The article deals with methods of forecasting the level of aviation safety operation of aircraft systems on the basis of methods of evaluation the risks of negative situations as a consequence of a functional loss of initial properties of the system with critical violations of standard modes of the aircraft. Mathematical Models of Risks as a Danger Measure of Discrete Random Events in Aviation Systems are presented. Technological Schemes and Structure of Risk Control Procedures without the Probability are illustrated as Methods of Risk Management System in Civil Aviation. The assessment of the level of safety and quality and management of aircraft, made not only from the standpoint of reliability (quality and consumer properties), but also from the position of ICAO on the basis of a risk-based approach. According to ICAO, the security assessment is performed by comparing the calculated risk with an acceptable level. The approach justifies the use of qualitative evaluation techniques safety in the forms of proactive forecasted and predictive risk management adverse impacts to aviation operations of various kinds, including the space sector and nuclear energy. However, for the events such as accidents and disasters, accidents with the aircraft, fighters in a training flight, during the preparation of the pilots on the training aircraft, etc. there is no required statistics. Density of probability distribution (p. d. f.) of these events are only hypothetical, unknown with "hard tails" that completely eliminates the application of methods of confidence intervals in the traditional approaches to the assessment of safety in the form of the probability analysis.