Use the Poisson approximation to estimate the probability of firstpassage failure of a linear oscillator excited by stationary, Gaussian, white noise that is mean-zero and has autospectral density S_{0} . The oscillator has resonant frequency \omega _{0} and damping \zeta =0.01 , and failure occurs if X(t) exceeds the level 4\sigma _{stat}=4(\pi S_{0})^{1/2}/(2m^{2}\zeta \omega ^{3}_{0})^{1/2} within the time interval 0\leq \omega _{0} t\leq 250 .