Approximate Solution of First-Passage Problem

by Mircea Grigoriu, (M.ASCE), Assoc. Prof. of Civ. Engrg.; Cornell Univ., Ithaca, N.Y.,

Serial Information: Journal of the Engineering Mechanics Division, 1982, Vol. 108, Issue 5, Pg. 991-999

Document Type: Journal Paper


The first-passage time probability is approximated for Markovian processes of diffusion type from the mean crossing rate of random sequences or moving averages obtained from these processes by sampling or averaging. Simple rules are developed for selecting sampling intervals and averaging periods. The approach is applied with satisfactory results to the analysis of the reliability of a brittle prismatic bar, with random strength, loaded axially.

Subject Headings: Markov process | Axial loads | Brittleness | Bars (structure) | Moving loads

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