## 5 Numerical Illustration
Using Equations (2) and (3), the tolerance cost and machining time are calculated for each operation with alternative processes and its corresponding best machine is shown in Figure 5. In all 11 combinations of alternative processes, the same tolerance mentioned in case 1 and case 2 by [PERSON] et al. (2013) is assumed for each operation. The alternative process and its corresponding machine-allocated tolerance of each sub-stage/operation and its tolerance cost and machining time are presented in Tables 2 and 3. The best result is shown as shaded text in both Tables 2 and 3. Figures 6 and 7 show a comparison of the tolerance cost and machining time for the existing problem presented in [PERSON] et al. (2013) and the proposed method; it can be seen that the proposed method works well, considering tolerance cost, machining time, and both as objective functions. Figure 5: Best machine for process of each operation/sub-stage after implementation of the first stage. \begin{table}
\begin{tabular}{c c c c c c c c c c c} \hline \hline  & \multicolumn{1}{c}{**Process No. (Machine No.) Table 10 in [PERSON] et al. (2013) Case 1**} & & & & & & & & \\ \hline  & \multicolumn{1}{c}{**O1**} & \multicolumn{1}{c}{**O2**} & \multicolumn{1}{c}{**O3**} & \multicolumn{1}{c}{**O4**} & \multicolumn{1}{c}{**O5**} & \multicolumn{1}{c}{**O6**} & \multicolumn{1}{c}{**O7**} & \multicolumn{1}{c}{**O8**} & & & \\ \hline  & \multicolumn{1}{c}{**0.060784**} & \multicolumn{1}{c}{**0.061882**} & \multicolumn{1}{c}{**0.039412**} & \multicolumn{1}{c}{**0.041831**} & \multicolumn{1}{c}{**0.055569**} & \multicolumn{1}{c}{**0.070471**} & \multicolumn{1}{c}{**0.062745**} & \multicolumn{1}{c}{**0.056824**} & & \\ \hline
1 & 1(1) & 1(1) & 2(2) & 3(1) & 1(1) & 2(2) & 3(1) & 1(1) & 35.15 & 75.64 & 83.41 \\
2 & 1(1) & 1(1) & 2(2) & 3(1  
Table 4 represents the % of savings in both tolerance cost and machining time as compared to the existing method and the proposed method. Case Study 2: Knuckle Joint Assembly  
In practice, the availability of machine time will restrict the selection of the machine for performing a process, which will influence the tolerance cost and machining time. Therefore, in this work, the available machine time is considered as a constraint in selecting the machine. The methodology is demonstrated using a knuckle joint assembly (Figure 8), consisting of six components performed in ten sub-stages. Two critical dimensions are considered for the proper functioning of the product. It is assumed that nine processes are performed using ten machines. Equations (16) and (17) are used to determine the critical dimension, and the tolerances of the critical dimensions are estimated using Equations (18)-(21). Table 5 shows the dimensions, sub-stages, tolerance symbols, and tolerance stake-up of the knuckle joint assembly. Figure 5.0  
Figure 5.1  
Figure 5.2  
Figure 5.3  
Figure 5.4  
Figure 5.5  
Figure 5.6 \begin{table}
\begin{tabular}{c c c c} \hline
**Details** & **Case 1** & & **Case 2** \\ \hline Existing Method & 37.32 & 68.21 & 35.72 & 68.90 \\ Proposed & 36.30 & 57.74 & 33.50 & 54.90 \\ Method & 2.73 & 15.35 & 6.22 & 20.32 \\ \hline \end{tabular}
\end{table} 
Table 4: % Savings in tolerance cost and machining time. Figure 7: Comparison of machining time of the proposed method with the existing problem presented in [PERSON] et al. (2013). \[T=\sum_{i=1}^{no}MT_{i} \tag{23}\]  
Table 6 shows the cost and time function constants of each process of the knuckle joint assembly. The possible operation-process and process-machine feasibility matrix and the available time of the individual machines are presented in Tables 7 and 8, respectively.