Nuclear fusion, the process by which the Sun generates energy, is proposed as one solution to secure the future of global energy supply. If successful it will provide an unlimited source of clean energy. Probably the most promising approach to harnessing fusion for energy production is that of the Tokamak device, a magnetic confinement device of toroidal shape, here enormous magnetic fields are used to contain the 100 moC plasma. The first wall blanket of fusion devices (the protective shield on the inside of the reactor vessel) must withstand high heat fluxes, the power handling capabilities of such installations is a significant limiting factor in the future feasibility of thermonuclear fusion for energy production. This study presents a computational methodology for the evaluation of such designs in the presence of uncertainty in assembly tolerance. Methods for the analysis of first wall installations are outlined, including an initial Monte Carlo study of the first wall to develop understanding of the complex effects of tile misalignment. Approaches to local and global sensitivity analysis in order to rank the effects of particular dimensions of displacements, and the use of parallel coordinate plots to develop an intuitive method to visual sensitivity analysis in high dimensional domains.