Upper and lower bounds are derived for the probability that a nonstationary process, not necessarily of white noise type, will cross given barriers in a specified time interval. As an example, the probability of failure of a structure with mechanical response represented by a damped oscillator of one degree of freedom, as a result of a nonstationary Gaussian input, is evaluated under the condition that the structure will fail if the absolute value of the displacement exceeds a critical value. Numerical results suggest that the present method estimates the probability in a narrow interval over a sufficiently wide range of probability values so that the method might be useful in reliability analysis. Applications to structures subject to earthquake accelerations are suggested.
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Masanobu Shinozuka (1964) studied this question.