**2. Materials and Methods**

Methods for selecting priority avenues for lowering the injury rates at the facilities of the Arctic circle are an important basis for occupational safety. The development of mineral resources of the Arctic zone has been a priority for Russia and the global community. The human factor becomes one of the main factors of efficiency in the extreme environmental conditions of the Arctic. When it comes to Russia, the problem is exacerbated by the fact that the vast and resource-filled territory of the Arctic zone is only populated by slightly over 2 million people, which necessitates attracting rotational workers from other regions.

The adverse environmental conditions of the Arctic zone, paired with the difficult labor conditions for the miners (such as polar nights, excessive noise and vibration levels and other), lead to the injury risks being higher compared to regions with more favorable conditions. In order to reduce the injury risks, the occupational health and safety systems at mining facilities need to be constantly improved upon, and the first step of this process is the assessment of labor safety conditions [20–22].

The results of the occupational safety assessment allow for the selection of priority directions for reducing the occupational injuries (Figure 4).

**Figure 4.** Algorithm for selecting priority avenues for reducing the injury rate.

The first step in the selection is to determine the risk structure (Figure 5). The overall risk—aside from its occupational component, which is determined by labor conditions— includes background risk, which is determined by the unfavorable ecological situation and the adverse environmental effects such as harsh climate conditions, high precipitation, low air temperatures, strong winds, polar nights, polar days, and lack of ultraviolet radiation.

**Figure 5.** Injury risk diagram for the Arctic region.

To calculate the overall risk of injuries in the Arctic regions of Russia, we used official statistical data [23]. Figure 6 illustrates the calculation results.

**Figure 6.** Overall injury risk for the Arctic zone.

In general, the injury rate in the Arctic zone displays a decade-long downward trend. The only outlier in this case is the Chukotka Autonomous District, where we see an increase of 22%.

Figure 6 shows that the linear correlation dependencies of injury rates on time are characterized by the correlation coefficient of over 0.75 and have individual regression coefficients that determine the trends in injury rates over the 10-year period. For each linear correlation dependence of the injury risk for the regions of the Arctic zone, the mean value (M) was calculated, which describes the central trend, and the standard error (SEM) indicating the accuracy of the average value calculation was computed.

Figure 7 shows the main causes of occupational accidents for the Arctic zone of Russia.

**Figure 7.** Causes of accidents for the Arctic zone.

As shown in Figure 7, the highest risk of accidents relates to poor management, violations of labor procedures as well as employees' misconduct and unsatisfactory maintenance of workplaces. The listed causes of accidents are organizational due to the insufficient professional training of employees, as well as their low motivation to follow the safety regulations at work.

At the core of the procedure for determining the risk structure lies the assumption that the overall injury risk is the result of the combined effects of two types of risk: the overall risk for the territories of the Arctic zone (*R*F.N.t.), which is calculated based on the average risk for Russia (*R*RF.av.), and the risk determined by the external factors, stemming from the territories themselves (*R*EXT.C.).

In turn, the overall injury risk for the mining enterprises (*R*M.I.t.) is calculated based on the value of *R*EXT.C. and the risk stemming from the individual company's operations (*R*I.A.). Risk analysis of the occupational injury rates at the mining enterprises pre-supposes that the risk structure for them is identical to the one for the corresponding territory.

The equations linking these risks are based on the addition law of probability and can be written as follows [24,25]:

$$R\_{\text{F.N.t.}} = R\_{\text{RF.av.}} + R\_{\text{EXT.C.}} - R\_{\text{RF.av.}} \cdot R\_{\text{EXT.C.}} \tag{1}$$

$$R\_{\rm M.I.t.=} = R\_{\rm EXT.C.} + R\_{\rm IA.} - R\_{\rm EXT.C.} \cdot R\_{\rm IA.} \tag{2}$$

Knowing the overall injury risks for a given territory (*R*F.N.t.), a given enterprise (*R*M.I.t.), and knowing the average risk for the Russian Federation (*R*RF.av.) makes it trivial to calculate the external risks for each territory (*R*EXT.C.), as well as the injury risks (*R*IA.).

Equation (1) makes it possible to represent the background injury risks for the separate territories as follows:

$$R\_{\text{EXT.C.}} = \left(R\_{\text{FN.t.}} - R\_{\text{RF.av.}}\right) / \left(1 - R\_{\text{RF.av.}}\right) \tag{3}$$

With the background risk value being known, the occupational risk for a particular enterprise (*R*I.A.) can be written as follows (Equation (4)):

$$R\_{\rm LA.} = (R\_{\rm ML.t.} - R\_{\rm EXT.C.}) / (1 - R\_{\rm EXT.C.}) \tag{4}$$

The *R*F.N.t., *R*RF.av., *R*M.I.t., and *R*I.A. risk values were determined based on the statistical data for each region for a given period, and then correlation and regression analysis was performed.
