Geoffrey Lyman

7/28/2019 Geoffrey Lyman

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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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Geoffrey Lyman