Life Cycle Inventory (LCI) Stochastic Approach Used for Rare Earth Elements (REEs), Considering Uncertainty

  • Dariusz SALA
  • Bogusław BIEDA


The purpose of the paper is to present the results of the stochastic modelling with uncertainty
performed with the use of Monte Carlo (MC) simulation with 10,000 cycles and a confidence interval of
95 %, as recommended. Analysed REEs were fitted by lognormal distributions by using the Crystal Ball®
(CB) spreadsheet-based software after defining the geometric mean value (μg) and the standard deviation
(σg), automatically calculated (matches) the lower, as well as, upper boundaries of lognormal distribution.
The number of replications of a simulation affects the quality of the results. The principal output report
provided by CB and presented in this study consists of the graphical representation in the form of the
frequency chart, percentiles summary, and statistics summary. Additional CB options provide a sensitivity
analysis with tornado diagrams. The data that was used for MC simulation of the LCI model includes
available and published data concerning associated with the REEs. This paper discusses the results and
show that the adopted approach is applicable for any REEs used in the LCI studies under uncertainty. The
results obtained from this study can be used as the first step in performing a full LCA analysis and help
practitioners as well as decision-makers in the environmental engineering and management.