# Error propagation methods for LCA—a comparison

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## Abstract

### Purpose

The analysis of uncertainty in life cycle assessment (LCA) studies has been a topic for more than 10 years, and many commercial LCA programs now feature a sampling approach called Monte Carlo analysis. Yet, a full Monte Carlo analysis of a large LCA system, for instance containing the 4,000 unit processes of ecoinvent v2.2, is rarely carried out by LCA practitioners. One reason for this is computation time. An alternative faster than Monte Carlo method is analytical error propagation by means of a Taylor series expansion; however, this approach suffers from being explained in the literature in conflicting ways, hampering implementation in most software packages for LCA. The purpose of this paper is to compare the two different approaches from a theoretical and practical perspective.

### Methods

In this paper, we compare the analytical and sampling approaches in terms of their theoretical background and their mathematical formulation. Using three case studies—one stylized, one real-sized, and one input–output (IO)-based—we approach these techniques from a practical perspective and compare them in terms of speed and results.

### Results

Depending on the precise question, a sampling or an analytical approach provides more useful information. Whenever they provide the same indicators, an analytical approach is much faster but less reliable when the uncertainties are large.

### Conclusions

For a good analysis, analytical and sampling approaches are equally important, and we recommend practitioners to use both whenever available, and we recommend software suppliers to implement both.

## Keywords

Analytical methods Gaussian error propagation IOA LCA Monte Carlo Sampling methods Uncertainty## Notes

### Acknowledgments

This article has been written in the context of the UNEP/SETAC working group on uncertainty. Members of this group include, besides the authors of this article, Andreas Ciroth, Ralph Rosenbaum, Mark Huijbregts, Fausto Freire, Tom McKone, Olivier Jolliet, and Enrico Benetto. The group’s activities and the writing of this article have been made possible through the financial support of The Sustainability Consortium. This work was also financially supported by the National eResearch Collaboration Tools and Resources project (NeCTAR) through its Industrial Ecology Virtual Laboratory and by the Australian Research Council through its Discovery Projects DP0985522 and DP130101293. Two anonymous referees have provided valuable comments that helped improving on an early draft of this article.

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