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.
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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.
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