The paper considers the fault tree evaluation using the list processing technique. A tree sequence is newly introduced as a representation of the fault tree; it represents completely the branching structure of the tree. The properties and algorithms concerning the tree sequence are indicated. A method for computing the probability of occurrence of the top event is presented, which is featured by the recursive implementation of partition and reduction of the fault tree, through the combined use of the reverse Polish sequence and the tree sequence. This method enables us to evaluate the fault tree containing not only common primary events but also mutually exclusive primary events. By this method we can obtain the results in reasonable computation time for a fairly large scale fault tree having a few hundred primary events. The method can also be used for sensitivity analysis.

Relations among three types of tree polynomials are clarified. A method for calculating those coefficients is given. Then introduced is an index of graph related to the coefficients. This index expresses to what an extent the given graph destroys spanning trees of the complete graph.