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Some Properties of Logic-Trees Containing Mutually-Exclusive Primary-Events

The paper analyzes logic-trees containing mutually exclusive primary events. A logic-tree is similar to a fault-tree, but can contain successes as well as failures. s-Coherent structure function and other basic terms are defined. Some useful properties of s-coherent structure functions are presented which include, as special cases, the previous results for logic-trees containing no mutually exclusive primary events. A method is provided for obtaining an effective upper bound to probability of occurrence of the top event for logic-trees with s-noncoherent structure functions.