Research Article
Dec 1969
Upper Bound for Two-Sided Barrier Problem
Publication: Journal of the Engineering Mechanics Division
Volume 95, Issue 6
Abstract
An upper bound is derived for the probability that a random process X (t) will take values outside an interval [ – λ1 (t), λ2 (t) ] for 0 ≤ t ≤ T, in which λ1 (t) and λ2 (t) are nonnegative continuously differentiable curves. The random process is assumed to be separable, have mean zero, and to be mean square differentiable at least once. The upper bound is shown to be less than one previously obtained by Shinozuka and Yao. Under the additional assumption that X(t) is normal, expressions for the upper bound are found, and are shown to depend on the joint probability density of X(0), X(t), and X(t). In order to evaluate the expressions, the integral of a bivariate normal distribution must be evaluated. The results of computations for symmetric barriers [ λ1 (t) = λ2 (t) ] are shown, and conditions under which significant differences between the new upper bound and that previously derived can be expected are indicated. It is shown that significant improvements may result when stationary rather than transient random processes are considered.
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Published In
Journal of the Engineering Mechanics Division
Volume 95 • Issue 6 • December 1969
Pages: 1369 - 1378
Copyright
© 1969 American Society of Civil Engineers.
History
Published in print: Dec 1969
Published online: Feb 3, 2021
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Authors
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Arnold L. Sweet
Assoc. Prof. of Aeronautical, Astronautical and Engr. Sciences, Purdue Univ., Lafayette, Ind.
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