A Monte Carlo framework for probabilistic analysis and variance decomposition with distribution parameter uncertainty

Probabilistic methods are used with modeling and simulation to predict variation in system performance and assess risk due to randomness in model inputs such as material properties, loads, and boundary conditions. It is common practice to assume that the input distributions are known. However, this discounts the epistemic uncertainty in the values of the distribution parameters, which can be attributed to the availability of limited data to define the input distributions. This paper proposes a Monte Carlo framework for unified treatment of both aleatory and epistemic uncertainty types when assessing system performance and risk. A Bayesian philosophy is adopted, whereby epistemic uncertainty is characterized using probability theory. Several computational approaches are outlined for propagation and sensitivity analysis with distribution parameter uncertainty. As a result of the outlined framework, the overall influence of epistemic uncertainties can be quantified in terms of confidence bounds on statistical quantities such as failure probability, and the relative influence of each source of epistemic uncertainty is quantified using variance decomposition. The proposed methods are demonstrated using both an analytical example and a fatigue crack growth analysis.