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In the introductory part, the history development is presented, and it points out the importance of using the Fault Tree Analysis - FTA method for analysis of the reliability and safety of technical systems. By analyzing a number of references related to the FTA method, the FTA methodology is established, and explanation of some steps by this method is given in this paper. As an example of the practical application of methods, the failure of the solar concentrators is analyzed.For the failure analysis of the considered device, it is necessary to know the structure, functioning, working conditions and all factors that have a greater or less influence on its reliability. Along with an explanation of certain parts of the fault tree, the estimation of the significance of certain events is done, and it is considered to be able to eliminate causes of failure or to minimize the consequences of failure.