t
n
On
the variance estimated in step 1
s2 = sample variance of the estimated ratio
and
2
Ss
estimated variance of final TRU value
The last term in this equation was also inadvertently left out of the program, but the effect is
again relatively minor.
The estimated Sp was stored along with the final estimated TRU activity. In those cases where the
data were used in kriging, the Sp values were incorporated in the equations used to find the
optimum set of weights for the weighted moving average estimate. The effect of this was to make
values having larger errors have less influence on the computed
j, than values with smaller errors.
Also the variance of the kriging error was larger because these measurement variances were taken
into consideration. Hence, the end effect of taking the propagated error into account was to make
the 0.5 sigma upper bound on the final estimates larger.
Ranges and Distributions of Actual Errors
As shown in Figure B-20-1, the actual standard deviation estimate from the error propagation
described above ranged from near 0 to over 50 pCi/g. Most of the standard deviation values were
30-40 percent of the TRU values as illustrated in Figure B-20-2. The two propagated errors which
exceed 100 percent of the TRU value are associated with 2414m values that were near or below
the minimum detectable activity.
The propagated errors include the counting error plus 10 percent of the 241 Am value from the IM P,
which typically ranged from 0.5 to 2.5 pCi/g, as shown in Figure B-20-3, with a few values outside
this range.
Also included were an estimated error on the TRU/Am ratio and on the factor used to
correct for brush cover. Figure B-20-4 is a histogram of the estimated errors for all the ratios used
on the northern islands, and Figure B-20-5 shows the experimentally-determined brush correction
factors. Only a counting error plus 10 pereent for the IMP 241 am value was included because the
pCi/g, yet estimating the standard deviation from the counting errors gives 1.35 pCi/g.
The
counting errors overestimate the standard deviation because of the addition to the error of an
arbitrary 10 percent of the actual value to allow for differences in the parameters which affect the
factor which converts counts to pCi/g.
yo
reproducibility of the IMP value, as shown by Figure B-20-6, indicated that no other contribution to
the sample variance needed to be added. In fact, the sample standard deviation for this set is 0.41
The computed TRU values inelude a correction for detector effective area changes, but no error
term for the correction factor. As shown by Figure B-20-7, these errors were almost always less
than 0.5 square centimeter (for a theoretical area of 19 square centimeters). This gives an error of
The propagated error values were taken into consideration in making the kriging estimates of 0.25
and 0.5 hectare averages. The standard deviation of the kriging error is affected by the propagated
errors, the variogram model used, and the geometry of the sampling points used for each estimate.
Figure B-20-8 shows the dstribution of standard deviations of the kriging error for northern islands
for a standard neighborhood of sampling points, which is either a 3x3 or 4x4 array of points.
standard deviation is typically less than 6 pCi/g.
wa
less than 3 percentin the correction factor; in most cases the error was less than 1 percent.
The
Other Errors not in Propagation Computation
alpha spectroscopy of soil chemistry results, seen in Figure B-20-10, were not included. They were
left out because they affect the TRU value only indirectly, through the TRU/Am ratio, for which a
standard deviation was included in the propagation. Another error not included was that due to soil
B-20-3
ewe
There are some other errors which were not ineluded in the propagation, but which can be
estimated. The counting errors on the laboratory gamma scans of soil, seen in Figure B-20-9, and