Application of the GUM approach to estimate uncertainty in measurements of sustainability systems

This work incorporates measurement uncertainty estimation into the model framework proposed by dos Santos and Brandi (Clean Technol Environ Policy, doi:10.1007/s10098-015-0919-8, 2015). It brings the metrology science procedures to sustainability situations by incorporating the use of the GUM framework (GUF) together with the Monte Carlo method (MCM) (BIPM, Evaluation of measurement data—guide to the expression of uncertainty in measurement 2008a; Evaluation of measurement data—Supplement 1 to the “Guide to the expression of uncertainty in measurement”—propagation of distributions using a Monte Carlo method 2008b). The GUF uses the law of propagation of uncertainties and the MCM the propagation probability distributions. This scheme is applied to analyze the Integration and Logistic Infrastructure sustainability dimension of a biofuel supply chain in six countries (Santos et al. 2014). An initial set of specific indicators (input quantities) satisfying well-established criteria is used to aggregate indicators in a methodological manner into a single aggregate indicator. The Canberra and the normalized Euclidean distances are assumed as model functions. As recommended by the GUM approach, Supplement 1 (BIPM, Evaluation of measurement data—Supplement 1 to the “Guide to the expression of uncertainty in measurement”—propagation of distributions using a Monte Carlo method 2008b) is used to compare the GUF and the MCM results, adopting the GUM recommendation to perform the MCM with 106 random trials. This allows the determination of the numerical statistical results with the precision level required for comparing the sustainability level of the six countries. It was shown that the use of the GUF is not validated to treat the adopted model functions. The two fundamental reasons are the limitation of the GUF concerning the truncation of the Taylor’s expansion and the deviation of the probability density function from the normal distribution (BIPM, Evaluation of measurement data—Supplement 1 to the “Guide to the expression of uncertainty in measurement”—propagation of distributions using a Monte Carlo method 2008b; Couto et al., Theory and applications of Monte Carlo simulations 2013). This result was predictable because of the nonlinear dependence on the indicators of the Canberra and the normalized Euclidean distances. The MCM calculations have shown that the uncertainties depend on the choice of the aggregate metrics, consequently affecting the countries sustainability ranking. The results demonstrate that Canberra and the Euclidean metrics separate the developed from the developing countries in clusters. The calculations for the single sustainability indicator and its uncertainty suggest that the Euclidean distance separates the countries better than the Canberra distance and, thus, it may be considered more adequate to represent the sustainability metrics Integration and Logistic Infrastructure sustainability dimension of a biofuel supply chain.