Systematic treatment of circular logics in a fault tree analysis

An occurrence of a circular logic (CL) has been a problematic issue in a fault tree analysis (FTA). A variety of methods have been developed to solve and/or to treat the CL in a fault tree (FT). The CL may be generated if a system is finally supported by itself in a FT structure. The circulation of supporting relations among several systems can result in such a self-supporting relation of a system. The present article suggests a treatment method of the CL. The main idea to treat a CL is to use the initial condition of a system before its failure. A decision rule for two types of CLs is introduced to remove or break CLs depending on the initial conditions of a system. It has been shown that a CL can be properly handled through real examples of CL from a Probabilistic Safety Analysis (PSA). In addition, an algorithm is proposed to automatically treat the CLs for complex FT containing numerous CLs.