## 3 System Flexibility Digital Representation
### Flexibility Definition and Analysis
\begin{table}
\begin{tabular}{l l l} \hline \hline  & **Definition** & **System** \\  & & **Flexibility** \\ \hline Product varieties & types of products produced by the system & + \\ Product similarity & similarity level of the products in structural & – \\  & and process & – \\ Process changeability & product process path changeability index & + \\ Process conversion capacity & efficiency of the production system to convert & + \\  & between two different product varieties & + \\ Machine versatility & versatility level of the machine & + \\  & extensibility ability of the production system & \\ Machine extensibility & when facing the introduction of new & + \\  & products & \\ ‘+’: Positive correlation; ‘\(-\)’: Negative correlation & \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Metrics definition and Relationship between metrics and system flexibility. Figure 2: Production system structure descriptive metamodel. The number of product types refers to the number of product types that can be produced by the production system. The higher the quantity of product types produced, the stronger the ability of the production system design scheme to meet the needs of multivariety product production. Product similarity refers to the similarity level of the products in structural and process. The lower the similarity level between the products that can be produced by the production system, the higher capacity for the production system to produce different types of products. Process changeability refers to the changeability index for product process path. The more process paths a product can choose in the production process, the higher the probability that the system can continue the production when a certain equipment fails, which means the greater production system flexibility. Process conversion capacity refers to the efficiency of the production system to convert between two different product varieties, which is proportional to the system flexibility. Machine versatility refers to the versatility level of the machine. Machine in mechanical processing can be divided into dedicated machines (such as boring machine saw machine) and general machines (such as CNC, Turning and milling compound, etc.). A dedicated machine is customized for a specific processing process and has the ability to operate only one process, and general machine is capable of two or more processes. If the production machine in the system has a higher degree of versatility, it shows that the system's inherent ability is higher as well as its flexibility. Machine extensibility refers to the extensibility ability of the production system when facing the introduction of new products. The stronger the expansion capability, the greater flexibility. Production systems in the design phase should not only have the ability to meet the needs of products, processes, and machines for new product production, but also have the ability to respond to environmental changes. In Figure 2, the production system has the ability to respond to changes in demand. For this reason, environmental adaptability is defined as a flexibility dynamic evaluation metric for PSDS. The environmental changes that the production system may encounter include internal and external environmental changes. Changes in the internal environment include device failure, tool wear, transmission congestion, etc. Changes in the external environment include production orders insertion emergency, raw materials insufficient supply, etc. Considering that this paper is a study on the design phase of the production system, we believe that the most likely or predictable environmental change is device failure within the production system. Therefore, the flexibility dynamic evaluation for PSDS mainly studies the response ability of the system to the possible device failure rate. The stronger the capability is, the higher the flexibility level of the system will be.