Highly exothermic catalytic reactions are often carried out in fixed bed, multi-tubular reactors that use a graduated catalyst activity profile. By increasing the effective catalytic activity in zones along the axial coordinate, the decreasing driving force that occurs as reactants are consumed can be compensated by increasing catalytic activity. This not only helps balance the heat generation rate along the reactor with the heat removal capabilities but it allows the attainment of very high conversion of one or more reagents while maintaining high reactor productivity. Partial oxidation reactions often use such strategies to manage the heat of reaction while minimizing the amount of recycle required. Industrial examples of such processes include ethylene oxychlorination to 1, 2-dichloroethane, propylene oxidation to acrylic acid and ortho-xylene oxidation to phthalic anhydride. Lower activity zones of catalyst are often created by diluting active catalyst pills with similar-sized pills of inert materials. This avoids the need to develop several catalyst formulations for a single process and allows fine-tuning of catalyst zoning profiles. However, loading a mixture of active and inert pills into a reactor tube is an inherently statistical process, which produces non-uniform activity profiles. The effect of this statistical non-uniformity has been studied for the case where tubes are loaded from catalyst drums - an essentially infinite reservoir, but not for the case where the correct amounts of catalyst and diluent are pre-weighed for each tube before loading. This method ensures the total number of active pills in the diluted zone is always correct but it does not eliminate the random axial activity variability that is inherent in sampling from mixtures of active and inert pills. When loading a reactor tube from a pre-weighed single tube aliquot, the reservoir is finite; the loading process is a series of Bernoulli trials without replacement and the statistics of loading are described by the hypergeometric distribution. We have modeled the behavior of reactor tubes loaded in this way for tube to pill diameter ratios (N) between 3 and 10, which covers the typical range of commercial practice for such reactor systems. While the total number of active pills is always correct for this type of reactor tube, the statistical variability in the axial activity profile can cause significant numbers of tubes to run away, despite the fact that the tube would be stable with a flat activity profile. This effect is exacerbated by smaller tube to particle ratios (N values) and greater extents of catalyst dilution. While this loading scheme is still subject to statistical variability, our results show that tubes loaded from pre-weighed, single tube aliquots perform significantly better than those loaded from an infinite reservoir (55 gallon drum for example) where the correct total activity is not guaranteed and the catalyst loading statistics are described by the binomial distribution. (C) 2012 Elsevier Ltd. All rights reserved.