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11/27
4 Using intervals for worst-case analyzes
4.1 Problem formulation
In the equations detailed in section 3 for monolayer materials, the objective functions are either
0
,
,
, ,
P Fo
F Fo Bi K L C
C
=
or
max
0
P Fo
C
=
such that
max
0
,
,
, ,
P Fo
F Fo Bi K L C
C
SML
=
=
where SML is a specific migration
limit defined by the regulation or by other considerations. As an example, a packaging industry
with appropriate knowledge on the formulation of its material will prefer to estimate
0
,
,
, ,
P Fo
F Fo Bi K L C
C
=
, based on its foreseen application (type of contact, contact time) and on a
accurate estimate of
0
P Fo
C
=
. The final objective is to compare the estimate (possibly
overestimated) of
0
,
,
, ,
P Fo
F Fo Bi K L C
C
=
, noted
0
,
, , ,
^
P Fo
F
Fo Bi K L C
C
=
, with the SML. By contrast a food
industry, with a poor knowledge on the packaging material, will prefer to get an estimate
(possibly underestimated) of
max
0
P Fo
C
=
, noted
max
0
^
P
Fo
C
=
, by assuming that the contamination is equal
to the SML. In this case, the final objective is to obtain evidence from the provider that he uses
the tested substance at a concentration lower than
max
0
^
P
Fo
C
=
.
Whatever the considered objective, estimating
0
,
,
, ,
P Fo
F Fo Bi K L C
C
=
or
max
0
P Fo
C
=
, it is important to deal
with uncertainties related to in put parameters or in the conditions of use of the packaging
material in a way that enforces the confidence that the decision makers have in the estimates.
Since this opinion must be shared by the different sides of the decision process
provider/producer, producer/final user, producer/control authority easy-to-use and transparent
methods, which minimizes the risk of putting on the market products are contaminated over a
specific limit, are encouraged.
In absence of reaction or other sources of contamination than the packaging material, the
maximum amount of contaminant in food cannot exceed the initial amount in the packaging
material. This situation is a priori the worst of the worst scenarios. It is however more difficult to
construct other worst-case scenarios with less stringent conditions. As it is presented for
multilayer materials, the number of parameters can be pretty huge and the effects can be
antagonist. The physicochemical parameters can be arbitrary classified into molecular transport
controlled properties (diffusion coefficients, mass transport coefficients) and thermodynamically
controlled properties (partition coefficients, Henry-like coefficient or solubility). How to weight
them? As an example, it is not trivial to decide whether the scenario R
D
=R
H
=0 and R
K
>0
(thermodynamically controlled contamination) is safer than the scenario R
D
>0, R
H
=R
K
=0
(transport controlled contamination) for monolayer materials. As a result a robust classification of
scenarios is required.