An Algorithm for Obtaining Simplified Prime Implicant Sets in Fault-Tree and Event-Tree Analysis

Some fault trees or event trees use NOT logic in expressing an accident sequence. The number of prime implicant sets (PIS), a generalization of a minimal cut set and includes logical NOT as well as AND and OR, is apt to exceed general computer capacity. In order to deal with this problem, this paper assumes that component failure probability is far smaller than component success probability. Three steps are developed to delete certain sets of basic events from the fault tree of an accident sequence so as to obtain upper side approximate probability calculations and this with the number of PISs enumerated reduced to a practical level in most cases. Asymptotic convergence is proved and numerical examples are provided.