Pellet heat and mass transfer coefficients inside packed beds do not have definite deterministic values, but are stochastic quantities with a certain distribution. Here, a method is presented to incorporate the stochastic distribution of pellet properties in reactor design and operation models. The theory presented is illustrated with a number of examples. It is shown that pellet-scale statistics have an impact on cooled tubular reactor design and operation. Cooled tubular reactor design is determined to a large extent by the objective that run away inside the reactor tubes be avoided. We obtain the highest conversion if conditions in the tubes are such that the pellet and reactor run-away mechanisms are in balance. This determines an optimum amount of particles on a diameter inside a cooled tubular reactor. This optimum is influenced by the distribution of transport coefficients over the pellets. Because of the pellet-scale statistical behaviour, a certain percentage of the tubes will always suffer run away if we operate close to the run-away region. If we have certain fluctuations in the coolant temperature, reactor pressure or load, any of these can damage a certain amount of tubes. As these fluctuations occur often, the performance of the cooled tubular reactor will deteriorate with time. The effects, as shown in this study, may cause an increase in inherent reactor instability. Therefore, if these effects are taken into account, a more conservative reactor design emerges.