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Sampling with Discrete
Contamination
Geoff Lyman: Materials Sampling & Consulting
Florent Bourgeois: Materials Sampling & Consulting Europe
University of Toulouse
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Motivation
The international grain trade operates understrict quality control constraints:
Critical analytes are:
Mycotoxins (Ochratoxin A and deoxynivalenol (DON) GMOs
Pesticide residues
Heavy metals Mycotoxins and GMOs are trace components
and are highly heterogeneous in cargos
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Motivation
OTA can reach a concentration of >10 000 ppb
on a single kernel of wheat
The allowable limit is 5 ppb in a cargo.
There is NO data on OTA distribution in cargos
It is desirable to have a means of estimatingthe variance (and distribution) of sampling for
mycotoxins and GMOs
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The Problem
If OTA and GMOs occur in slugs of relatively
high concentration in the shipment, it takes
only a small number of slugs to put the
shipment off spec.
Sampling by taking increments may have a
high probability of missing the slugs, making
the sampling variance potentially large
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The Solution
The sampling variance for stratified sampling
can be determined by considering slugs placed
at random over a stratified sampling scheme.
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The Solution
The statistical analysis is based on a Bernoulli
process (we hit or miss the sample increment
with each slug)
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The Problem
The result is valid when the slug size is smallerthan the extent of the stratum (a single slug
cannot hit more than one increment)
The result is correct to first order for randomstratified sampling and random sampling
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The Solution
For increments smaller than the slug, which isthe usual case, the relative sampling SD is,
2
2
1 21
E 3
Sc
S
L u v vn
n m u vc u
m = slugs
n = increments
L = consignment mass
u = slug mass
v = increment mass
cS = sample concentration
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The Solution
This result extends to 2 and 3 dimensions withcorrections for geometry of the slug and
increment
However, to get a real picture of sampling risk,we need the full distribution of the sampling
uncertainty, not just the variance
This demands simulation of the process
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The Solution
The sampling process is easy to simulate The lot concentration is held at 2 ppb (
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Examples (2 ppb average)
22.2 tonnes between increments
20 slugs, 200 kg
Slug conc = 1000ppb
RSD = 229%
100 slugs, 200 kg
Slug conc = 200ppb
RSD = 102%
100 slugs, 2200 kg
Slug conc = 18ppb
RSD = 30%
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Conclusions
High
heterogeneity
High probability of false negatives
Positives overestimate average
concentration
Moderateheterogeneity
False negatives still probablePositives may overestimate average
concentration
Low
heterogeneity
No false negatives
Results nearly normally distributedVariance is still significant compared to
analytical variance (~10% RSD)
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