Statistical model for determining the quality of cargo work JSC "Uzbekistan Railways»

. The object of the study is the joint-stock company "Uzbekistan railways", engaged in the transportation of goods and passengers. The article uses statistical data that determine the quality of cargo work of “Uzbekistan railways” JSC as primary di gital data. Based on the results of the study, a mathematical model of the dynamics of operational indicators is constructed. The article proposes and justifies statistical methods of data processing of the transportation process. The statistical model is based on the most significant indicators of operating expenses of cargo transportation of JSC "Uzbekistan railways". Significant statistical indicators are cargo turnover; operating fleet of locomotives in freight traffic, locomotive performance; locomotive capacity; local speed; average weight of a freight train; locomotive downtime under loading, unloading; downtime at a technical station; loading volume. The model will significantly improve the quality of management decisions made by the management of the relevant structures.


Introduction
In the Republic of Uzbekistan, large-scale work is being carried out to organize an effective transport system that meets the needs of the economy and the population in transport services by all means of transport. Currently, the spatial connectivity of all regions of the country has been ensured, structural reforms have been carried out in the field of passenger and cargo road and air transport, and conditions have been created for active and effective integration into the global transport space.
At the same time, the transport system of Uzbekistan must solve a number of serious problems that reduce the efficiency of its activities. This will require serious institutional changes aimed at improving the country's transport policy, ensuring a sharp increase in the quality and volume of passenger and cargo transportation, reducing their cost to consumers, increasing the volume of cargo transit through Uzbekistan and forming a competitive market for transport and logistics services, improving the level of safety, environmental friendliness and innovation of all types of transport. In our opinion, the digitalization of the economy of the Republic of Uzbekistan determines the need for the formation of an intelligent transport system in JSC "Uzbekistan Railways".
In order to further improve the transport system of Uzbekistan, provide affordable and high-quality transport services for businesses and the public, and increase the competitiveness of the country's transport sector, it is necessary to actively introduce innovations, intelligent transport systems, and advanced information and communication technologies into the transport sector. The results of statistical digital data related to freight transport primarily characterize the efficiency of freight work on railway transport. The applied results of the research, based on the data of the digital economy, are considered in this article. The issues of model building operational performance of the railway system was investigated Wroblewski I. P., Basharina, O. Yu., Bazilevsky, M. P., Noskov S. I., and more others. Intelligent transport systems use economic, statistical and mathematical methods as the main research methods, and a mathematical model of the object or process under study is constructed. The paper uses as primary digital data -operational indicators that determine the quality of cargo work of JSC "Uzbekistan Railways" and builds a mathematical model of the dynamics of operational indicators. In the works of these authors, this evidence-based conclusions about the need to build a regression model for the dynamics of performance indicators of railway transport.

Analysis and results
In our research, based on the research of the above-mentioned authors, we offer our own methodological approach to the development of an appropriate mathematical model of an intelligent transport system. We define the effective indexes -highlight weekend performance (group Y). the control factors (group X); and characteristics reflecting the state of the "external environment", in which operational regulation at the local level (group Z). Performance indicators that determine the quality and specificity of freight transportation JSC "Uzbekistan Railways" presented in the Table 1. As shown in Table 1, the two groups of indicators include operational and control factors. The first group "Operational indicators" includes indicators related to the main transportation activities of railway transport. These indicators characterize the volumetric and qualitative performance data of the proposed model. The most important volume indicator is cargo turnover and cargo loading. From a number of qualitative indicators, the model includes locomotive performance and car downtime.
The second group of indicators included in the model are control factors that directly affect the volume of cargo transportation.
To study the dependence of the cargo turnover indicator on various factors-signs, as the analysis showed, it is optimal to use dynamics series. The dependence of the indicators was studied by us for 2011-2020. As the initial data, we used the data of the statistical reports of JSC "Uzbekistan Railways" on the volume and quality indicators of cargo turnover, grouped as arguments-factors in Table 1. To obtain an economic model of the forecasting process under the EXCEL program on the PC, calculations were performed and the corresponding results were obtained.
The mathematical problem is formulated as follows: it is required to find a functional expression of the relationship between the phenomenon and the factors that determine them, i.e., the search for a function: (1) where: f-is the function of the relationship of indicators; F1,F2,..., Fn -factor indicators.

