Top-down Algorithm for Obtaining Prime Implicant Sets of Non-Coherent Fault Trees

An algorithm for finding all the prime implicant sets is given for non-coherent fault trees involving gates other than simple AND and OR, e.g., EOR and NOT. The sets are a generalization of min cut sets and can be used in quantitative and/or qualitative system reliability analysis. The algorithm is a top-down analysis and avoids sum of product expressions of top event, which usually involve a large number of terms. Each step of the algorithm is clearly defined and it is proven that all prime implicant sets can be obtained. The algorithm is efficient, and rather complicated trees can be handled manually.