One of the most important features in science and practice for ensuring the machines and their components’ reliability is the use one of the mathematics’ areas - theory of probability and mathematical statistics. Most textbooks on the theory of probability and mathematical statistics deal with infinitely large aggregates. Since even the sample’s representativeness does not allow fully describing the entire aggregate, this should be taken into account at the stage of calculation and design. These facts led to the need for the transition from the sample data to the general aggregate data of the final volume. For this transition, we used the graphical method, which allows going from the sample, for example, with a volume of n=10-100, to the general aggregate Nc=103-106 using the extrapolation method.

Increasing the machines‘ reliability remains an urgent task of the world mechanical engineering, the solution of which is aimed at significantly reducing the number of the machines‘ critical, basic and other elements (parts) failures. To solve this problem, a need to move from the sample data to a general sub-total of a finite volume is indicated, the theoretical foundations for ensuring the machine parts‘ reliability for the assigned target life are formulated and the economic feasibility of increasing the machine parts‘ reliability is analyzed.

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