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In the field of designing power supply systems of open pits an important role is attributed to the problems of components reliability analysis, which can be solved by integrated application of different analysis methods for individual types of electrical equipment and network devices in power supply systems. The purpose of the work is to establish optimal parameters for an open-pit mine power supply at mining and processing complexes, and to conduct research that allows a technical and economic model of the system to be created. It has been established that mathematical statistics provides a number of methods for establishing the homogeneity (or heterogeneity) of the population of random variable values. When analyzing the data of failure statistics of electrical equipment, the method of comparative estimate of two sample averages (compared to the method of comparing the empirical distribution with the normal distribution or the moving average method) is the most acceptable. The paper presents accident rates of electrical equipment of open-pit substations and network devices of the quarry processed on the basis of data, also presents the relationship between the reliability of the circuit and its elements and shows the influence of protection reliability on the reliability of the circuit. Methods of optimizing open-pit power supply systems are presented, which consist in the use of first-order gradient methods, second-order methods or the so-called quadratic optimization methods, and random search methods. A group of gradient methods is the most widespread for solving nonlinear programming problems, among which the method of steepest descent should be considered primarily. The combination of random search with the penalty function method makes it possible to determine conditional extrema for the problem of optimizing the electrical grid and system operation mode. The method of random descent, which consists in determining the minimum of the target function according to an appropriate algorithm, is also considered, in which the direction of motion is generally given by a random vector uniformly distributed over a hyposphere.

The calculation accuracy and efficiency of reliability analysis of prefabricated box culvert components are studied using the probability density evolution method based on the actual project. Firstly, the function of prefabricated box culvert is established, the generalized probability density evolution equation of the function is derived, and the finite difference method is used to solve the problem. Secondly, the probability density function is integrated to get the failure probability of components, and then the corresponding reliability index is obtained. Finally, it is compared with Monte Carlo method to analyze the applicability of probability density evolution method. The results show that: in the process of solving the reliability of prefabricated box culvert components, the probability density evolution method fully considers the randomness of component parameters and the probability relationship between sample points based on the relationship between physical system and stochastic system. Compared with Monte Carlo method- probability density evolution method can avoid random convergence effectively, and improve the accuracy and efficiency of calculation under the premise of guaranteeing the unique result. [ABSTRACT FROM AUTHOR]