To the question of establishing safety coefficient and assurance coefficient at a given probability of non-destruction of load-bearing structures
Ensuring high reliability of unique high-critical products at the design stage is an actual task that the aerospace industry faces. For high reliability indicators, at the design stage, it is necessary to ensure the basic property of the product - its strength, with a high probability of non-destruction. It is provided by introducing the corresponding coefficients - «safety coefficient» and «margin of safety» into the strength calculations. The necessity in these coefficients is based on the spread of values of external loading factors: magnitude of forces, combination of forces, kind of actions, place of connection, etc. In this case, the safety coefficient is related to external factors. The margin of safety refers to internal factors: the spread of the mechanical characteristics of the product material, the spread of the geometric dimensions of the product, etc. To determine, with a given probability, the safety coefficient and margin of safety, it is necessary to know their dependence on the combination of spread of external and internal factors. The purpose of this work is to determine the mathematical connection between the internal factors of the spread and the safety coefficient, external factors of the spread and the margin of safety, the combination of these factors and the probability of non-destruction of structures. In this work the values of internal and external factors, which affect the strength and probability of non-destruction of the product and have the boundaries of the spread of their values, using the tools of probability theories, were characterized as random variables, the values of which are determined by the distribution density, expected value and variance. I this work there was found a high dependence of the product strength on the spread of its geometric characteristics and tools were defined to determine the total spread of the values of the main strength characteristics of the product with a given probability of non-destruction. The practical significance of the results of this work can be achieved in the aerospace industry, in particular, at the design stage of unique high-critical products.