## 4 Case Study
### Results Discussion  
Table 5 shows the quantitative evaluation results of the proposed evaluation method on the flexibility of the motor commutator production system design scheme. Flexibility in the case mainly considering the ability of the production system to meet the demand for new products' production. The comprehensive flexibility evaluation index in Table 5 represents the ability of different design schemes to meet the production requirements of new products. It can be seen that the comprehensive flexibility evaluation index of Scheme B is 6.19905, which is larger than 1.51175 in Scheme A. It means that Scheme B is more capable of meeting the needs of enterprises than Scheme A. The acquisition of the comprehensive flexibility evaluation index of the design scheme mainly considers two factors. One is the ability of the PS to meet the enterprise's requirements reflected by the system structure. The other one is the capacity of the production system (PS) to deal with equipment failure, obtained by simulation and prediction. The evaluation results show that the static flexibility evaluation index of Scheme A is 0.12995 and the dynamic flexibility evaluation index is 0.08596, while the static flexibility evaluation index of Scheme B is 0.44542 and the dynamic flexibility evaluation index is 0.071853. Numerical comparison indicates that the two design schemes have basically the same processing capacity in the face of possible equipment failure, but are quite different in meeting the production requirements of enterprises. The capacity of scheme A to meet the production requirements of enterprises is much smaller than that of Scheme B.  
A holistic analysis of the case can be found, the two design schemes presented in this study have obvious contrasting characteristics, which also brings better verification effect to the application of the proposed digital twin flexibility evaluation framework. Comparing the values of the two schemes' characteristic parameters, Scheme B can produce more product varieties than A, and Scheme B has the larger number of product families than that of Scheme A, while the quantity of process types and machine types are equal in Scheme A and Scheme B. Furthermore, Scheme A is a rigid production line, while Scheme B is constructed by independent production platforms which are linked by AGV. Therefore, it can preliminarily judge that Scheme B is more flexible than Scheme A, and the proposed flexibility evaluation method can better verify the predicted results.  
According to the application results of the case, it can be found, based on the digital twin flexibility evaluation framework, the flexibility evaluation of the motor commutator PSDS is carried out quickly. The comprehensive flexibility evaluation indexes of the two design schemes not only consider the ability of the system itself to meet the production requirements of the enterprise, but also predicts the performance of the system in the face of possible failures. More importantly, the final evaluation results also integrate the enterprise's subjective demand for flexibility in the production process.  
\begin{table}
\begin{tabular}{l l l} \hline \hline  & **A** & **B** \\ \hline Static flexibility evaluation index & 0.12995 & 0.44542 \\ Dynamic flexibility evaluation index & 0.08596 & 0.071853 \\ Comprehensive flexibility evaluation index & 1.51175 & 6.19905 \\ \hline \hline \end{tabular}
\end{table}
Table 5: Flexibility result of commutator PSDS.