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Unavailability or Unreliability of a system can be found with a given error-bound by a proper approximate fault-tree analysis. In essence: Using a given maximum error, the set of mincuts is reduced, and the rest of the mincuts are processed such that at the end an approximate value of system unavailability or unreliability is found, which is too high by at most the given maximum error. Finally, it is discussed how to combine this new method with the well-known method of using Bonferroni inequalities. For practical work the results of this paper are summarized in an algorithm.