Point-in-time and extreme-value probability simulation technique for engineering design Articles uri icon

publication date

  • March 2013

start page

  • 29

end page

  • 36


  • 41

International Standard Serial Number (ISSN)

  • 0167-4730


  • Engineering design of structural elements entails the satisfaction of different requirements during each of the phases that the structure undergoes: construction, service life and dismantling. Those requirements are settled in form of limit states, each of them with an associated probability of failure. Depending on the consequences of each failure, the acceptable probability varies and also the denomination of the limit state: ultimate, damage, serviceability, or operating stop. This distinction between limit states forces engineers to: (i) characterize both the point-in-time and extreme probability distributions of the random variables involved (agents), which are characterized independently, and (ii) use the appropriate distribution for each limit state depending on the failure consequences. This paper proposes a Monte Carlo simulation technique, which allows the generation of possible outcomes for agents holding the following conditions: (i) both the point-in-time and the extreme value distributions are appropriately reproduced within the simulation procedure, and (ii) it maintains the temporal dependence structure of the stochastic process. In addition, a graphical representation of both distributions on a compatible scale is given, this graph clarifies the link between point-in-time and extreme regimes and helps quantifying the degree of accuracy of the simulation results. In addition, new insights for the development of First-Order-Reliability methods (FORM) combining point-in-time and extreme distributions simultaneously are provided. The method is illustrated through several simulation examples from well-known distributions, whereas its skill over real data is shown using the significant wave height data record from a buoy located on the Northern Spanish coast.


  • extreme-value distribution; level iii method; mixture distribution; monte carlo simulation; point-in-time distribution; temporal autocorrelation