Safety Engineering and its branches are undetachable elements of any systematic process in which there is an interaction between human and machine. Also, developments in systems modeling and analysis methods have increased efficiency and maneuverability of safety engineering techniques. One of such methods which originates from modeling of discrete event systems is Petri net. These nets have various kinds with different capabilities. Hence, incorporating them in reliability and safety problems makes them more flexible. On the other hand, because of static nature of many failure an alysis methods and lack of dynamic techniques in safety science, utilizing dynamic tools such as Petri nets seems to be inevitable. In this thesis, we consider three goals. Firstly, proposing a fuzzy risk analysis method based on correspondence of Stochastic Petri nets and Markov Chai secondly, proposing a novel algorithm in order to determine firing sequences of Petri nets; and finally, implementing concept of counters from linear systems point of view in the field of sequential failure analysis. In the first goal, a novel ranking algorithm which is able to handle generalized trapezoidal fuzzy numbers was presented and its capabilities in covering drawbacks of existing approaches was proved. Then, on the basis of this algorithm and introduction of some efficient risk factors our novel dynamic risk analysis was proposed. In the second goal, according to lack of a documented method in determination of firing sequences leading to sequential failures, a set of algorithms were presented and their precision was analyzed. At the end in the third goal, using DIOID algebra we analyzed linear and nonlinear systems dominating connections in Petri nets and utilized its results in calculation of sequential failure probabilities. Computational results of this method demonstrated a high reduction in computation complexity which proves capability of this technique. It noteworthy to mention that the proposed algorithms in this research are comprehensive and can be used in other fields. Results of the proposed methods demonstrate precision, accuracy, and ease of use in contrast with the existing techniques.