## 3 System Flexibility Digital Representation
### Flexibility Definition and Analysis
[PERSON] [28] believes that labor flexibility enables labor to be exposed to a wide range of manufacturing tasks and can expand the skill and knowledge warehouse of labor. Therefore, hybrid flexibility and labor flexibility are taken as the characteristics of product innovation study. Real-time capability, quality of service, adaptive range and user interaction were considered by [PERSON] [29] as evaluation indexes for system reconfigurable flexibility, and a digital evaluation model is constructed to quantify the index by focusing on the fault compensation capability of the system. According to the definition for system flexibility, the production system flexibility in the scheme design phase is mainly manifested as the ability of the production system to meet the demand for producing new products. The system flexibility level is reflected by the system's inherent capability, which can be obtained by analyzing the system structural attributes. Therefore, the Unified Modelling Language (UML) is utilized to construct the system descriptive metamodel to describe system generic attribute information in the design phase by presenting the attribute information of different system components and the relationship between them. UML can standardize and visualize the whole process of entities, properties, relations, structures, states and dynamic changes of things [30,31]. Furthermore, UML provides mechanisms that enable new kinds of modelling elements to be defined and also enable relate the information to new modelling elements [32,33]. In the design phase, the most basic and important components include: product component, process component and machine component [34]. System descriptive metamodel describes system generic attribute information in the dimension of product, process and machine in Figure 2. In Figure 2, 1.. * indicates that there is at least one instance, 1 indicates that only one instance can be created. The product component covers the whole product information of the production system, and the basic building block is the product variety. A product component consists of one or more product varieties, and these product varieties belong to different product families. The process component reflects the process operation information, including the process operation capacity, process operation sequence, etc. The machine component covers all machine-able equipment types, machine processing capacity, machine layout, machine conversion capacity and other machine information owned by the production system. Therefore, combining with the specific description of production system structural attributes, this paper puts forward the static characteristic evaluation metrics for production system flexibility from product, process, and machine dimension. The product dimension metrics include: number of product varieties, product similarity. The process dimension metrics consist of process changeability and process conversion capacity. Machine dimension metrics comprise machine versatility and machine extensibility. The definition of the metrics is described in Table 1, and the relationship between static evaluation metrics and system flexibility is also shown. According to the production system flexibility definition in the design phase and the system characteristic performance, only the product similarity metrics are inversely proportional to the system flexibility. Product similarity represents the structure between the types of products that the production system can produce. The higher the similarity between the products that the production system can produce, the lower the capacity of the production system to produce different kinds of products. Other characteristic metrics are proportional to the system flexibility.