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The paper is concerned with the analysis of fault trees and describes an algorithm for deriving a reduced Boolean sum-of-product (s-o-p) expression from a description of the structure. The algorithm was developed initially as an analytic procedure for combinational logic networks and employs a reverse Polish notation to describe the structure which is then converted to an equivalent s-o-p expression. This procedure is equally applicable to fault tree analysis but care must be exercised in interpreting the Boolean result as a probability relationship. This aspect is discussed and a simple test and modification procedure described, enabling the original Boolean s-o-p expression to be converted into an equivalent s-o-p expression which can be interpreted directly as a probability relationship.