The problem of calculating the probability of first-passage failure, Pf, is considered, for systems responding to a short pulse of nonstationary random excitation. It is shown, by an analysis based on the “in and exclusion” series, that, under certain conditions, Pf tends to Pf*, the probability calculated by assuming Poisson distributed barrier crossings, as the barrier height, b, tends to infinity. The first three terms in the series solution provide bounds to Pf which converge when b is large. Methods of estimating Pf from these terms are presented which are useful even when the series is divergent. The theory is illustrated by numerical results relating to a linear oscillator excited by modulated white noise.

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