In 2012, we evaluated and presented at the CORESTA Congress^[1] the probable impact of emission ceilings as proposed by the joint working group of the WHO Study group on Tobacco Product Regulation (TobReg)^[2] using experimental data and we demonstrated the necessity of considering the correlation between all of the analytes for which a ceiling is to be applied. Indeed, if only one analyte is considered in isolation the relation order is total and the decision depends on the position of a single numeric value with respect to a threshold. In this case, the most important issue is the determination of a suitable threshold according to various criteria based on different considerations ranging from toxicology to method/product variability. But when several analytes (dimensions) are involved, the relation order becomes partial making the problem imprecise and complex and raises the question: what is the best regulatory approach to limiting the quantities of multiple analytes together? We refer to this problem as the multiple-ceiling (MC) problem. The MC problem will require the evaluation of several related fields of decision-mathematics, depending on which approach would be chosen. Indeed, there are, and remain, several alternative approaches, the choice of which ultimately depends to some extent on what specific considerations regulators want to base their decision.

The objective of this presentation is to introduce the MC problem and to discuss the technical limitations.

[1] X. Cahours, T. Verron, S. Purkis, S. Colard (2012). Product compliance mapping. CORESTA Congress (Sapporo, Japan)
[2] World Health Organization (2008). The scientific basis of tobacco product regulation, second report of a WHO Study Group (TobReg). WHO Technical Report series 951.