Investigation of Systems with Normally and Exponentially Distributed Random Parameters by the Method of “Golden” Binary Structuring

The binary structuring of CDF expands the range of characteristic points on the contours of the corresponding dependencies, which do not depend on the probability distribution law of random values. Modeling the differential spectra of the exponential distribution by the points of the “golden” division shows that the corresponding implementation is not unique. Many arbitrary relationships are based on the geometric mean, which significantly expands the possibilities of application for diagnosing complex systems of already developed optimization methods. Despite the universality of Gauss's law for diagnosing the reliability of systems, the two-parameter representation of the probability density function limits its application, as the height and width of the contour are interrelated, forcing to search for more complex models. This paper proposes one of the approaches to solving this problem by binary structuring of probability parameters according to the “golden” proportion.