Methods of Analyzing Random Point Structures in Solving Some Applied Engineering Problems

The article describes a method to solving a practical engineering problem related to the process of reading of random structures using an integrator that can capture only a certain number of point objects. Methods to solving this problem are described, based on creating of efficient software tools that use branched analytical manipulations on a computer in their work. One of the ways to solve this problem is the creation and use of a specialized system that performs an analytical calculation of the volume of polyhedra in n-dimensional space. The second way is integration method using calculations with two free parameters. A number of exact analytical formulas have been found that can be directly used in various fields related to probability theory, mathematical statistics, queuing theory and others. The work demonstrates it is necessary to use a large set of software and mathematical tools in solving many engineering problems.