Pu concentrations in such "paired" samples is often low. In a desert environment where resuspension plays an important role in determining vegetation concentrations, differences among species have also been found (Romey et al. 1975). This suggests the need in such an area to avoid lumping species together when computing average concentrations or correlation coefficient s. The design of small mammal studies is complicated by a lack of close correlation (at least in desert environments) between concentrations in animal tissues and those in surrounding soil. Designs for these kinds of studies Must consider those variables that might account for the observed variation. Thus, it might be possible to stratify over time, space, species, depth of soil, weather conditions, etc., in order to estimate the components of variance. SAMPLING FOR CLEANUP There have been a number of instances where cleanup operations or decontamination procedures have been undertaken to remove or stabilize radionuclide contamination in soil. Wallace and Romney (1975) discuss the procedures and experience gained at a number of locations and give an extensive reference list. A companion reference is Rhoads (1976), who gives a position Paper on treatment of certain Pu-contaminated areas on the Nevada Test Site. Our concern here is with the elements of a sampling program that might be applicable to the question of whether a cleanup operation is required. Two sampling approaches under the general title of "acceptance sampling" are presented below as possible procedures for deciding whether cleanup is required. Only the bare essentials are given here. Setting up these plans would require attention to many design details. The two approaches are called acceptance sampling by (1) attributes and (2) measurement. We begin with acceptance sampling by attributes. A criterion for deciding when cleanup is tequired might include an upper limit on soil concentrations that should not be exceeded by most samples. The proportion of soil samples collected that exceed this limit can be used to decide whether cleanup is necessary or if a cleanup operation has been successful. The basic idea is to specify (1) an activity level, L, for soil; (2) a Proportion, p), of samples with activities greater than L that is acceptable, i.e., for which cleanup is not required; (3) a Proportion, pz of samples with activities greater than L that is not acceptable, i.e., for which cleanup is required; (4) the allowable risk, a, of wrongly concluding that cleanup is_ necessary; and (5) the risk, 8, of wrongly concluding that cleanup is not necessary. Once these quantities have been specified, it is possible to determine (1) the number of samples, n, required in order to meet the a and B specifications, and (2) a rejection number, r, such that cleanup is required if r or more of the n samples have activities greater than L. This approach assumes a willingness to tolerate a certain proportion, p;, of samples with activities greater than L without cleaning up the area. Of course, p; can be specified to be as close to zero as we please. 582 The risk, 8, would, presumably, be specified near zero since the consequences of not cleaning up a contaminated area might result in undue risk to the inhabitants of the area. The "power" of the design is 1-8, i.e., 1-8 is the probability that the area is cleaned up when it should be cleaned up (when the proportion of soil in the area with activities greater than L is po). The number of samples, n, and the rejection number, r, can be determined for given values of p,, po, a, and B using tables prepared by Burstein (1971). The above approach is known as “acceptance sampling by attributes," the elements of which are discussed elsewhere, e.g., Freeman et al. (1948) and Burr (1976). We note that attribute sampling is ordinarily used in situations where the "attribute" can be measured accurately for each element examined and decisions about a given population (often a quantity of manufactured product) are to be made on the basis of the sampled elements. Hence, we are neglecting "counter error" here and assuming decisions are to be made on the basis of whether or not sample elements from a given area (e.g., soil aliquots) indicate that a proportion of such elements are above some set limit. Turning now to acceptance sampling by measurements, the cleanup decision is based on average soil concentrations rather than on the proportion of samples with concentrations exceeding L. Using the average approach, it is necessary to specify both an acceptable and unacceptable average soil concentration denoted by yy; and uz, respectively, as well as the a and B risks defined above. It is also necessary to specify a value for the anticipated standard deviation (oc) of the concentration values. This average concentration approach requires that the sample mean, (x), be normally distributed, which may be approximately true even if the individual sample concentrations are skewed (commonly the case in transuranic studies). Nevertheless, it may be preferable to transform the data to logarithms so that the test is made on the basis of the average logarithm of concentrations. This approach requires that yy, U2, and o also be in log units. Once uy), u2, 5, &, and 8 are specified, it is relatively simple to determine the number of samples, n, to collect and the critical value, K (Burr, 1976, pp. 325-328). Letting x be the average concentration of the n collected soil samples, the decision is made to clean up the sampled area if x > K. pp. No cleanup action is taken if x < K. 332-336) for the usual case when o is unknown. See Burr (1976, The choice between the attribute and average concentration approach to deciding the cleanup question hinges on the normality assumption. Quoting from Burr (1976, p. 324), "Unless we can build up evidence on the distribution of measurements, we had better stay with the method of attributes." However, the attribute approach may call for substantial numbers of samples (Burr, 1976, p. 347). If the average concentration approach is used, and if transuranic concentrations in adjacent soil samples are not independent, then a useful estimate of the average concentration x might be obtained using an estimation procedure called Kriging (Davis, 1973, pp. 381-390; Delfiner and Delhomme, 1975). Kriging makes use of the correlation structure (if it exists) to obtain an optimum weighted average. We are presently engaged in research to determine the kinds of correlation structures that might exist for transuranics in soil. A disadvantage of the attribute approach is that the additional information available concerning a correlation structure is not used in the decision-making process. 583