0.2% of the time. (The current public health risk isn’t such that it makes sense to increase
the rejection by a factor of 25). Using the previous error rates with an AQL of 0.0033%, the
sample size is 1550 and the RQL is 0.19%, 57 times higher than the AQL.
If instead, one said that 10 times higher than this is the AQL, using the previous error rates
with an AQL of 0.033%, the sample size is 155 and the RQL is 1.9%, again 57 times higher
than the AQL. Here the current estimated level of 0.0033% would fail 0.5% of the time
instead of 0.2% of the time.
Based on the low incidence of positives currently observed (0.2% to 0.02% of samples of
60), most likely only 1 individual sample is contaminated. With this low level of positives, the
probability of the second individual sample being contaminated is 5 orders of magnitude
below that of the probability of 1 individual sample being positive (using the binomial
distribution).
4.3. Role and validity of assumptions
The lot (acre, 5 acre plot, etc.) can be thought of as comprised of many individual units the
size of the collected samples. One can then envision that, say, 0.01% of these units are
contaminated. These contaminated units could be randomly distributed across the plot or
clustered in various locations within the plot. If sample units are taken randomly from the
plot, the units will be independent with probability of contamination 0.01%. These are called
Bernoulli Trails, and the use of the binomial Distribution is appropriate for analysis. The
random sampling provides for the equal probability of selecting a contaminated unit at each
sampling, regardless of clustering. The Binomial Distribution was used to make the
calculations in section 4.2.
When the number of samples times the probability of contamination (NP) is moderate, say
<10, the Poisson distribution is a good approximation to the binomial. With N=60, P just
needs to be < 17%, which is certainly true for produce contamination.
Independence of samples is assumed. If one happened to choose two units off the same
head of lettuce, it would be more likely to have the same probability of contamination as the
other unit off the head than samples from heads that are separated geographically, and
would not be independent. But, with random sampling, it is very unlikely that 2 samples
from the same head would be selected.
5. Recommendations for a sampling plan for routine sampling (Russ Flowers, Dan Morse, Joe
Holt)
5.1. Location of samples collected
If the contamination is randomly distributed within the field, one is just as likely to find the
contamination using a random sample as a systematic sample (Z-Pattern, etc.). If the
contamination is not random, a concentration of sampling within the suspect area will be
more effective at finding contamination. For instance, if historically one has determined that
contamination occurs in the first 3 rows of the north side, concentration of sampling in that
area would be more effective at finding contamination.
