## 3 Applications to a Waste Separation System
### Results of the Parameter Estimation  
The estimation of the system parameters was carried out using the iterative circle represented in Figure 4 for the parameters marked in Table 1. The simulation stop criteria were defined by the Kolmogorov-Smirnov test of two samples in addition to the 20% confidence interval. As will be seen later, this criterion is strict enough to stop the iteration. \(N=3000\) sample size was used, which is large enough to not affect the result [29].  
The proposed parameter estimation method was implemented in the MATLAB environment. The expert-based data, the system model, and the data about system feed form the inputs of the simulator, and the estimated distributions of parameters and outputs (as well as goodness values, if the outer circle is also used) are given back as results. One experiment in the inner iteration circle until convergence took approximately 12 s. The method is quite efficient in case of simple stationery system models wherein differential equations are not necessary to solve. However, computational demand is strongly dependent on the complexity of the system model  
Figure 11: Empirical probability density functions (PDFs) of the outputs along the iteration steps. The lines turn black from orange as the iteration is progressing.  
Figure 10: Empirical cumulative density functions (CDFs) of the outputs along the iteration steps. The lines turn black from orange as the iteration is progressing.  
Comparing these results with those of [29], it can be concluded that standard deviations are much smaller for iron and aluminum production, and the medians are more likely within the limits of experts. Therefore, the output estimation is more precise with  
Figure 12: Empirical cumulative density functions (CDFs) of the \(r_{3}^{Aluminium}\) parameter along the iteration steps. The lines turn black from orange as the iteration is progressing.  
Figure 13: The estimated and the expert-based outputs. The former are represented by boxes with a red line in the median, and the latter by markers (red o, green x, and blue diamond) at the edges of the provided intervals by the three experts.  
the improved method used in this paper. This result implies that the estimated parameter distributions must also be more accurate than those provided by the experts.  
Regarding parameter estimation, the results belonging to the LDPE component can be seen in Figure 14.  
The estimation results can be compared to the expert knowledge based on Figure 14. As seen, estimated distributions fall into the intervals covered by expert-based information in all the cases. Otherwise, the estimated output is nearly normal because it depends on the product of five uncertain parameters, so the differences equalize.  
Figure 14: Estimated and expert-based distributions of the estimable parameters and output belonging to LDPE.  
As also seen in Figure 14, in some cases experts gave disjunct intervals. It can be easily assumed that, in these cases, one of them is wrong. The estimated distributions usually cover only the preferable one of these intervals, and the other is neglected. Therefore, if the estimated distributions are used for sampling the parameters, some wrong information is eliminated, and thus more exact output estimation can be provided, as was declared above.  
Individual expert judgments can also be evaluated according to the estimation results. In Section 3.5, the method is introduced in detail.