First-Crossing of Second-Moment Variables

by Daniele Veneziano, (A.M.ASCE), Assoc. Prof.; Mass. Inst. of Tech., Cambridge, Mass.,

Serial Information: Journal of the Engineering Mechanics Division, 1979, Vol. 105, Issue 5, Pg. 747-759

Document Type: Journal Paper


The second-moment approach to safety is extended to cases when malperformance is modeled as a first-crossing event of a random sequence. For this purpose, one needs to calculate Tchebysheff's bounds to the probability that any component of a random vector with given mean value and covariance matrix exceeds a critical value. Theoretical results include improved Tchebysheff's bounds for the crossing probability of both stationary and nonstationary second-moment sequences. Numerical results are given in terms of neq, being the length of an equivalent uncorrelated stationary sequence with the same Tchebysheff bound.

Subject Headings: Probability | Safety | Vector analysis | Matrix (mathematics) | Numerical methods | Professional societies | Numerical models

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