Analysis of the aviation safety management system by fractal and statistical tools

World civil aviation is an open-source system that is affected by a large number of related and non-related factors. Aviation safety is one of the prioritized directions in the industry. Its managerial decision-making is primarily based on a versatile analysis of security data in which the choice of the appropriate mathematical apparatus is fundamental. This article suggests applying fractal-statistical analysis to evaluate the aviation safety management system in terms of determining the random distribution of quantitative dynamics of aircraft crashes with lethal consequences in the period from 1946 to 2017. This allows us to verify the adequacy of probabilistic approaches appliance in analyzing the dynamics of aviation disasters. The results of research carried out on the basis of the Hurst exponent have allowed us to conclude that the dynamics of aviation disasters is characterized by the effect of "spatial memory". In other words, these are "hidden laws" which further investigation can become an effective tool for the development of proactive methods in managing aviation safety.