Guarantees and risks in the technical regulation of transport construction

. As a result of the analysis of the methods of quantitative and qualitative assessment of the degree of risk, the theoretical and probabilistic approach of Professor V.V. Stolyarov was chosen to assess technical and environmental risk, based on the probabilistic nature of the parameters studied, in relation to road facilities.The allocation of risks within functional subsystems makes it possible to more accurately determine the ways of risk management in practice. As a characteristic of the degree of danger of a road section, the total risk is used as a complex indicator that can occur on this section under the combined influence of all road parameters simultaneously. Along with the discussion of the concepts of risk, the concept of guarantee is introduced. The concepts of guarantees and risks are introduced on the basis of a random variable distribution graph using the example of a normal distribution. In addition to the technical component of the risk, its economic component is also considered.

Since the beginning of the 90s of the last century, various quality management systems have been actively implemented as an integral part of the administrative management of the enterprise.They stated an assessment of the risk of using substandard products, however, which was not paid attention to by specialists.In general, the quality management system is based on the principle of "universal minimization of variance".
At the same time, environmental management based on environmental risk assessment was introduced in legislative and regulatory and methodological documents of environmental protection.
However, risk management procedures gained revolutionary significance after the adoption of Federal Law No. 184 "On Technical Regulation".It stated the mandatory nature of technical regulations, taking into account the degree of risk of harm.The law declares the mandatory fulfillment of the minimum requirements for the safety of technical regulation facilities.
Such a new state of technical rationing based on risk management can be recognized as a new technical philosophy.
There is a departure from meeting the needs of the owner of the object (state, agency, monopoly) by integral (generalized reliability indicators, for example, service life or operating time for failure) to meeting the security needs of a particular consumer.At the same time, rationing is carried out according to established and ranked risk hazard factors [1,2,[6][7][8].
The thesis "Risk cannot be experienced" is true, the risk must be assessed (investigated).The risk cannot be tested for failure.
The results of the application of the new system of technical regulation include the concepts of "induced uniformity", "minimization of the coefficient of variation", compliance with the required level of responsibility and "shortened and thickened distribution tails", "decorrelation of the output parameter".
An important result was also a reduction in costs (by one, sometimes up to those orders) for obtaining and analyzing the required information to make a decision on comparing projects of specific objects of technical regulation.

