Synthesis of Fault Trees: An Example of Noncoherence

The Lapp & Powers (L&P) fault-tree model of a nitric acid cooling process is explored to a greater level of depth than in the previous round-robin correspondence on the controversy over exclusive-or (XOR) gate G7 in the L&P fault tree. In this paper, the minimalized logic equations for success or failure of G7 are derived, and the subsystem reliability function is calculated. The subsystem reliability vs component reliability function is U-shaped; this is not an abnormality, but a result of the XOR failure logic. The overall system reliability vs component reliability function, however, is J-shaped. Some further comments are made on the relevance of this problem to the study of s-noncoherent and fail-safe systems.