We consider in-depth mechanical, geometric, analytic models of assessment the reliability of systems based on the use of the scheme of cases, Euler-Venn diagrams, generating functions, state diagrams. The methods of qualitative and quantitative assessment of the reliability on the established time interval, based on structural reliability, the importance of a structural element, the sensitivity of the reliability of the system taking into account the duplication of most significant and unreliable elements. Common approaches are illustrated by solving problems of the analysis and synthesis of...