Introduction. Currently, intensive work is underway in the Russian Federation and abroad to improve the safety of working and living conditions for citizens. In particular, safety of the population [1] is determined by fundamental legislative acts in our country [2]. However, despite this, the number of accidents, fires and man-made emergencies has not decreased. Major accidents, fires, and emergencies on a federal or interregional scale pose a particular danger to the public and enterprises.

Fire prevention work is carried out both in our country and abroad. For example, Portugal actively develops a strategy to prevent fires. A group of specialists analyzes the causes of fires for subsequent amendments to the country's legislative framework [3]. The catastrophic fires in the Brazilian forest in 2020 and 2021 have served as an impetus for developing measures to prevent future fires. New ways of prevention have been proposed, and successful fire management strategies have been created [4].

Based on the above, we can conclude that it is necessary to further update the existing measures to improve the safety of businesses and employees, as well as to develop new measures that take into account modern conditions and requirements. This is the aim of our research.

Materials and Methods. The analysis was based on the classical rule for calculating the risk (probability) of a negative situation [5]. The effectiveness of the fire safety assessment form for a particular facility depended on the expected risks of fire and casualties (R(ср.ф)) [6]. In other words, for an object corresponding to a certain class of functional fire hazard, a negative situation was modeled — the occurrence of a fire, and then, using the classical sum law [7], the risk of death was determined [8], depending on the purpose of the object, the causes of fire, and the social status of victims (R(ср.о)). Numerical values for the calculations were taken from statistical data on fires in the Russian Federation for 2022, which were freely available on the Internet on official resources. The calculations were performed using an engineering calculator with an extended set of functions that provided the required accuracy and support for complex mathematical operations.

Results. To develop measures necessary to ensure safety of the facility and its personnel, it is important to assess the current state of the company and determine the conditions under which both the company and its employees are protected from hazards associated with the production process.

According to fire safety standards [9], the forms of assessments, their positive and negative values [10], were defined, which are presented in Table 1 [11].

Positive and negative provisions of the existing compliance conditions are presented in Table 2.

In turn, the conditions for ensuring the safety of the facility are fulfilled when implementing the safety system outlined in the flowchart (Fig. 1)

Taking into account positive and negative assessments of the safety of enterprises and their employees, Tables 3, 4, 5, and 6 present additional fire hazard assessments and measures to improve their implementation.

Improvements and additions were based on the principles of ensuring and improving the safety of employees and property of the enterprise.

The analysis conducted allowed us to develop new methodological principles for assessing and ensuring the safety of an enterprise based on risk management.

A general existing principle for safety assessment and conditions is presented in Figure 2 in the form of a block diagram.

The existing methodological principle of fire safety assessment and assurance is presented in the form of a general flowchart, since the norms provide for nine forms and five conditions that are not interrelated with each other, respectively (Fig. 3).

Taking into account the above, the methodological principle “one form of assessment — one compliance condition” was proposed to solve the problem of the relationship between the form of assessments and the conditions of compliance (Table 7) [12].

This principle will ensure all safety conditions, taking into account the chosen necessary form of assessment. It also clearly shows which form is implemented under certain conditions. The chosen principle will not allow replacing assessments with ineffective forms to achieve the necessary compliance conditions.

Ensuring the safety of employees and enterprises according to the proposed principle is presented in the form of a flowchart, which provides methodological support (Fig. 4).

Thus, fire safety is ensured through the implementation of the attached forms and conditions. Figure 5 illustrates the implementation of the methodology in a flowchart.

For the practical implementation of the proposed methodological principle, it was necessary to analyze the actual risks of negative situations. The existing principles of ensuring fire safety are presented in the form of a flowchart in Figure 6.

It follows from this principle that all compliance conditions can be investigated for any form of assessment.

Considering statistical indicators on fires, the probabilistic criteria for actual risks are provided in Table 8.

In this table, fire probability at the facility is determined by the formula [13]:

(1)

The probability of death from fires at facilities is determined by the formula:

(2)

The probability of death from fires:

(3)

where Nп — number of fires, pcs; Nо — number of objects, pcs.

Data on the risk of death from fires is presented in Table 9.

The probability of death of people depending on the causes (Rпр.г.), that is, from exposure to primary and secondary fire hazards [14], is determined by the formula:

(4)

where Nпр.г — number of people killed, depending on the causes, people; Nнас.РФ — number of people killed, depending on the causes, people.

Table 10 provides the data on the probability of death of the population of the Russian Federation in terms of their social status.

The probability of death from fires in terms of people social status is determined by the formula:

(5)

where Nсоц.п — number of people who died in the Russian Federation in 2022, according to their social status, people.

Next, we will combine the indicators of calculated risks by distributing the objects of fire according to the causes and social status of the victims. For convenience, we will use a symbol to represent the objects: 1, 2, 3…

The related data is provided in Table 11.

Then, using the formula below, we determine the overall probability of death of people, depending on their social status and causes:

(6)

where N — number of probabilities of negative events related to fires.

The calculated information is presented in Table 12.

This table shows the minimum and maximum values of average probabilities. This data can be used by stakeholders and services to take preventive measures, up to the coordination of government policy, to prevent fires and deaths.

Next, we proceed to determining the expected risks, depending on the forms of assessments and conditions for compliance with fire safety regulations at the facilities. The implementation of fire safety measures at facilities of different functional fire hazard classes [15] involves various forms and conditions, including additional ones, as shown in Figure 7.

The expected risks for facilities by functional purpose (Rср.ф) are determined by the formula:

(8)

The calculated values are summarized in Table 13.

The table shows the minimum and maximum values of the probability of negative events. The above-mentioned methodological principle of fire safety assessment is presented in the form of an algorithm in Figure 8.

The proposed methodological principle for assessing the safety of people in fires improves the current procedure established by the legislation of the Russian Federation. This principle is based on actual values of risk of adverse events, which allows interested parties to take necessary preventive measures in advance.

Discussion and Conclusion. Updating the existing principles for assessing the safety of facilities, their employees, and the public based on regulatory documents and those proposed through risk management of potential negative situations allows interested individuals and legal entities to choose the most appropriate forms and conditions for implementation. Mathematical calculations presented in the study allow us to justify the benefits of proposed measures. Applying the principle of predictable risks supports the impossibility of achieving unconditional safety for an enterprise and its employees due to a significant number of unpredictable negative situations resulting from natural and human-made causes.

The practical significance of this research lies in the fact that the methodological approach proposed by the authors is based on mathematical calculations. By taking into account the potential risks, it is possible to develop preventative measures to avoid and minimize negative consequences associated with emergencies, accidents, workplace injuries, and fires.

The results of the work are especially relevant for owners of businesses and other infrastructure facilities. Their primary concern is ensuring the safety of their employees and the general public. Owners will be able to choose an appropriate form of assessment, not only based on the functional classification of the fire risk of the facility, but also considering the minimal risk of death if certain conditions are met. This will allow them to redistribute financial resources within the organization to meet specific fire safety requirements based on the chosen form of assessment.