The computation of the probability of survival/failure of technical/economic structures and systems is based on an appropriate performance or so-called (limit) state function separating the safe and unsafe states in the space of random model parameters. Starting with the survival conditions, hence, the state equation and the condition for the admissibility of states, an optimizational representation of the state function can be given in terms of the minimum value function of a closely related minimization problem. Selecting a certain number of boundary points of the safe/unsafe domain, hence, on the limit state surface, the safe/unsafe domain is approximated by a convex polyhedron. This convex polyhedron is defined by the intersection of the half spaces in the parameter space generated by the tangent hyperplanes to the safe/unsafe domain at the selected boundary points on the limit state surface. The approximative probability functions are then defined by means of the resulting probabilistic linear constraints in the parameter space. After an appropriate transformation, the probability distribution of the parameter vector can be assumed to be normal with zero mean vector and unit covariance matrix. Working with separate linear constraints, approximation formulas for the probability of survival of the structure are obtained immediately. More exact approximations are obtained by considering joint probability constraints. In a second approximation step, these approximations can be evaluated by using probability inequalities and/or discretizations of the underlying probability distribution.