On the Bound of First Excursion Probability

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Abstract
Because of its direct relation to the reliability or the safe performance of mechanical and structural systems subjected to random external disturbances, the bounding technique of the first excursion probability is studied. In particular, the lower bound of the probability proposed previously by one of the present authors is improved. Numerical examples indicate that the improvement is significant. The present method of improvement requires the knowledge of the joint density function of the random process at two arbitrary instants. Other than this, the method is universal; it can apply to stationary or nonstationary, Gaussian or non-Gaussian processes. General expressions for lower and upper bounds are also derived in this study and their potential usefulness is pointed out.

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