Analytical justification of formulas for calculating the probability of failure-free operation for simple reliability models

In the majority of works connected with research of reliability of production and other technical systems the Kolmogorov axiomatics is applied. The corresponding analytical apparatus allows to solve problems of maximization of probability of performance of production tasks (for example, daily schedule of steel smelting or monthly production plan). Evaluation of reliability of both production and information systems is a mandatory procedure in their design and is based on the construction of a special structural scheme, called the system model for calculating its reliability. It should be noted that Kolmogorov’s axioms are formulated for a system consisting of two elements. The corresponding graphical explanation of axiom equity is based on an imaginary experiment on a random drop of a certain point on a unit square, inside of which there are two intersectingcircles whose planes are proportional to the probability of reliable operation of the corresponding elements. But there is no mention that the centers of circles should be at a certain distance from each other. In this paper, for the known Kolmogorov axioms underlying the classical probability theory, their analytical conclusion is given.