Pipeline systems under thermal loads are frequently used in different industries, such as the power plants and petrochemicals. Unlike the analytical method of elastic center, which is capable to analyze only one branch of Pipeline with pipe members parallel to the coordinate system, the method of stiffness removes these limitations. In this article the stiffness method is introduced for the analysis of Pipeline systems. Based on this method, the piping system may include any number of piping braches. The straight pipe elements in the branch may have any general orientation and the bend elements may have any arbitrary angle. The computer program designed based on this method may compute the nodal displacements at the ends of the straight or bend elements and present three components for loads and three components for moments. Once the free-body diagram of each piping elements with nodal forces and moments are drawn, then the engineering codes are employed to design the piping system for safe operation.

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The traditional event tree analysis uses a single probability to represent each top event. However, it is unrealistic to evaluate the occurrence of each event by using a crisp value without considering the inherent uncertainty and imprecision a state has. The fuzzy set theory is universally applied to deal with this kind of phenomena. The main purpose of this study is to construct an easy method to evaluate human errors and integrate them into event tree analysis by using fuzzy concepts. A systematic fuzzy event tree analysis algorithm is developed to evaluate the risk of a largescale system. A practical example in of offshore oil Pipeline is used to demonstrate this procedure.