Dynamic bounds coupled with Monte Carlo simulations

M. Rajabalinejad*, L.E. Meester, P.H.A.J.M. Van Gelder, J.K. Vrijling

*Corresponding author for this work

Research output: Contribution to journalArticleAcademicpeer-review

20 Citations (Scopus)


For the reliability analysis of engineering structures a variety of methods is known, of which Monte Carlo (MC) simulation is widely considered to be among the most robust and most generally applicable. To reduce simulation cost of the MC method, variance reduction methods are applied. This paper describes a method to reduce the simulation cost even further, while retaining the accuracy of Monte Carlo, by taking into account widely present monotonicity. For models exhibiting monotonic (decreasing or increasing) behavior, dynamic bounds (DB) are defined, which in a coupled Monte Carlo simulation are updated dynamically, resulting in a failure probability estimate, as well as a strict (non-probabilistic) upper and lower bounds. Accurate results are obtained at a much lower cost than an equivalent ordinary Monte Carlo simulation. In a two-dimensional and a four-dimensional numerical example, the cost reduction factors are 130 and 9, respectively, where the relative error is smaller than 5%. At higher accuracy levels, this factor increases, though this effect is expected to be smaller with increasing dimension. To show the application of DB method to real world problems, it is applied to a complex finite element model of a flood wall in New Orleans.

Original languageEnglish
Pages (from-to)278-285
Number of pages8
JournalReliability engineering & system safety
Issue number2
Publication statusPublished - Feb 2011
Externally publishedYes


  • Dynamic bounds
  • Monotone
  • Monotonic
  • Monte Carlo simulation
  • Reliability analysis
  • n/a OA procedure


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