This paper refers to the numerical analyses of approximating random functions by canonical expansion approximations. Different formulations for calculating the resulting mean square error estimates are included. The proposed approximation is then adapted to obtain threshold crossing information of systems with separable non-stationary Gaussian random inputs. It is assumed that the simulation of the input environment requires the system analyses for different input models, as it, often occurs in the study of aerostructures with atmospheric turbulence disturbances. The illustrative example refers to a single-degree-of-freedom system with a time-variable damping parameter. When compared to another direct numerical approach the results of E[N+(0, 1)] show excellent agreement with a significant saving in machine time