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Existing network connection reliability parameters can't measure the connection situation of only some terminals in a specified terminal-set. To solve this problem, a new network connection reliability parameter, k/N-terminal reliability, is put forward. It is defined as the probability that at least k terminals of a specified terminal-set N in the network G(V, E, Phi) will connect for a given period of time when used under specified operation conditions, where NsubeV and 2lesklesn. The exact algorithm based on inclusion-exclusion principle is also given. An example is used to illustrate the applicability of this new parameter and its algorithm.