Aleatory and epistemic uncertainty in reliability analysis

In engineering applications, aleatory and epistemic uncertainties often coexist and interact. Therefore, accurately modeling these two types of uncertainty is critical for reliability analysis and uncertainty-aware decision making. This is for instance the case when quantifying failure probabilities of engineering structures under consideration of incomplete, insufficient, imperfect, or imprecise data or knowledge. Indeed, in such a case, the failure probability can at best be described using set-theoretical or Bayesian descriptors, rather than as a crisp number to explicitly acknowledge this epistemic uncertainty. However, despite this problem being well-described in theory, we observe that there still exists a gap between the theoretical developments on the one hand, and practical engineering applications of the uncertainty modeling approaches on the other. More precisely, even though the treatment of aleatory and epistemic uncertainty is well understood, they are often still mixed implicitly, or even explicitly in engineering calculations. Therefore, this paper provides a practical engineering guide that should help select the appropriate modeling framework, be it p-boxes, fuzzy probability models, or hierarchical probability approaches, when faced with problems that are affected by both aleatory and epistemic uncertainty. By assessing the type and extent of the information and the purpose of the analysis, this work provides specific recommendations for choosing appropriate modeling methods and presents a comprehensive analysis of failure probability. Additionally, this work highlights the importance of sensitivity analysis in identifying the key parameters that most influence the failure probability. This focus enables engineers to prioritize target data collection, thereby reducing epistemic uncertainty and enhancing the credibility of reliability assessment.