# Deep-Learning Software Reliability Model Using SRGM as Activation Function
## 4 Numerical Examples
### Results of Dataset 2  
Table 6 lists the estimated parameter values of the SRGM assuming an NHPP using Dataset 2 and the structure of the software reliability model using deep learning. It also shows the estimated parameter values and structure of the proposed deep-learning software reliability model. The parameter \(b\) of the proposed software reliability model was estimated to be 0.76. The structure of the proposed deep-learning software reliability model is the same as that for Dataset 1. Figure 4 shows the computed estimates of \(m(t)\) for each model and deep-learning structure.  
Table 7 presents the results for the 10 criteria based on the estimated values. The proposed deep-learning software reliability model had the best results of 34.9817, 0.9995, 5.9145, 5.9145, 5.9145, 5.9145, 5.8070, 0.9571, and 96.9617 for the MSE, R\({}^{2}\), RMSPE, MAE, MEOP, TS, and PC criteria, respectively, for seven of the ten criteria. Among the recurrent neural networks, LSTM showed the second-best results of 265.2696, 1.6538, 0.9958, 16.2892, 16.1755, 15.8759, 2.6661, and 148.8709 for MSE, PP, R\({}^{2}\), RMSPE, MAE, MEOP, TS, and PC, while RNN showed the best results in PRR. In addition, among the previously proposed SRGMs, PNZ exhibited the best results for all the criteria. For prediction, preSSE yielded the best result of 133.128 for RMD, followed by 146.460 and 174.911 for GO and the proposed model, respectively.  
\begin{table}
\begin{tabular}{c c c c c c c c c c c c} \hline
**No.** & **Model** & **MSE** & **MAE** & **PRR** & **PP** & **R2** & **RMSPE** & **MEOP** & **TS** & **PC** & **preSSE** \\ \hline  
roposed model & 1.5764 & 1.2555 & 0.0173 & 0.0191 & 0.9995 & 1.2555 & 1.2197 & 0.9968 & 8.7077 & 4.728 \\ \hline \end{tabular}
\end{table}
Table 5: Comparison of all criteria from Dataset 1.  
\begin{table}
\begin{tabular}{c c c} \hline
**No.** & **Model** & **Estimation and Structure** \\ \hline
1 & GO & \(\hat{a}=1200.6573\), \(\hat{b}=0.02594\) \\
2 & IS & \(\hat{a}=1090.2373\), \(\hat{b}=0.03435\), \(\hat{b}=0.21312\) \\
3 & ZFR & \(\hat{a}=395.6997\), \(\hat{b}=0.01072\), \(\hat{a}=0.13188\), \\  & \(\hat{\beta}=1.29491\), \(\hat{c}=1.07014\), \(\hat{p}=1.06829\) \\
4 & YID 1 & \(\hat{a}=735.9191\), \(\hat{b}=0.04609\), \(\hat{a}=0.00821\) \\
5 & YID 2 & \(\hat{a}=560.7125\), \(\hat{b}=0.06328\), \(\hat{a}=0.01755\) \\
6 & PZ & \(\hat{a}=0.02306\), \(\hat{b}=0.00172\), \(\hat{a}=0.00172\), \\  & \(\hat{\beta}=0.02247\), \(\hat{c}=0.92125\) \\
7 & PNZ & \(\hat{a}=249.3358\), \(\hat{b}=0.44707\), \\  & & \(\hat{a}=0.05410\), \(\hat{b}=86.96286\) \\
8 & TP & \(\hat{a}=16.13260\), \(\hat{b}=0.01055\), \(\hat{c}=0.07844\), \(\hat{b}=0.00020\), \\  & \(\hat{c}=0.86459\), \(\hat{p}=1.07014\), \(\hat{q}=1.06829\) \\
9 & RMD & \(\hat{a}=53.30543\), \(\hat{b}=0.02660\), \\  & \(\hat{a}=22.98703\), \(\hat{b}=0.01071\) \\
10 & Vub & \(\hat{a}=8.59529\), \(\hat{b}=0.50025\), \(\hat{a}=0.00184\), \\  & \(\hat{\beta}=17.01916\), \(\hat{N}=39,113.5827\) \\
11 & TC & \(\hat{a}=0.07169\), \(\hat{b}=1.02720\), \(\hat{a}=0.32387\), \\  & \(\hat{b}=2.09164\), \(\hat{N}=3111.1052\) \\
12 & 3P & \(\hat{a}=1.44644\), \(\hat{b}=0.00468\), \(\hat{b}=2.31208\), \\  & \(\hat{c}=30.67715\), \(\hat{N}=163.2977\) \\
13 & DPF 1 & \(\hat{a}=912.3438\), \(\hat{b}=0.00016\), \\  & \(\hat{c}=0.56449\), \(\hat{b}=145.4555\) \\
14 & DPF 2 & \(\hat{a}=955.6838\), \(\hat{b}=0.00280\), \\  & \(\hat{c}=34.39205\), \(\hat{b}=177.6015\) \\
15 & UDPF & \(\hat{b}=2.75584\), \(\hat{a}=27.11226\), \\  & \(\hat{\beta}=3.15487\), \(\hat{N}=1490.17003\) \\
16 & DNN & Hidden layer = 4, Optimizer = [PERSON], Epoch = 100 \\
17 & RNN & Difference = 1, Optimizer = [PERSON], Epoch = 100 \\
18 & LSTM & Difference = 1, Optimizer = [PERSON], Epoch = 100 \\
19 & GRU & Difference = 1, Optimizer = [PERSON], Epoch = 100 \\
20 & Proposed model & \(\hat{b}=0.76\), Hidden layer = 4, Optimizer = [PERSON], Epoch = 100 \\ \hline \end{tabular}
\end{table}
Table 6: Parameter estimation and structure of models from Dataset 2.  
Figure 4: Prediction of all models for Dataset 2.