In some multi-tubular fixed bed catalytic reactors, a graduated activity profile in the axial direction is created by loading several "zones" of catalyst, each with a different target catalytic activity. This is often achieved by diluting active catalyst pellets with inert materials and can help balance the heat generation and heat removal capabilities of the reactor. Partial oxidation reactions where one or more of the reagents undergoes very high conversion often use such strategies and some examples are ethylene oxychlorination to 1,2-dichloroethane, propylene oxidation to acrylic acid and ortho-xylene oxidation to phthalic anhydride. Loading a mixture of active and inactive particles into a reactor tube is an inherently statistical process, which produces non-uniform activity profiles within the reactor tubes. In the present work, we have evaluated the impact of this purely statistical axial activity variation on the performance of a reactor for the conversion of ortho-xylene to phthalic anhydride. The simulations include tube to particle diameter ratios (N) between 3 and 10, which covers the typical range of commercial practice for such reactor systems. We have found that even when the intended zoning profile is well within the stable operating regime, significant numbers of reactor tubes are likely to run away for systems with 50% catalyst and N values of 4-6. These runaways are caused by axial activity variations rooted in the purely statistical sampling process of adding a mixture of active and inert particles into the reactor tubes. Higher dilutions and smaller values of N make this situation worse. The work shows that the frequency of runaway reactor tubes correlates reasonably well with the relative standard deviation of the binomial distribution that describes the active catalyst sampling statistics divided by N. A strategy is proposed for establishing particle size and dilution ratios that minimize the likelihood of runaway tubes. In commercial practice, imperfect catalyst-diluent blending, particle segregation during storage and handling and careless catalyst loading will all increase the likelihood of runaway tubes, so the present analysis represents an optimistic view of the axial activity profile issue. (C) 2012 Elsevier Ltd. All rights reserved.