \dots & Sub\_{\pi}(Char\_{1}) \\ \dots & \dots & \dots \\ Sub\_{1}(Char\_{k}) & \dots & Sub\_{\pi}(Char\_{k}) \\ 1 & \dots & 1 \\ \dots & \dots & \dots \\ 1 & \dots & 1 \end{pmatrix} \cdot S\_{\circ} \cdot Obj = \begin{pmatrix} 1 & \dots & Ef\_{n,1} \\ \dots & \dots & \dots \\ Ef\_{1,k} & \dots & Sub\_{\pi}(Char\_{k+1}) \\ 1 & \dots & Sub\_{\pi}(Char\_{k+1}) \\ \dots & \dots & \dots \\ Ef\_{1,f} & \dots & 1 \end{pmatrix} \cdot \tag{9}$$

Operation « � » has the following properties:

Obj ¼ f g Sub1;…; Subn , Subi ¼ f g Char1;…; Chark : (4)

, which can be equal to zero or be negative (that means it has the

1

� � <sup>¼</sup> Ef i,m, (8)

1

CCCA

: (6)

CCCA: (7)

(5)

Each object can have several characteristics. Dependence of objects and their characteristics is estimated in the matrix of properties. In the columns, the subject-matters of the IPI object are indicated; in the lines, characteristics are indicated; at the intersection, their correspondence is

The subject has many means of impact that do not always correspond with articles of the IPI object; this is proposed that the set of means of the subject's impact is defined as S ¼

Each of the means of impact Sj is applied for the purpose of changing the property Subið Þ Charm and affects different objects and their characteristics in different ways. The result of such a

opposite effect to the aims of IPI) and can be positive (it means it can have an effect

For the case when the IPI object possesses articles with characteristics, and the subject has means of impact, this is proposed to obtain the matrix of efficiency of IPI; in the columns, the articles of the IPI object are indicated; in the lines, characteristics are indicated; at the intersec-

> Ef <sup>1</sup>,1, <sup>1</sup> Ef <sup>1</sup>,1,<sup>2</sup> … Ef <sup>1</sup>, <sup>1</sup>,l Ef <sup>1</sup>,2, <sup>1</sup> Ef <sup>1</sup>,2,<sup>2</sup> … Ef <sup>1</sup>, <sup>2</sup>,l … ……… Ef n, <sup>1</sup>k<sup>1</sup> Ef n, <sup>k</sup><sup>2</sup> … Ef n, k,l

Subið Þ Charm ; Sj

where the efficiency is provided when the matrixes are added in stages, which means that several IPI tools can affect one characteristic. The formal model of IPI implementation can be

Subið Þ Charm ; Sj � � <sup>¼</sup> Ef i,m,j

Sub1ð Þ Char<sup>1</sup> Sub2ð Þ Char<sup>1</sup> … Subnð Þ Char<sup>1</sup> Sub1ð Þ Char<sup>2</sup> 1 … Subnð Þ Char<sup>2</sup> … ……… 1 Sub2ð Þ Chark … Subnð Þ Chark

denoted (Eq. (5)):

238 Probabilistic Modeling in System Engineering

f g S1;…; Sn .

change will be denoted Ef i,m,j

corresponding with the goals of the IPI).

Realization of IPI for m-characteristics (Eq. (6)):

tion, their correspondence is denoted (Eq. (7)):

written in the following form (Eq. (9)):

S ¼

0

BBB@

The sum of all impacts on the m-characteristic is described by Eq. (8):

X l

j¼1

Obj ¼

0

BBB@


$$\mathbf{1} \cdot \mathbf{S}\_{\circ} = \begin{cases} \text{1, if the property continues being absent,} \\ \text{Sub}\_{\circ}(\text{Char}\_f) \text{, if the property has appeared.} \end{cases} \tag{10}$$

The result of the malefactor's attack on the IPI object is a matrix of properties, which will take the changed form (Eq. (11)):

$$\text{Obj} = \begin{pmatrix} 1 & \text{Ef}\_{1,2,l} & \dots & 1 \\ \text{Ef}\_{2,1,j} & 1 & \dots & \text{Sub}\_{\text{n}}(\text{Char}\_2) \\ \dots & \dots & \dots & \dots \\ 1 & \text{Sub}\_2(\text{Char}\_k) & \dots & \text{Sub}\_{\text{n}}(\text{Char}\_k) \end{pmatrix} . \tag{11}$$

Some of the properties resulting from IPI may remain unchanged; others are replaced by Ef i,m,j .

