[en] The appropriate treatment of uncertainty is now widely recognized as an essential component of performance assessments (PAs) for complex systems. When viewed at a high-level, the uncertainty in such analyses can typically be partitioned into two types: (1) stochastic uncertainty, which arises because the system can behave in many different ways and is thus a property of the system itself, and (2) subjective uncertainty, which arises from a lack of knowledge about quantities that are believed to have (or, at least, are assumed to have) fixed values and is thus a property of the analysts carrying out the study. The 1996 PA for the Waste Isolation Pilot Plant (WIPP) carried out at Sandia National Laboratories (SNL) will be used to illustrate the treatment of these two types of uncertainty in a real analysis. In particular, this PA supported a compliance certification application (CCA) by the US Department of Energy (DOE) to the US Environmental Protection Agency (EPA) for the certification of the WIPP for the geologic disposal of transuranic waste. Insights on the conceptual and computational structure of PAs for complex systems gained from these and other analyses are being incorporated into a new software system under development at SNL to facilitate the performance of analyses that maintain a separation between stochastic and subjective uncertainty