In this work, we explore how uncertainty in component dimensions affects final product tolerances for warheads. We focus on quantifying uncertainties arising from the machining process and examine how they influence the final weight and center of mass (COM). We begin by deriving analytical forms for the quantities of interest (QoI) based on the fundamentals of three-dimensional integration. The input parameter space is then characterized by assumed statistical distributions, determined by knowledge of the machining process. From here, a Monte Carlo (MC) approach is implemented using matlab's ndgrid to determine resulting distributions on the QoI. In doing so, we show the likelihood of meeting final product requirements, based on our knowledge of uncertainties in the warhead components. This technique is presented in a general form to provide a tool for quantifying uncertainty for warheads of varying geometries.