Inspection procedures involving the sampling of items in a population often require steps of increasingly sensitive measurements, with correspondingly smaller sample sizes; these are referred to as multilevel sampling schemes. In the case of nuclear safeguards inspections verifying that there has been no diversion of Special Nuclear Material (SNM), these procedures have been examined often and increasingly complex algorithms have been developed to implement them. The aim in this paper is to provide an integrated approach, and, in so doing, to describe a systematic, consistent method that proceeds logically from level to level with increasing accuracy. The authors emphasize that the methods discussed are generally consistent with those presented in the references mentioned, and yield comparable results when the error models are the same. However, because of its systematic, integrated approach the proposed method elucidates the conceptual understanding of what goes on, and, in many cases, simplifies the calculations. In nuclear safeguards inspections, an important aspect of verifying nuclear items to detect any possible diversion of nuclear fissile materials is the sampling of such items at various levels of sensitivity. The first step usually is sampling by ``attributes`` involving measurements of relatively low accuracy, followed by further levels of sampling involving greater accuracy. This process is discussed in some detail in the references given; also, the nomenclature is described. Here, the authors outline a coordinated step-by-step procedure for achieving such multilevel sampling, and they develop the relationships between the accuracy of measurement and the sample size required at each stage, i.e., at the various levels. The logic of the underlying procedures is carefully elucidated; the calculations involved and their implications, are clearly described, and the process is put in a form that allows systematic generalization.
