The paper presents the origin, philosophy, characteristic features, and capacities of an innovative Petri-Nets-based method-Analysis of Topological Reliability of Digraphs (ATRD). It combines the capacities and compensates for the draw-backs of the techniques-Physical Modelling Graph and Petri Nets. Created as an alternative to the traditional Fault and Event Tree method, ATRD has qualities making possible its orientation to events-changes of the system state, as well as to processes-tracing the influence of these changes. Its capacities can be widened with the use of fuzzy rules, neural networks or physical models for obtaining parametric availability of the elements and for modelling possible operator's actions. This allows the integration of the ATRD method in the general scheme for prognosis and decision-making in complex system operation. In addition the unification of the identical elements models, modelling based on the technological criterion of success, treatment of the elements behaviour in terms of possibility and obtaining reliability measures for each element and system make the ATRD method easy for modelling, sensitive and prospective for the search of the balance between risk and safety in complex system use.