Methods
From the point of view of mathematical statistics, risk can be understood as the ratio of the area of the "tail" of the histogram of the normal distribution, located in the boundaries between the critical value and three sigma, to the total area of the right or left histogram of the distribution, approximated by a normal or other law.If the analyzed numerical series contradicts the normal distribution, you can use its reduction to relative values (logarithm).
Statistical theory requires that frequency data satisfy three conditions: 1) the data should provide a sufficient number of cases or observations to demonstrate stability; 2) observations should be repeated in the aggregate of observations; 3) observations should be independent.
According to the decision of the Customs Union Commission No. 621 of April 7, 2011, the choice of forms and schemes of conformity assessment should be carried out taking into account the total risk from an unreliable conformity assessment and harm from the use of products that have passed the conformity assessment.
The choice of rationing methods for risk degrees is based on Fig. 1, taking into account the work of M.M.Bekmagambetov [2].
Comparison of real and critical distributions that do not contradict the normal law, when assessing risk, is recommended to be carried out by the tails of distributions -their visual illustration.
The analysis of Fig. 1 showed the variability (variability) of the distribution tails.The distribution tails can shorten, lengthen, thicken and lengthen.
A new criterion for analyzing the degree of risk in the form of the tail state of a normal distribution is proposed, as well as the following combinatorics of the states of changes in the tails of distributions of the form (a, b), where a = -1, or 0, or 1, b = -1, or 0, or 1.
-1 means a smaller state, 0 -keeping the same or average, 1 -increasing.
Example 2. Thickening and preserving the length for the tail of the normal distribution means (1, 0) -the degree of risk has become greater.
The test results are subject to a random distribution.In view of the action of random factors affecting the test results.In the road sector, the manufacture of each unit of production in a series or in a batch is also subject to a variety of random influences, therefore, as a rule, the output parameters of products also change randomly.
Since the parameters of product quality are important for the consumer, it becomes necessary to check the conformity of products with accepted quality standards.If in the conditions of single and small-scale production there is a possibility of 100% verification, then in the conditions of mass production such a possibility is so economically inefficient that it is not applied in practice.The most effective quantitative parameters of the quality level of products are the indicators of guarantee and risk.
The concepts of guarantees and risks are easy to understand by considering the distribution graph of a random variable.Let's consider these concepts using the example of a normal distribution.
Figure 2 shows a graph of the normal distribution of a conditional random variable In Fig. 2, the parameter measured during the tests is postponed along the abciss axis, and the number of tests in which the corresponding parameter value is obtained is postponed along the ordinate axis.The total number of tests in which the parameter value is obtained within the interval ab is called the statistical weight or simply the weight.It is clear that the weight is equal to the integral of the blackened area.
The absolute statistical weight in the interval ab is represented by an ordinary number, but it will clearly depend on the total number of tests, so in practice a relative statistical weight is used, determined by the formula , where ω is the relative weight of the interval ab; n is the number of tests within the interval ab; N is the total number of tests.
In the case of a continuous distribution of a random variable, the discrete numbers are replaced by the corresponding integrals: . Here in the numerator is an integral on the segment ab, and in the denominator is a complete integral over the entire domain of determining a random variable.
The concept of defining guarantees and risks follows from the above reasoning.Let's assume that the consumer of the product needs some parameter not to go beyond a certain value.For example, it did not exceed the specified value.Graphically, this can be depicted as follows (Fig. 3): The image in Fig. 3 is interpreted as follows: with the available distribution of a random variable, there is a guarantee that a single sample will have a parameter no more than A equal to the integral of the graph in the range from 0 to A. Accordingly, there is a risk that the parameter will exceed the permissible limit of A, which is equal to the integral in the range from A to ∞. Quantitatively , relative guarantees and risks are determined by the formulas: Guarantees: .From what has been said, it becomes clear that guarantees and risks are complementary values, i.e.
In general: Guarantees + Risks = full probability.Despite the fact that the above arguments are given for the case of guarantees not exceeding a given parameter, guarantees and risks are determined in exactly the same way for cases of not reducing the parameter below a certain limit.
All the above calculations are completely free to apply to any kind of distribution: exponential, hypergeometric, Weibula, etc.The differences will only be in the form of functions for calculating integrals.
As an assessment of the degree of risk (risk measure), you can use a mathematical expectation in the form of: . Such an assessment is used in cases when decisions are made based on averages, when uncertainty (stochasticity of the process) is reasonably or consciously ignored.
Another estimate is the variance of the distribution: . This risk assessment assesses the uncertainty of the process.As an assessment of the degree of risk, a measure of expected utility can be used: , -some real function.As an integral hazard characteristic, you can use the indicator of the total risk that occurs on a given section of the highway under the influence of all road parameters simultaneously if there are, for example, two reasons on the site that generate risky situations, each of which separately leads to a risk, respectively equal to and .V.V.Stolyarov, when considering the special case of the presence of two reasons on the site that generate risky situations, proposed the following formula for determining the total risk [2]: where r 1 and r 2 are the magnitude of the risk of each of the two causes, respectively; P 1 is the possible probability of a change in the magnitude of r 1 when exposed to r 2 (negative impact due to the reason generating r 2 ); P 2 is the possible probability of a change in the magnitude of r 2 when exposed to r 1 (negative impact due to the reason generating r 1 ).
In this case , the formula for determining the total risk has the form: . If there are reasons on a section of the highway that cause risk values: , the formula is used -1 once.For the first time, the formula calculates the total risk for any two risk values.Subsequent calculations are also carried out in accordance with arbitrary indexing of risk values.In this case , the formula will take the form: . Any sequence of addition of risk values leads to the same total risk, which, with an unlimited number of ri values (0≤ ri≤1), remains less than or equal to one.
1.The sources of risk during operation are the technical characteristics and operational condition of structural elements: the carriageway; edge strips, curbs and dividing strip; roadbed; artificial structures; means of traffic management; road fencing; structures of road service and road improvement; artificial lighting.
2. The main factors determining the possibility of risks on the highway during its operation are considered.
3. Operational measures are being developed, which should be aimed at compliance with the following basic principles to ensure the creation of safe conditions for the transportation of goods and passengers by road during their established service life: The concept of risk should be multidimensional, and its assessment largely depends on the information available during its assessment and measurement.
It is important to note that in addition to the technical component of the risk, its economic component is also considered.
The concept of risk will ensure the effectiveness of design, construction, repair, operation and planning of risk reduction works aimed at improving the reliability and economic efficiency of the operation of the highway and structures on them in terms of stricter requirements for safety, environmental and social acceptability.Using this technique, it is proposed to take into account the degree of influence of each by introducing weighting coefficients into the formula to determine the total risk as a complex indicator.
The results of the work of the risk assessment software package based on the calculation of the tail area of the normal distribution are shown in Fig. 4. In column A, the measurement (test) results are substituted -no more than 5000 values.
The border of guarantees and risk is inserted into the critical value cell (any value from minimum to maximum is possible).In the green cells, answers are given in the form of percentages of guarantees and risks.

Conclusion
As a result of the analysis of the methods of quantitative and qualitative assessment of the degree of risk, the theoretical and probabilistic approach of Professor V.V. Stolyarov was chosen to assess technical and environmental risk, based on the probabilistic nature of the parameters studied, in relation to road facilities.
An algorithm for the formation of risks and taking them into account when assigning the types of work performed during the operation of road facilities is proposed

Fig. 2 .
Fig. 2. Selection of risk assessment rationing methods Graph of the normal distribution of a random variable

Fig. 3
Fig. 3 Is the distribution of the areas of guarantees and risks, in the case of guaranteed not exceeding the permissible value of the parameter

Fig. 4
Fig.4 Results of the work of the risk assessment software package based on the calculation of the area of the "tail" of the normal distribution