This subject responds to the contemporary trend of changes from the deterministic approach to the fully probabilistic approach in the design and reliability of parts of machines, structures and systems in human society. This subject relates to theory of reliability, statics and probability. Important terms are random (stochastic) variables and their interpetations, identifications and ways of generation. Main focus is on the application of SBRA (Simulation-Based Reliability Assessment ) Method, i.e. application of the Monte Carlo (MC) Method, as a tool for fully probabilistic reliability assessment determination (i.e. specific applications in mechanics, technics, connection with another numerical methods, familiarization with application software etc.). In the introduction are explained the basic conceptions of the theory of probability, statistics, reliability, MC method, SBRA method and their new development tendencies "Integrated – fully probabilistic Design" (ID). Into ID, which can exert a direct influence of economy, ecology, politics etc., belongs Performance-Based Design (PBD), Life-Cycle Assessment (LCA), Risk Engineering (RE) etc. Acquired knowledge are needed for success scientific work, research, development and innovations in industry.