Simulation‐Based Excursion Statistics

Failure of an engineered system is typically associated with extremes in properties and/or loads characterizing the system. Since detailed field studies are usually unavailable, system properties are best modeled as random functions during the design or analysis process. To assess system reliability, the challenge is to establish relationships between parameters of the random function model and occurrence of threshold excursions or extremes. This paper estimates level excursion statistics of the two‐dimensional Gauss‐Markov model through simulations of an associated local average process. Among the statistics obtained are the mean number of excursions, their areas, and a new cluster measure that reflects the spatial distribution of the excursion regions. Motivated by the lack of analytical results for processes that are not mean‐square differentiable and by the limitation of the few available theories to high threshold levels, the methodology yields empirical results that can be used directly in reliability analyses and that can be easily extended to higher dimensions and nonstandard excursion measures.