**3. Results**

*3.1. Results of Calculating the Occupational and Background Risks for the Arctic Zone*

The results of the *R*F.N.t., *R*RF.av. *R*M.I.t., and *R*I.A. risk values were determined on the basis of statistical data for each region of the Arctic zone over the past 10 years, which were then subjected to correlation and regression analysis—see Table 1.

**Table 1.** Background risks of occupational injury for the Arctic zone (103).


Table 1 provides the background risk values for each Arctic zone territory, calculated using Equation (3).

The data from Table 1 show that the background risk levels have remained practically the same in the past decade. It should be noted that the Krasnoyarsk Territory displays the lowest average background risk values, while the Nenets Autonomous Area has the highest ones.

Figure 8 illustrates the relationship between background risk and injury risk for each region, indicating that background risk has an impact on the magnitude of overall injury risk. The results indicate that the background risks can have significant impact on the overall injury rates. As such, the background risk accounts for 35% of the overall risk in the Nenets Autonomous Area and for over 30% in the Chukotka Autonomous Region and the Sakha Republic (Yakutia).

Thus, by determining the risk structure, we can elucidate the relations between its determining factors, and whether they are controllable or uncontrollable [26].

**Figure 8.** Share of the background risks and occupational risks in the overall injury risks.

The controllable factors in this case are the factors linked to the enterprises' operations, and the uncontrollable ones comprise the external conditions determined by the environment (such as air pollution), placement of workers' habitations, length of the polar day and night, intensity of the UV radiation, location of the facilities, weather conditions, etc. The external conditions affect the mental and physical states of the workers.

#### *3.2. The Specifics of Determining the Priority Directions for Reducing Injury Rates at the Kirov Branch of "Apatit", JSC*

We use the vertically integrated Kirov branch of "Apatit" (based in Murmansk) as an example subject for our methodology. The company incorporates the following: the United Kirovsky mine, the Rasvumchorr mine, the East mine, and the Central mine. The original data used in the study were taken from the reports by the State Committee for Supervision of Industrial and Mining Practices (Rosgortekhnadzor), the internal reports by the Kirov branch of "Apatit", and the reports collected by other authors [27]. The calculated occupational risk values are presented as linear functions in Figure 9.

**Figure 9.** Occupational injury rates at the mines of Apatit.

Figure 9 illustrates that all the mines of the company have seen a decrease in injury rates over the 10-year period studied. The risk trend is described by a linear function with the correlation coefficient exceeding 0.7, with the confidence interval being 0.95.

At the East mine, the occupational injury rate of the first few years is largely different from the other mines' and the company as a whole. However, by 2018, the injury rates have become comparable to other mines'. For each linear correlation dependence of the injury risk for the mines of the Kirov branch of Apatit, the mean value (M) and standard error (SEM) were calculated.

The occupational risk situation at the mines is characterized by the following two indicators: the average risk of injury ( *R*) and the average rate of change - *V* in the risk of injury. The average rate of change in the injury risks corresponds to the linear correlation's regression coefficient, and the average injury risk represents the mean between the injury risks at the beginning and at the end of the period in question [28,29]. The relative changes in values ( Δ *R*, Δ *V*) are calculated as the ratio of the average injury risk and the average injury risk of change at a specific mine to the company-wide values.

On the basis of the data on occupational injury rates at the Apatit company from 2008 to 2018, we have calculated the occupational injury risks for the four mines [30,31].

Table 2 shows the relative changes in occupational injury risks and the rate of changes in the injury risks ( Δ *R* and Δ *V*) respectively) for the four company mines.

**Table 2.** Values of the relative change in injury risks (Δ*R*) and the relative change in their rates -Δ*V* and their reciprocals 1/Δ*V* for the company mines.


The relative change in the injury risk rate and the relative injury risk value serve as the basis for the "basic injury rate matrix", where the reciprocal of the relative change in the injury risk rate is shown on the X axis, and the relative value of risk, on the Y axis.

For the sake of clarity, the segments of the matrix that correspond to various occupational injury risks are colored differently: green means acceptable labor safety; yellow— satisfactory; red—unsatisfactory; dark red—critical.

The matrix allows for the results of comparative assessment of occupational injury risks at different company enterprises to be visualised and primary measures for their reduction to be determined [32–34].

Figure 10 shows the matrix of relative change in injury risk rates for the mines of the Kirov branch of the "Apatit" company. The results of the analysis and the calculated average values of the changes in injury risk rates over the decade make it possible to assess the occupational safety measures in their entirety.

**Figure 10.** Matrix of the relative change in injury risk rates at the mines of the Kirov branch of "Apatit", JSC.

> Figure 11 shows the "Matrix of changes in occupational injury risk levels over a 10-year period at the mines of the Kirov branch of "Apatit", JSC".

**Figure 11.** Matrix of changes in occupational injury risk levels over a 10-year period at the mines of the Kirov branch of "Apatit", JSC.

As shown in Figure 11, over the last decade, labor safety conditions pertaining to the occupational injury risks at the Kirov mine were satisfactory; at the Rasvumchorr mine—unsatisfactory; at the East mine—critical; at the Central mine—between satisfactory and unsatisfactory.

The analysis provided allows for the assessment of labor safety conditions pertaining to occupational injury risks both over the last 10 years and during the current period of enterprise operation [35,36].

The assessment makes it possible to determine the priority avenues for reducing injury risk and improving occupational safety.

In conclusion, it should be noted that the article advocates the methodology of identifying the enterprise with higher occupational injury rate in comparison with others within the company as a whole based on the comparative analysis of the occupational injury rates at specific enterprises and companies including these enterprises. The proposed methodology allows companies to identify the priority directions for improving occupational safety, which will be targeted at specific enterprises.

For further research, it is useful to develop software to implement the proposed algorithm for identifying the priority areas for reducing occupational injury rates.
