# Integrated Design of Process-Tolerance for Remanufacturing Based on Failure Feature
## 2 Materials and Methods
### Feasible Process Plans Generation
#### 2.2.3 Feasible Process Plans Generation Based on CBR  
CBR realizes retrieval by calculating the similarity between new cases and existing cases. The similarity can be divided into local similarity and global similarity, where the local similarity is the similarity between two attributes, and the global similarity is the similarity between two cases. The relationship between local similarity and global similarity is as Equation (1). \[sim(N,E)=\sum_{i=1}^{n}\omega_{i}sim\Big{(}c_{i}^{N},c_{i}^{E}\Big{)} \tag{1}\]  
where \(N\) is the new case and \(E\) is the existing case; \(n\) is the number of influence factors; \(c_{i}^{N}\) and \(c_{i}^{E}\) are the \(i\)th factors of new case and existing case respectively; \(sim(c_{i}^{N},c_{i}^{E})\) is the local similarity of \(i\)th factors between new case and existing case; \(\omega_{i}\) is the weight of \(i\)th factors, which obtained by experts through AHP, the specific process can be referred to [21]. For local similarity, different data types require different calculation methods. Therefore, data of matching set \(G_{i}\) are divided into three types: numerical data, enumerated data, and character data, and their corresponding similarity calculation models are established. 1. Numerical data similarity calculation model. Numerical data consist of a series of continuous values in an interval (such as failure quantification). The similarity calculation model of numerical data is given by Equation (2). \[sim(c_{i}^{N},c_{i}^{E})=1-\frac{|c_{i}^{N}-c_{i}^{E}|}{max(c_{i})-min(c_{i})} \tag{2}\] \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Failure Feature** & \begin{tabular}{c} **Volumetric Damage** \\ **Amount Interval** \\ \end{tabular} & \
\begin{tabular}{c} **Quantified Score** \\ **Equation** \\ \end{tabular} &
\begin{tabular}{c} **Quantified Score** \\ **Interval [0, 10]** \\ \end{tabular} \\ \hline \multirow{4}{*}{Wear} & 0 & — & 0 \\  & \(0\leq x\leq 1.5\) mm & \(q=\frac{x-0}{1.5-0}\times 5\) & \((0,5)\) \\  & \(1.5\) mm \(\leq x\leq 3.0\) mm & \(q=\frac{x-1.5}{30-15}\times 5+5\) & \([5,10)\) \\  & \(x\geq 3.0\) mm & 10 & 10 \\ \hline \multirow{4}{*}{Corrosion} & 0 & — & 0 \\  & \(0\leq x\leq 1.3\) mm & \(q=\frac{x-0}{1.3-0}\times 5\) & \((0,5)\) \\  & \(1.3\) mm \(\leq x\leq 2.6\) mm & \(q=\frac{x-1.3}{2.6-1.3}\times 5+5\) & \([5,10)\) \\  & \(x\geq 2.6\) mm & 10 & 10 \\ \hline \multirow{4}{*}{Crack} & 0 & — & 0 \\  & \(0\leq x\leq 1.5\) mm & \(q=\frac{x-0}{15-0}\times 5\) & \((0,5)\) \\ \cline{1-1}  & \(1.5\) mm \(\leq x\leq 3.0\) mm & \(q=\frac{x-1.5}{30-15}\times 5+5\) & \([5,10)\) \\ \cline{1-1}  & \(x\geq 3.0\) mm & 10 & 10 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: The failure quantification standard of used gearbox. where \(max(c_{i})\) and \(min(c_{i})\) are the maximum and the minimum values that can be obtained in all cases of \(c_{i}\), respectively. 2. Enumerated data similarity calculation model. Enumerated data consist of a series of discrete values in an interval (such as surface dimension). The size of the failure surface (very small, small, medium, large, very large) can be represented by discrete data (0.1, 0.3, 0.5, 0.7, 0.9, respectively). The similarity calculation model of enumerated data is given by Equation (3). \[sim(c_{i}^{N},c_{i}^{E})=1-\frac{\left|c_{i}^{N}-c_{i}^{E}\right|}{H_{i}} \tag{3}\]  
where \(H_{i}\) is the maximum discrete values that can be obtained in all cases of \(c_{i}\). 3. Character data similarity calculation model. Character data calculate the local similarity through the complete matching of keywords (such as surface shape, material, etc.). When the keywords are matched, the local similarity is 1, otherwise the local similarity is 0. The similarity calculation model of enumerated data is given by Equation (4). \[sim(c_{i}^{N},c_{i}^{E})=\left\{ \begin{array}{cc}1&c_{i}^{N}=c_{i}^{E}\\ 0&c_{i}^{N}\
eq c_{i}^{E}\end{array} \right.