The mixture assessment or allocation factor: conceptual background, estimation algorithms and a case study example

Environmental Sciences Europe

Table 2 Numerical comparison of MAF_exact and MAF_90%

	Mixture 1	Mixture 2	Mixture 3	Mixture 4	Mixture 5
RQ Substance 1	0.8	80	80	80	90
RQ Substance 2	0.1	10	10	10	1
RQ Substance 3	0.05	5	9	4	4
RQ Substance 4	0.05	5	0.7	4	3
RQ Substances 5–10	0	0	0.05	0.33	0.33
Initial RQ sum	1	100	100	100	100
No of compounds for 90% of RQ sum = MAF_90%	2	2	2	2	1
RQ sum after applying MAF_90%	0.7	2	2.3	4	100
MAF_exact	1	4	5.71	10	10
RQ sum after applying MAF_exact	1	1	1	1	1

All mixtures used in this example are arbitrary, but follow the typical Pareto-like distribution of RQ values found in relevant mixtures. In mixtures 1–4, the first 2 components provide 90% of the RQ sum, i.e., MAF_90% is 2 for each mixture. However, the distribution of RQ values in the tail is different between mixtures 1—4, and, as a consequence, the RQ sum after applying MAF_90% is different for the different mixtures, varying between 0.7 and 4. In mixture 5, 90% of the RQ sum is provided by the first compound, and MAF_90% is therefore 1, leading to a massive risk underestimation. In contrast, MAF_exact captures the full variability in the RQ distribution in the different MAF_exact values, and the resulting RQ sum is always exactly 1 (the pre-defined acceptability criterion)