## 5 Numerical Illustration
\begin{table}
\begin{tabular}{c c c c c c c c c c c c c c c c} \hline \hline _P.No._ & \(A\) & \(B\) & \(X1\) & \(Y1\) & \(tmin\) & \(tmax\) & \(M1\) & \(M2\) & \(M3\) & \(M4\) & \(M5\) & \(M6\) & \(M7\) & \(M8\) & \(M9\) & \(M10\) \\ \hline \(P1\) & 2.5 & 0.22 & 4.7 & 1.3 & 0.030 & 0.09 & 1.3 & 1.2 & 0 & 0.8 & 0.9 & 0 & 1.3 & 0 & 0.7 & 0 \\ \(P2\) & 3.9 & 0.18 & 3.8 & 0.8 & 0.020 & 0.07 & 0.9 & 0 & 0.75 & 0.82 & 0 & 1.2 & 1 & 0 & 1.8 & 1.6 \\ \(P3\) & 2.9 & 1.23 & 4.1 & 1.5 & 0.030 & 0.13 & 0 & 1.3 & 1.1 & 0 & 1.4 & 0 & 1.4 & 0 & 0 & 0.9 \\ \(P4\) & 3.9 & 2.15 & 3.9 & 2 & 0.009 & 0.10 & 0 & 1.1 & 0 & 1.7 & 0 & 1.6 & 1 & 1.7 & 0 & 0 \\ \(P5\) & 1.7 & 1.09 & 3.1 & 0.6 & 0.020 & 0.14 & 0 & 0.7 & 1.1 & 0 & 0 & 1.8 & 0 & 0.8 & 0 & 1.5 \\ \(P6\) & 2.3 & 1.22 & 2.1 & 0.9 & 0.010 & 0.13 & 1.8 & 0 & 1.7 & 0 & 0.9 & 0 & 1.3 & 0 & 0.9 & 0 \\ \(P7\) & 1.7 & 0.4 & 4.2 & 1.2 & 0.007 & 0.15 & 1.7 & 0 & 1.2 & 0 & 1 & 1.8 & 1.7 & 1.1 & 0.9 & 0 \\ \(P8\) & 3.2 & 1.1 & 2.9 & 1.1 & 0.010 & 0.15 & 0.8 & 0 & 1 & 1.7 & 0 & 1.4 & 1.1 & 0 & 1 & 1.6 \\ \(P9\) & 2.1 & 0.08 & 5.2 & 1.7 & 0.030 & 0.17 & 0 & 1.1 & 0 & 0.7 & 1.8 & 0 & 1.1 & 0 & 0 & 0.8 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Cost and time function constants of each process of knuckle joint assembly. Figure 8: Knuckle joint assembly (KJA). \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Name of the Component** & **Dimension No.** & **Operation/Sub-Stage No.** & **Tolerance Symbol** & **Tolerance Stack-Up** \\ \hline Width of fork top & \(d1\) & \(O1\) & \(t_{d1}\) & \(t_{O1}\) \\ Dimension of fork space & \(d2\) & \(O2\) and \(O3\) & \(t_{d2}\) & \(t_{O2}+t_{O3}\) \\ Width of bottom fork & \(d3\) & \(O4\) & \(t_{d3}\) & \(t_{O4}\) \\ Center distance of hole in spacer & \(d4\) & \(O5\) and \(O6\) & \(t_{d4}\) & \(t_{O5}+t_{O6}\) \\ Center distance of hole in pin & \(d5\) & \(O7\) and \(O8\) & \(t_{d5}\) & \(t_{O7}+t_{O8}\) \\ Width of collar & \(d6\) & \(O9\) and \(O10\) & \(t_{d6}\) & \(t_{O9}+t_{O10}\) \\ Critical dimension 1 & \(\gamma 1\) & \(t_{Y1}\) & \(t_{Y2}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Dimension and tolerance symbol of knuckle joint assembly. The convergence plot for tolerance cost and machining time for stopping criteria considered as 100 iterations are shown in Figure 9. The Pareto optimal solution for a sample run is shown in Figure 10. The tolerance cost and machining time for 31 runs are presented in Table 11. Out of these 31 runs, the best value is calculated using EDAS and CODAS multi-criteria decision-making techniques implemented by Adali & Tus (2019) [53]. The appraisal score (APS) and the assessment score (AS) obtained by implementing EDAS and CODAS method are presented in Table 11. Run number (_R.No._) 11 has the highest APS value in EDAS, and run number 7 has the highest AS value in CODAS (Highlighted in Table 11). The optimum allocated tolerances of each sub-stage are presented for both methods and are listed in Table 12, along with the tolerance cost and machining time for the required sub-assembly tolerances of 0.55 mm and 0.22 mm. The optimum total tolerance cost and total machining time are presented in Table 13 for the given sub-assembly tolerance values with the constraint of available machine time. \begin{table}
\begin{tabular}{c c c c c c c c c c c c c c c c c c  
Table 14 shows the machine engagement times of the individual machines to manufacture the knuckle joint assembly within the available machine time. For supporting the proposed method, the statistical analysis for EDAS and CODAS methods are executed through Minitab software. The statistical analysis results and probability plots for both the methods are presented in Figure 11. The probability values are 0.329 and 0.231 for the EDAS and CODAS methods, respectively. Since the value of probability is greater than 0.005 in both cases, it is clearly understood that the results obtained in 31 runs are from normally distributed data. Figure 10: Optimum Pareto front solutions. Figure 9: Convergence plot for tolerance cost and machining time.