Maintaining the capabilities of the nuclear weapons stockpile and performing the annual assessment for the stockpile’s certification involves a wide range of processes, technologies, and expertise. An important and valuable element helping to link those components is the quantification of margins and uncertainties (QMU) framework. In this book, the National Research Council evaluates: how the national security labs were using QMU, including any significant differences among the three labs; its use in the annual assessment; and, whether the applications of QMU to assess the proposed reliable replacement warhead (RRW) could reduce the likelihood of resuming underground nuclear testing. This book presents an assessment of each of these issues and includes findings and recommendations to help guide laboratory and NNSA implementation and development of the QMU framework. It also serves as a guide for congressional oversight of those activities.