The transition from the sample data to the total aggregate of the final volume and the analysis of this transition laws

Abstract

Abstract 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.