Modeling and simulation activities used in engineering analysis and design are subject to a variety of different uncertainties. These include inherent variations in model input variables (aleatory uncertainties) as well as imprecise or limited information about model parameters (epistemic uncertainties). The difference is that the epistemic uncertainties have the potential to be reduced over time through collection of new data or model refinement. This paper proposes a variance decomposition approach for sensitivity analysis of models with inputs that are subject to both types of uncertainty. The approach is based on analysis of the contributions of epistemic uncertainty in model input variables or probability distribution parameters to the uncertainty in a statistical quantify of interest, such as a failure probability. It is shown that alternative approaches, such as those that do not distinguish between the different uncertainty types, can fail to identify the most important sources of reducible uncert...