Development of an analytical method to break logical loops at the system level

Logical loops or circular logics are interpreted as circular supporting relations among systems or their fault trees. The logical loops are located in the merged fault tree that is created by combining the system fault trees. The inconsistent manual breaking of the logical loops could be one of the major sources of the uncertainty in the fault tree analysis. This paper presents an analytical method to break the logical loops at the system level. The analytical solution at the system level is obtained in a mathematical way without an actual manipulation of the fault tree. Then, the actual manipulation of the fault tree in the analytical solution is performed and the resultant broken fault tree is solved by the fault tree quantifier. The analytical solution is consistent regardless of the knowledge, experiences, skills, and practices of the reliability specialist. The analytical solution of this method is easy to understand or trace how to break the logical loops. Reliability analysts and concerned people can communicate how to break the logical loops with the help of the mathematical expression of the analytical solution.