[en] Computer codes, which transform a number of pseudoparticles through a simulated machine, form the backbone of accelerator design techniques. When minimization of beam loss within the machine is a primary design objective, it becomes necessary to consider beam behavior in detail, and questions of both the physics and computational aspects of the simulation are raised. Within the constraints of the former, the effectiveness of the latter can be increased for a given amount of computer resources by the use of statistical techniques. A statistical approach to determining the maximum beam size and hence required aperture of a machine is described and illustrated. The method draws upon statistical theory to treat the maximum radius attained by a finite group of particles passing through an accelerator as a statistical variable. Once the distribution of this variable is obtained, radius values can be found inside which a given percentage of the particles can be expected. Confidence bounds can be placed on these radii, and the results used to estimate the suitability of the accelerator apertures