## 4 Numerical Examples
### Analysis and Discussion of Model Performance Comparison Using LSE Estimation Parameter Values
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Model** & **Parameter Estimation Values** & \(\textit{MSE}_{\textit{predict}}\) & \(\textit{RMSE}_{\textit{predict}}\) & \(\textit{TS}_{\textit{predict}}\) & \(\textit{Bias}_{\textit{predict}}\) \\ \hline G-O model & \(a=4246.8\); \(b=0.000014\) & 1605.8 & 40.07 & 82.26 & 5.68 \\ \hline Delayed S-shaped model & \(a=57,610\); \(b=0.000147\) & 1221.5 & 34.95 & 71.75 & 4.9 \\ \hline Inflection S-shaped model & \(a=62.975\); \(b=0.040457\); \(\beta=705.52\) & 563.23 & 23.73 & 48.72 & 3.22 \\ \hline Yamada Imperfect-2 model & \(a=61.613\); \(b=0.00053\); \(a=0.019075\) & 1394.8 & 37.35 & 76.67 & 5.26 \\ \hline P-N-Z model & \(a=208.37\); \(b=0.014731\); \(\beta=121.27\); \(a=0.002079\) & 1073.1 & 32.76 & 67.25 & 4.57 \\ \hline Weibull distribution model & \(a=67.157\); \(b=0.000034\); \(c=1.7283\) & 1364.8 & 36.94 & 75.84 & 5.2 \\ \hline Wang model & \(a=220\); \(b=0.006693\); \(\beta=1.6576\); \(d=0.65349\) & 1913.5 & 43.74 & 89.8 & 6.26 \\ \hline Li model & \(a=220\); \(b=0.007648\); \(\phi=0.070065\); \(N=0.73774\) & 1766.1 & 42.02 & 86.27 & 5.99 \\ \hline PM & \(a=102\); \(b=0.047586\); \(\theta=0.32252\); \(d=0.15255\); & **9.13** & **3.02** & **6.2** & **0.39** \\ \hline \hline \end{tabular}
\end{table} 
Table 20: Model performance comparison using 85% of the data (DS3-3). \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Model** & **Parameter Estimation Values** & \(\textit{MSE}_{\textit{predict}}\) & \(\textit{RMSE}_{\textit{predict}}\) & \(\textit{TS}_{\textit{predict}}\) & \(\textit{Bias}_{\textit{predict}}\) \\ \hline G-O model & \(a=4246.8\); \(b=0.000014\) & 1605.8 & 40.07 & 82.26 & 5.68 \\ \hline Delayed S-shaped model & \(a=57,610\); \(b=0.000147\) & 1221.5 & 34.95 & 71.75 & 4.9 \\ \hline Inflection S-shaped model & \(a=62.975\); \(b=0.040457\); \(\beta=705.52\) & 563.23 & 23.73 & 48.72 & 3.22 \\ \hline Yamada Imperfect-2 model & \(a=61.613\); \(b=0.00053\); \(a=0.019075\) & 1394.8 & 37.35 & 76.67 & 5.26 \\ \hline P-N-Z model & \(a=208.37\); \(b=0.014731\); \(\beta=121.27\); \(a=0.002079\) & 1073.1 & 32.76 & 67.25 & 4.57 \\ \hline Weibull distribution model & \(a=67.157\); \(b=0.000034\); \(c=1.7283\) & 1364.8 & 36.94 & 75.84 & 5.2 \\ \hline Wang model & \(a=220\); \(b=0.006693\); \(\beta=1.6576\); \(d=0.65349\) & 1913.5 & 43.74 & 89.8 & 6.26 \\ \hline Li model & \(a=220\); \(b=0.007648\); \(\phi=0.070065\); \(N=0.73774\) & 1766.1 & 42.02 & 86.27 & 5.99 \\ \hline PM & \(a=102\); \(b=0.047586\); \(\theta=0.32252\); \(d=0.15255\); & **9.13** & **3.02** & **6.2** & **0.39** \\ \hline \hline \end{tabular}
\end{table} 
Table 18: Model performance comparison using 85% of the data (DS3-1). \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Model** & **Parameter Estimation Values** & \(\textit{MSE}_{\textit{predict}}\) & \(\textit{RMSE}_{\textit{predict}}\) & \(\textit{TS}_{\textit{predict}}\) & \(\textit{Bias}_{\textit{predict}}\) \\ \hline G-O model & \(a=3600\); \(b=0.000513\) & 29.79 & 5.46 & 1.41 & 0.73 \\ \hline Delayed S-shaped model & \(a=408.41\); \(b=0.015366\) & 1659.2 & 40.73 & 10.52 & 6.11 \\ \hline Inflection S-shaped model & \(a=2159.8\); \(b=0.001081\); \(\beta=0.25076\) & 51.27 & 7.16 & 1.85 & 0.99 \\ \hline Yamada Imperfect-2 model & \(a=156.87\); \(b=0.012401\); \(a=0.010266\) & 83.56 & 9.14 & 2.36 & 1.27 \\ \hline P-N-Z model & \(a=1013.5\); \(b=0.00246\); \(\beta=0.33974\); \(\alpha=0.00095\) & 58.24 & 7.63 & 1.97 & 0.97 \\ \hline Weibull distribution model & \(a=13,594\); \(b=0.00048\); \(c=0.73826\) & 1788.6 & 42.29 & 10.92 & 6.41 \\ \hline Wang model & \(a=220\); \(b=0.00395\); \(\beta=2.6086\); \(d=1.4774\) & 8394.4 & 91.62 & 23.66 & 13.84 \\ \hline Li model & \(a=520\); \(b=0.022143\); \(\phi=0.62431\); \(N=1.3252\) & 33,109 & 181.96 & 46.99 & 27.56 \\ \hline PM & \(a=400.01\); \(b=0.003037\); \(\theta=0.013051\); \(d=0.72174\); & **28.75** & **5.36** & **1.38** & **0.61** \\ \hline \hline \end{tabular}
\end{table} 
Table 19: Model performance comparison using 85% of the data (DS3-2).