# Digital Twins in Product Lifecycle for Sustainability in Manufacturing and Maintenance
## 5 Results
Table 2 compares the cost, risk assessment and standard error of the decision trees. Reinforced decision trees and random forest proved to be the most effective models. Correct classification rates were 100% and 97.64%, respectively. Decision rules were developed based on the trees, which were then implemented in the system. Example rules developed based on the second decision tree are:  
1. _if added material = \"ABS\" and main material = \"ABS\" then compatibility = \"good\"_
2. _if added material = \"ABS\" and main material = \"ASA\" then compatibility = \"good\"_ \begin{table}
\begin{tabular}{c c} \hline
**Class** & **Added Materials** \\ \hline
1 & SAN, PVC, PMMA, PC, PBT, ASA, ABS \\
2 & PS, PPE, PP, POM, PET, PE, PA \\
3 & PA \\
4 & SAN, PS, PP, POM, PMMA, PET, PE, PBT, ASA, ABS \\
5 & PVC, PPE, PC \\
6 & SAN, PC, PBT, ASA, ABS \\
7 & PS, PPE, PP, POM, PMMA, PET, PE, PA \\
8 & PVC \\
9 & SAN, PMMA, PET, PC, PBT, ASA, ABS \\
10 & PS, PPE, PP, PE \\
11 & PVC, POM, PA \\
12 & PP, PE \\
13 & PA, PVC, PC \\
14 & SAN, PS, PPE, POM, PMMA, PET, PBT, ASA, ABS \\
15 & PET, PC, PBT, ASA, ABS \\
16 & SAN, PA, PVC, PE, PS, PMMA, PPE, POM, PP \\
17 & PC, ABS, PMMA, ASA \\
18 & PA, SAN, PE, PVC, PET, PS, POM, PP, PPE \\
19 & PBT \\
20 & POM \\
21 & ABS, PVC, ASA, SAN, PA, PS, PBT, PE, PET, PPE, PP \\
22 & PMMA, PC \\
23 & PP \\
24 & PVC, PE, PA \\
25 & ABS, SAN, ASA, PS, PBT, PPE, PC, POM, PET, PMMA \\
26 & PS, PPE \\
27 & ABS, ASA, SAN, PA, PP, PBT, POM, PC, PMMA, PET, PE \\
28 & PS \\
29 & ABS, ASA, PA, POM, PBT, PP, PC, PPE, PE, PVC, PET, SAN, PMMA \\
30 & SAN, ABS, PVC, ASA, POM, PMMA \\
31 & PS, PP, PE \\
32 & PET, PPE, PA, PC, PBT \\ \hline \end{tabular}
\end{table} 
Table 1: Classes of added materials. \begin{table}
\begin{tabular}{c c c} \hline \hline  & \multicolumn{2}{c}{**Classifier Assessment**} \\ \cline{2-3}
**Classifier Type** & **Risk Cost/Assessment** & **Standard Error** \\ \hline C\&RT & 0.035217 & 0.110509 \\ CHAID & 0.201187 & 0.016060 \\ Reinforced decision trees & 0.000001 & 0.000001 \\ Random forest & 0.021846 & 0.011653 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Comparison of classifiers of material selection based on the added material. if added material = \"ABS\" and main material = \"PA\" then compatibility = \"limited\"
4. if added material = \"ABS\" and main material = \"PE\" then compatibility = \"limited\"  
The rules were imported into an existing module for determining material compatibility: main and added product (Figure 8). The result is a system that facilitates a company's operations in the following areas: eco-designing, planning manufacturing and monitoring manufacturing while accounting for maintenance in sustainable manufacturing. Figure 9 depicts a system architecture that incorporates digital twins in areas of importance to the company for which it was developed by us. It provides a dynamic virtual representation of a physical object/process at selected stages of its life cycle. Our DT system includes physical processes chosen area: eco-designing, manufacturing planning and monitoring. In databases, we have descriptions of these physical processes. Systems can both present observations concerning the current state of the system and answer the questions \"what-if\". Many decision trees have been defined for each decision problem in these three areas and in their specific tasks. Some trees from various areas are shown in Figures 4-6. Figure 7 shows the evaluation of an exemplary tree. All trees were assessed in this way, and the best ones were selected. The best decision trees are in the knowledge base. Decision rules were created from the trees, which are included in computer applications. The computer programs aid engineers in creating new solutions. Figure 9 shows the architecture of a DT system in the company.