Nuclear waste drums can contain a collection of radioactive components of uncertain activity and randomly dispersed in position. This implies that the dose-rate at the surface of different drums in a large assembly of similar drums can have significant variations according to the physical makeup and configuration of the waste components. The present paper addresses this problem by treating the drum, and its waste, as a stochastic medium. It is assumed that the sources in the drum contribute a dose-rate to some external point. The strengths and positions are chosen by random numbers, the dose-rate is calculated and, from several thousand realizations, a probability distribution for the dose-rate is obtained. It is shown that a very close approximation to the dose-rate probability function is the log-normal distribution. This allows some useful statistical indicators, which are of environmental importance, to be calculated with little effort.

As an example of a practical situation met in the storage of radioactive waste containers, we study the problem of "hotspots." These arise in drums in which most of the activity is concentrated on one radioactive component and hence can lead to the possibility of large surface dose-rates. It is shown how the dose-rate, the variance, and some other statistical indicators depend on the relative activities on the sources. The results highlight the importance of such hotspots and the need to quantify their effect.