## 4 Results  
### Comparison of Goodness of Fit  
We estimate the parameter of all nine models at \(\mathrm{t_{1},t_{2},\ \ldots,t_{13}=\{1249,\ 4721,\ \ldots 58,633\}}\) from data set 1. The parameters of all nine models were also estimated at \(\mathrm{t_{1},t_{2},\ \ldots,t_{19}=\{1,\ 2,\ \ldots,\ 19\}}\) from data set 2. Then, we use the least squares estimation (LSE) method with Matlab and R. Table 4 summarizes the parameters estimated for all the SRGMs in Table 1. Tables 5 and 6 compare all the models using the criteria presented in Section 2, for both data sets. For the reasons mentioned above, except for \(\mathrm{R}^{2}\), to have smaller values in most of the criteria is considered better. On the contrary, the larger the value of \(\mathrm{R}^{2}\) is, the better.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Model** & **Data Set 1** & **Data Set 2** \\ \hline GO & a = 33.01, \(\mathrm{b}=0.000058\) & a = 104.806, \(\mathrm{b}=0.0131\) \\ DS & a = 31.013, \(\mathrm{b}=0.000144\) & a = 28.34, \(\mathrm{b}=0.156\) \\ IS & a = 33.009, \(\mathrm{b}=0.000058,\ \beta=0.00001\) & a = 30.71, \(\mathrm{b}=0.137,\ \beta=3.152\) \\ YID & a = 33.009, \(\mathrm{b}=0.000058,\ \alpha=0.0000001\) & a = 42.489, \(\mathrm{b}=0.03,\ \alpha=0.027\) \\ PNZ & a = 32.74, \(\mathrm{b}=0.00006\) & a = 30.589, \(\mathrm{b}=0.138\) \\ \(\alpha=0.000001,\ \beta=0.002\) & \(\alpha=0.00001,\ \beta=3.179\) \\ PZ & a = 33.008, \(\mathrm{b}=0.000058\) & a = 0.00001, \(\mathrm{b}=0.138\) \\ \(\alpha=10.000,\ \beta=0.000,\ c=0.001\) & \(\alpha=0.00001,\ \beta=3.179,\ c=30.595\) \\ DP2 & a = 62.32, \(\mathrm{y}=0.000004\) & \(\alpha=867.712,\ \mathrm{y}=0.011\) \\  & m\({}_{0}=15.200,\ \mathrm{t_{0}}=0.000\) & m\({}_{0}=4.999,\ \mathrm{t_{0}}=0.173\) \\  & a = 0.0099, \(\mathrm{b}=0.721\) & a = 0.071, \(\mathrm{b}=1.218,\ \alpha=1294.000\), \\  & \(\alpha=1.001,\ \beta=61.100,\ \mathrm{N}=52.24\) & \(\beta=2555.000,\ \mathrm{N}=44.940\) \\ New model & a = 0.001, \(\mathrm{b}=1.502,\ \alpha=0.414\), & a = 0.001, \(\mathrm{b}=6.169,\ \alpha=0.179\), \\  & \(\beta=9125.8,\ \mathrm{t_{0}}=151.304,\ \mathrm{N}=39.171\) & \(\beta=75096,\ \mathrm{t_{0}}=0.001,\ \mathrm{N}=25.744\) \\ \hline \hline \end{tabular}
\end{table}
Table 4: Estimation of parameters for both data sets.  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Index** & **Time** & **Failure** & **Cum. Failure** & **Index** & **Time** & **Failure** & **Cum. Failure** \\ \hline
1 & 1249 & 4 & 4 & 8 & 40,594 & 4 & 30 \\
2 & 4721 & 6 & 10 & 9 & 49,476 & 1 & 31 \\
3 & 8786 & 4 & 14 & 10 & 55,596 & 0 & 31 \\
4 & 13,669 & 3 & 17 & 11 & 58,061 & 1 & 32 \\
5 & 19,094 & 6 & 23 & 12 & 58,588 & 1 & 33 \\
6 & 24,750 & 1 & 24 & 13 & 58,633 & 0 & 33 \\
7 & 32,299 & 2 & 26 & - & - & - & - \\ \hline \hline \end{tabular}
\end{table}
Table 2: Data set 1.  
In Table 5, the values for the new model of MSE, PRR, PP, SAE, PRV, and RMSPE are the lowest in comparison with those of the other models. Furthermore, the R\({}^{2}\) value is 0.9937, which is the largest. Although the value of AIC is not the lowest among the values of all the SRGMs, we can safely say that the proposed model is sufficient to fit better than the other SRGMs for data set 1.  
In Table 6, in the values of the new model, it can also be seen that its value of AIC is not the smallest among those of all the SRGMs. However, the values of MSE, PRR, PP, SAE, PRV, and RMSPE for the proposed model are significant. In general, when all the values are considered, the new model proposed in this work is the optimal among all the SRGMs for data set 2.