Engineering analysis with probability boxes: a review on computational methods

Matthias G.R. Faes, Marco Daub, Stefano Marelli, Edoardo Patelli, Michael Beer

Research output: Contribution to journalArticlepeer-review


The consideration of imprecise probability in engineering analysis to account for missing, vague or incomplete data in the description of model uncertainties is a fast-growing field of research. Probability-boxes (p-boxes) are of particular interest in an engineering context, since they offer a mathematically straightforward description of imprecise probabilities, as well as allow for an intuitive visualisation. In essence, p-boxes are defined via lower and upper bounds on the cumulative distribution function of a random variable whose exact probability distribution is unknown. However, the propagation of p-boxes on model inputs towards bounds on probabilistic measures describing the uncertainty on the model responses is numerically still very demanding, and hence is subject of intensive research. In order to provide an overview on the available methods, this paper gives a state-of-the art review for the modelling and propagation of p-boxes with a special focus on structural reliability analysis.
Original languageEnglish
Article number102092
Number of pages11
JournalStructural Safety
Early online date22 Jun 2021
Publication statusPublished - 30 Nov 2021


  • imprecise probability
  • literature review
  • P-boxes
  • reliability analysis
  • surrogate modelling


Dive into the research topics of 'Engineering analysis with probability boxes: a review on computational methods'. Together they form a unique fingerprint.

Cite this