Copulas Theory for Probabilistic Assessment: Overview with Application to Airplane Performance Analysis

The high degree of complexity and uncertainty associated with aerospace engineering applications has driven systems analysts toward the use of probabilistic and statistical analysis tools in order to understand and design for that uncertainty. Common themes in aerospace applications of probabilistic theory include the assumed independence of random variables and the arbitrary or unjustified use of certain probability distributions to represent random variables. These incorrect assumptions are often unknowingly used in systems analysis and can lead to inaccuracies in uncertainty quantification, poor decision making, and flawed designs. Copulas theory can be used in conjunction with the inversion method to mitigate both of these concerns while improving the accuracy of probabilistic assessments and enabling decision makers to better represent the uncertainty associated with the problem at hand. This paper provides a basic introduction of copulas to the aerospace audience with a focus on the needs of the practitioner. We provide a method for the selection of copulas and also demonstrate where copulas can be applied through three representative applications of copulas in a canonical airplane performance analysis problem.