Engineering analysis with probability boxes: A review on computational methods - Faes, Matthias G.R.; Daub, Marco; Marelli, Stefano; Patelli, Edoardo; Beer, Michael (Structural safety, 2021)
•Imprecise probabilities allow for explicitly taking epistemic uncertainty into account.•P-boxes are of interest for engineering analysis due to their mathematical straightforward description.•An overview of methods for construction of p-boxes based on available information is given.•The state-of-the-art in propagation schemes for p-boxes is discussed. 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.