A stochastic model is described which enables quantitative assessment of the efficiency of safeguards operations in reprocessing or fabrication plants. The a priori assumption, or “zero-hypothesis” is that there has been no diversion of fissile material, the inspector’s task being to invalidate it. To detect diversion, the inspector can resort to three criteria: The first criterion sets an upper bound M for the total mass uncertainty. When the latter reaches M, the inspector will take a plant-wide inventory. The second criterion enables the inspector to decide whether or not an estimated mass balance is compatible with the agreed model, and the third criterion connects the mass uncertainty to the time it lasts; moreover, it settles the number of strategic points within the plant. As an application of the mathematical model developed, systematic cheating strategies are studied. Under the rules assumed, a diverter will achieve maximum total withdrawal at minimum probability of being caught by following a strategy of erratic withdrawal and occasional reinsertion. This renders it necessary for the inspector to assess an upper limit to the positive mass balance, a quite unexpected result.