Discussion regression results
The most important effective factor affecting the level of costs is the cargo turnover indicator. It is he who makes it possible to identify the factors-signs, so that it is possible to quickly respond to the changing working conditions of JSC "Uzbekistan Railways".
The main functions considered by us in the selection of the analytical expression were calculated by the types of connection: logarithmic power, rectilinear, hyperbolic, and the equation of the models of interdependence is compiled for the enlarged indicators [1][2][3][4][5].
The most reliable predictive figures are obtained when selecting a relationship based on the multiple correlation coefficients, the F value, and the approximation error in % for the rectilinear type of relationship. The logical analysis made it possible to link the volume and financial indicators and determine the form of communication.
As an example of the calculation of a one-factor model, the data of attributes-factors that affect the volume of cargo turnover-are taken. The initial data is presented in Table 2. The characteristics of one-factor models of the dependence of financial indicators on the volume of products produced are presented in Table 3. The data shown in Table 2 contains information in dynamics for 10 years, including 2011-2020. The one-factor model takes into account two volume and quality indicators that directly affect the operational cargo turnover, which tends to decrease from 21076.1 million tons.km in 2012 to 17697.6 million tons.km in 2016. The main reasons for this decrease are a decrease in the operating fleet of locomotives, the wear coefficient of which is more than 65% and a decrease in demand for rail transportation due to the choice of potential customers for transportation by road. However, starting from 2017 to 2020, there is an increase in the operational cargo turnover to 21418.8 million tons.km. The dynamics of changes in indicators is associated with an increase in the performance of locomotives. Based on the data in Table 1, we have constructed a one-factor model of the dependence of locomotive performance and available fleet on operational cargo turnover [6][7][8][9][10][11]. The characteristics of the choice of the form of communication for constructing a one-factor model of the dependence of the operational cargo turnover on the qualitative indicators of cargo transportation are presented in Table 3.
An equation corresponding to a higher value of the coefficient of determination is used if it does not contradict the economic meaning. In the case of a slight improvement in the model with a non-linear form, preference is given to the simplest and most convenient in calculations.  Table 3, we obtain that the largest coefficient of determination corresponds to the equation of a polynomial of the 2nd degree. The nonlinear function is accepted in the case of a significant significance of the nonlinear dependence, which is estimated as the difference between the largest coefficient of determination and the coefficient of determination of the linear function. If the difference does not exceed 0.1, the nonlinearity can be considered insignificant [12][13][14][15][16][17][18][19][20].
According to the analysis, the difference is 0.817 -0.786 = 0.031, i.e. < 0.1. Thus, the nonlinearity can be considered insignificant, which gives grounds for using a linear function as the main one that most fully describes the relationship of indicators.
The function can be represented in the form of an analytical expression: Y=16490.64+848.72* X After selecting the dependence on the value of the coefficient of determination, an economic assessment of the proposed equation was carried out. The linear relationship does not contradict the economic essence of the studied indicators, with an increase in the factorial attribute, a tendency to increase the effective attribute is revealed.
The dependence of economic phenomena on a large number of random and non-random factors is one of the characteristic features, in particular, of the indicators under consideration. The level of indicators of an intelligent transport system is formed under the influence of a complex of interacting factors acting with different magnitudes. The specificity of correlations requires the inclusion of the most important and significant factors in the model [20][21][22][23][24][25][26].
The selection of factors, giving them numerical expressions, identifying the nature and degree of their influence on the value under study is carried out by constructing a model that allows you to determine the desired value. The analysis of the dependence of financial indicators on several factors is carried out after checking them for multicollinearity, i.e. for independence from each other. When selecting factors, a qualitative, theoretical analysis is performed with the simultaneous use of statistical and mathematical criteria. The most appropriate selection is in three stages. At the first stage -with a priori analysis -no special restrictions can be imposed on the factors included in their preliminary list, since various variants of the same factor meters can be included [1].
The study identified the following factors affecting the level of operational cargo turnover of the main activity of JSC "Uzbekiston Temir yillari": -cargo shipped, thousand tons; -static load of a freight car, tons/car; -simple under one freight operation at the station, hour; -average daily mileage of the locomotive, km/day. At the second stage, a comparative assessment and exclusion of some factors were carried out based on a combination of qualitative analysis with an analysis of paired correlation coefficients and an assessment of their materiality. To do this, a matrix of paired correlation coefficients is compiled, measuring the closeness of the linear relationship of each factor with the effective factor and with each of the other signs-factors. To compile the correlation matrix, a qualitative analysis of the listed factors was carried out to include them in further consideration. Based on the numerical values of the sample factors and the results of solving the paired regression equations, a matrix of paired correlation coefficients is compiled (Table 4). If the values of the paired correlation coefficients are more than 0.8-0.85, multivariate analysis is not possible due to the multicollinearity of the factors.
The results of the analysis of the matrix of Table 4 show that the following factors are multicollinear among themselves:  Operational cargo turnover million tons-km;  Average daily mileage of the locomotive, km / day. To solve the multiple regression equation from two multicollinear factors, the one with the greatest relationship to the resulting feature is taken.
The main indicator with which the freight turnover is linked is the operating fleet of locomotives and the performance of one locomotive [6].
At the third stage, the model is constructed taking into account the selected featuresfactors. Based on the obtained equations of models of the relationship of the studied indicators, we made a forecast of the operational cargo turnover of JSC " Uzbekistan Railways" for 2021-2022, shown in Table 5.  Table 5, the forecast of operational cargo turnover for 2021-2022 indicates an increase, and the indicator of the statistical load -cargo loading also tends to increase from 50.1 to 50.5 tons per freight car. At the same time, the performance of the freight car will also increase to 269.87 million tons.km.
The results of the calculations are clearly shown in Table 6 and Fig. 1. A clear increase in the forecast indicators of effective operational cargo turnover is shown in Fig. 1. The results (Fig. 1) of the forecast can be seen that the rate of Operating turnover of JSC "Uzbekistan Railways" on 2021-2022 years has a growth of 3.4%, the fleet of locomotives 3.1 %, statistical load of 0.8 %, the performance of the locomotive is designed according to the forecast data will increase 0.3 %.

Conclusion
The constructed model is an element of the intelligent transport information system of statistical accounting and will allow to generate effective and analytical data necessary for forecasting the cargo turnover of JSC "Uzbekistan Railways".
The model is nonlinear, essentially open and recursive, that is, allowing the search for a solution by successive, from equation to equation, and appropriate calculations. The process of multivariate forecasting consists in setting various values of external variables within a certain scenario and then calculating the corresponding values of internal variables using the model. In order to automate this process, the authors developed a computer version of the model.
The model can be effectively used both in the analysis of general patterns in the interaction of the selected variables, and for solving a wide range of tasks of short -and medium-term descriptive forecasting of operational performance indicators of JSC "Uzbekistan Railways". This will significantly improve the quality of management decisions made by the management of the relevant structures.