#### 2.2.3. Mathematical model of information-psychological impact

The change in the property which undergoes IPI can be described by equation or model [11, 16–19] (Eq. (12)):

$$K = f(H, P),\tag{12}$$

where P is the characteristics of the IPI object, H is the characteristics of the IPI (means of impact), and K is the response (the level of change). As the characteristic of IPI, we will use H as the effectiveness of implementing the means of influencing the property Ef i,m,j . Thus, the equation takes the form (Eq. (13)):

$$K = f((Obj, S), P). \tag{13}$$

Eq. (12) makes it possible to evaluate the change in the properties and the response of an object to IPI. In our case, staff are considered as the IPI object. Eq. (13) of the change in the property and the human reaction to the effects is given in articles [11, 16–19] and has the form (Eq. (14)):

$$R\frac{d^2Y}{dt^2} + \frac{2F\sqrt{RA}}{QF\_0} \cdot \frac{dY}{dt} + \frac{A}{Q^2}Y = X,\tag{14}$$

security service includes a large number of highly skilled employees who can increase labor

Probabilistic Analysis of the Influence of Staff Qualification and Information-Psychological Conditions on…

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241

The estimation should be carried out separately for each component because maintenance of various components of the information system is implemented in different ways. This is proposed to define the malfunction as various malfunctions in the operation of the information system components that require staff intervention to eliminate them. This is proposed to understand vulnerability as a defect of information system that can violate its integrity, avail-

During the work activity, the staff of the information system may be in different psychological conditions. The effectiveness of the staff depends on what psychological state they are in. The

• Optimum working condition ensures the greatest efficiency of activity. It is characterized by the presence of a conscious goal of activity, high concentration of attention, aggravation of memory, and activation of thinking. The electroencephalogram shows that in this

• The state of tense activity arises in the course of work in abnormal situations. Mental tension develops directly in proportion to the difficulty of the task. Easy tasks are solved with minimal effort; complex and new actions require a higher degree of mental pressure. Mental tension is a physiological reaction of the organism, mobilizing its resources to perform more difficult tasks. Mental tension stimulates the physical and mental processes of the human body, which increases its adaptive abilities. The tension reaction develops in a responsible environment, as well as when people perform complex production tasks, if they change the stereotype of actions and habitat and if they are under the influence of extreme conditions. Under the influence of mental stress, vital body functions such as metabolism, circulation, and respiration change. If in the behavior of a person, there is some general concentration, the actions become clearer, the speed of motor reactions increases, and physical performance improves. At the same time, perception becomes aggravated, the process of thinking is accelerated, memory is improved, and concentra-

It should be remembered that the dependence of the efficiency of labor activity (working capacity) of employees on the level of tension of its functional systems is parabolic. It was found out that mental stress has a positive effect on the result of labor up to a certain limit. Exceeding the critical level of activation leads to a decrease in the results of labor up to a

• Fatigue is a functional state of a person, temporarily occurring under the influence of prolonged or intensive work, accompanied by a decrease in its effectiveness. Fatigue is caused by the depletion of body resources during prolonged or excessive activity and is characterized by a decrease in motivation to work, a violation of attention and memory.

productivity working together.

ability, and confidentiality and cause a malfunction.

following states can be distinguished as [3, 20, 29]:

tion of attention is increased.

complete loss of efficiency.

2.3.2. Impact of staff's psychological conditions on labor activity

state, the brain rhythms mainly lie in the beta range.

where F is the frustration; F0 means some value of the level of frustration, considered normal or threshold; A is the aggression; Q means the time parameter; R is the stiffness; X means the effectiveness of information-psychological impact; and Y is the reaction level. These parameters are measured in conditional scores. They can be estimated using psychological tests and an expert method. This is proposed to use Eq. (11) to estimate the change in the property of the IPI object as a result of the action. The transfer equation for Eq. (14) has the form (Eq. (15)):

$$W(p) = \frac{Q^2 F\_0}{RQ^2 p^2 F\_0 + 2QF\sqrt{RA}p + AF\_0}.\tag{15}$$
