The Equivalence of Reliability Diagrams and Fault-Tree Analysis

Many practicing engineers model their systems using reliability diagrams, while others use fault-tree analysis. The theoretical equivalence of the two techniques is described. System reliability can be expressed in two ways: probability of success and probability of failure approach, in terms of the tie-sets (forward paths) of a reliability diagram. Similarly, one can write two other expressions in terms of the cut-sets of the system reliability diagram. If one uses the fault-tree analysis approach, the probability of failure is written in terms of element failures by applying the rules of symbolic logic (union and intersection). This equation is identical with the tie-set probability of failure equation. Also by applying DeMorgan's logic theorem to the fault-tree probability of the failure equation, one obtains the tie-set probability of success equation. Thus the two techniques are shown to be identical. The choice between the techniques is a matter of convenience and familiarity.