## 3 Product Gene Theory
### Encoding Method of Product Gene  
Definitions described above explained the structure of a product gene unit. To apply it, a reasonable encoding solution is necessary to be established. Focusing on the problem, some typical encoding methods have been developed. For instance, [PERSON] et al. [29] proposed a feature-oriented encoding scheme based on the generalized positioning principle (GPP) by taking the functional surface as the basic gene carrier. [PERSON] et al. [36] presented an encoding approach for part and product series. [PERSON] et al. [5] proposed a two-level quality gene encoding method for quality diagnosis. Looking at the product quality evaluation problem, [PERSON] et al. [2] developed an encoding method based on letters. Large equipment contains a large quantity of heterogeneous quality information. Its encoding method of information should avoid information misunderstanding caused by inconsistent names, descriptions, and classifications to the greatest extent for its excellent application performance. Therefore, based on the principles of uniqueness, classification, high adaptability, integrity, and efficient retrieval, a sectional encoding method is developed in this paper to describe and store the information of elements in the product gene. The characteristics of this method are as follows:  
(1) Each element consists of three segments of data, they are separated with \"#.\" Therefore, an element can be expressed by \(EL=\) (\(ECS\#EVS\#EMS\)), where \(ECS\), \(EVS\), and \(EMS\) represent the codeof an element, the value set of attributes of the element and the metadata set corresponding to _EVS_. Here, the data format of _EVS_ corresponding to an _ECS_ is fixed. _EMS_ describes types of values in corresponding _EVS_. _EVS_ and _EMS_ can be expressed by _EVS_ = (_evs1_, _evs2_,..., _evs6_) and _EMS_ = (_ems1_, _ems2_,..., _ems7_) respectively. If values in _EMS_ are the same, then _EMS_ = _ems_. This approach can effectively reduce the number of encodings. (2) The first segment of each element is encoded according to its information set and element type. The values of the second segment uniformly represented by strings for improving the applicability of the encoding method. Then these values can be appropriately used according to the coding of the last paragraph. Table 1 shows the main data types in _EMS_. Five data types are applied to describe the values of _EVS_ of the product gene. For instance, the information of size and precision are defined with continuous numeric values, the information of measuring methods are defined with option values, the information of capabilities of workers are defined with discrete values, and so on. Assuming what is shown in Figure 5 is the product gene of a bearing spacer, according to the definitions in Table 1, the product gene of this bearing spacer should consist of three gene units. The meanings of codes in _GU_ (1) are explained in Table 2. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Composition of Attribute Code** & **Type of Value** & **Description** \\ \hline \multirow{7}{*}{Code of element\# (values set)\#(metadata set)} & Boolean (_B_) & It can be described by a binary number. \\ \cline{2-3}  & Option (_O_) & There are multiple options to be chosen and only one option can be chosen. \\ \cline{2-3}  & & \begin{tabular}{c} A discrete value is a discontinuous value or it \\ belongs to one of several discrete intervals. \\ \end{tabular} \\ \cline{2-3}  & Continuity (_C_) & \
\begin{tabular}{c} A continuous value is a continuous numeric value \\ which can be computed. \\ \end{tabular} \\ \cline{2-3}  & String (_S_) &
\begin{tabular}{c} A string value is described with a string which \\ consists of one or more characters. \\ \end{tabular} \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Encoding method and data types of product gene. Figure 5: Case data of a product gene of bearing spacer.