Sensitivity coefficient-based uncertainty analysis for multi-functionality in LCA

Purpose In LCA, a multi-functionality problem exists whenever the environmental impacts of a multi-functional process have to be allocated between its multiple functions. Methods for fixing this multi-functionality problem are controversially discussed because the methods include ambiguous choices. To study the influence of these choices, the ISO standard requires a sensitivity analysis. This work presents an analytical method for analyzing sensitivities and uncertainties of LCA results with respect to the choices made when a multi-functionality problem is fixed. Methods The existing matrix algebra for LCA is expanded by explicit equations for methods that fix multi-functionality problems: allocation and avoided burden. For allocation, choices exist between alternative allocation factors. The expanded equations allow calculating LCA results as a function of allocation factors. For avoided burden, choices exist in selecting an avoided burden process from multiple candidates. This choice is represented by so-called aggregation factors. For avoided burden, the expanded equations calculate LCA results as a function of aggregation factors. The expanded equations are used to derive sensitivity coefficients for LCA results with respect to allocation factors and aggregation factors. Based on the sensitivity coefficients, uncertainties due to fixing a multi-functionality problem by allocation or avoided burden are analytically propagated. The method is illustrated using a virtual numerical example. Results and discussion The presented approach rigorously quantifies sensitivities of LCA results with respect to the choices made when multi-functionality problems are fixed with allocation and avoided burden. The uncertainties due to fixing multi-functionality problems are analytically propagated to uncertainties in LCA results using a first-order approximation. For uncertainties in allocation factors, the first-order approximation is exact if no loops of the allocated functional flows exist. The contribution of uncertainties due to fixing multi-functionality problems can be directly compared to the uncertainty contributions induced by uncertain process data or characterization factors. The presented method allows the computationally efficient study of uncertainties due to fixing multi-functionality problems and could be automated in software tools. Conclusions This work provides a systematic method for the sensitivity analysis required by the ISO standard in case choices between alternative allocation procedures exist. The resulting analytical approach includes contributions of uncertainties in process data, characterization factors, and-in extension to existing methods-uncertainties due to fixing multi-functionality problems in a unifying rigorous framework. Based on the uncertainty contributions, LCA practitioners can select fields for data refinement to decrease the overall uncertainty in LCA results.