Coherency of fault trees; Coherent and non-coherent fault trees

Fault trees are classified according to their logic function. If during fault tree construction only AND gates and OR gates are used, the resulting fault tree is defined as coherent. If NOT logic is used or directly implied, the resulting fault tree is non-coherent.

Analysis of non-coherent fault trees using ternary decision diagrams, by Remenyte-Prescott, Rasa Andrews, J.D.

Fault tree structures can be categorised as either coherent or non-coherent. If during fault tree construction the failure logic is restricted to the use of the AND gate and the OR gate the fault tree is said to be coherent If however, the NOT gate is used or directly implied, the fault tree can be non-coherent. A more precise definition of coherency can be obtained by considering the structure function of the fault tree [2].

Non-coherent Fault Tree Analysis, by Sally Chdstian Beeson

Many analysts have heard the rule about avoiding, as much as possible, the use of the Boolean operator NOT for constructing fault trees (FTs) in system safety and reliability assessments. As we know, the "NOT" operator applied to an event produces the negated or complementary event (i.e., the negated event probability is one minus the probability of the original event). The existence of negated events in an FT makes its logic "non-coherent," a coined term that is by no means a misnomer. As an anecdotal reference, my personal experience in dealing with non-coherent FTs has been misleading so far (i.e., "giving wrong ideas," as defined in the Oxford English Dictionary).

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