The fact that not all coated fuel particles in a batch fail after the same irradiation history is due to manufacturing variations in values of individual particle parameters. Two methods of calculating the failure fraction as a function of burnup in terms of these statistical variations are discussed: (a) a random sampling of particles combined with a simple stress model, and (b) the convolution of the individual variations combined with an advanced stress model. These methods were applied to particles manufactured by two laboratories in support of the U.K. low-enriched fuel cycle high-temperature reactor design. Experimental values of variations in the following parameters were included: kernel diameter and porosity, thickness of buffer, seal, silicon carbide and inner and outer pyrocarbon layers (all assumed to be normally distributed), and the silicon carbide fracture stress (assumed to obey a Weibull distribution). It was concluded that the convolution approach was the more satisfactory method. The results enable one to identify which of the various parameters considered are the most worthwhile for manufacturers to put development effort into so as to reduce their variability. For the particles considered here, these are primarily silicon carbide fracture stress, followed by kernel porosity.