The probabilistic idea for the structure-function of a coherent system is suggested in the literature‎. ‎In this paper‎, ‎a primary model for this idea is defined‎. ‎This model leads to an extension of the class of coherent systems with binary (deterministic) structure functions‎. ‎Also‎, ‎in the stochastic comparison of the coherent systems with probabilistic structure functions‎, ‎it is shown that the concept of survival signature can successfully be used in this model‎. ‎‎T‎he well-known idea of the system signature is not usable here‎.

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