# Prediction and Comparative Analysis of Software Reliability Model Based on NHPP and Deep Learning
## 3 Numerical Example
### Results
#### 3.3.2 Results of Dataset 2
** & **Model** & **80\%** & **90\%** \\ \hline
1 & GO & \(\hat{a}=15383.72\), \(\hat{b}=0.00010\) & \(\hat{a}=37605.84\), \(\hat{b}=0.00005\) \\ \hline
2 & DS & \(\hat{a}=13332.14\), \(\hat{b}=0.00182\) & \(\hat{a}=53880.83\), \(\hat{b}=0.00091\) \\ \hline
3 & YID & \(\hat{a}=49.407\), \(\hat{b}=0.00121\), \(\hat{a}=0.66627\) & \(\hat{a}=10.855\), \(\hat{b}=0.00145\), \(\hat{a}=2.7890\) \\ \hline
4 & PZ & \(\hat{a}=564.590\), \(\hat{b}=0.2938\), \(\hat{a}=0.35523\), \(\hat{a}=0.35523\), \(\hat{a}=3566157.77\), \(\hat{b}=0.02095\), \(\hat{a}=0.14865\), \(\hat{b}=119107.58\), \(\hat{c}=3567.64\) \\ \hline
5 & PNZ & \(\hat{a}=166.155\), \(\hat{b}=0.01033\), \(\hat{a}=284.863\), \(\hat{b}=0.01104\), \(\hat{a}=0.06270\), \(\hat{b}=4.225\) & \(\hat{a}=0.07397\), \(\hat{b}=11.590\) \\ \hline
6 & TP & \(\hat{a}=4.1953\), \(\hat{b}=0.08837\), \(\hat{a}=49.417\), \(\hat{b}=0.06702\), \(\hat{a}=7.3884\), \(\hat{b}=2.8696\), \(\hat{a}=0.01198\), \(\hat{b}=0.02904\), \(\hat{c}=1.6579\), \(\hat{b}=0.04236\), \(\hat{b}=0.10460\) & \(\hat{c}=2.4430\), \(\hat{b}=0.20147\), \(\hat{q}=0.20537\) \\ \hline
7 & TC & \(\hat{a}=0.01344\), \(\hat{b}=1.9930\), \(\hat{a}=0.00754\), \(\hat{a}=0.00307\), \(\hat{b}=2.22599\), \(\hat{b}=0.39594\), \(\hat{b}=2857.101\) & \(\hat{a}=4.7647\), \(\hat{b}=118.747\), \(\hat{b}=73382.23\) \\ \hline
8 & Vtub & \(\hat{a}=1.0005\), \(\hat{b}=2.2792\), \(\hat{a}=0.00754\), \(\hat{a}=1.0128\), \(\hat{b}=1.1078\), \(\hat{a}=16.018\), \(\hat{b}=0.39594\), \(\hat{b}=1562.143\) & \(\hat{b}=1060.760\), \(\hat{b}=2049.573\) \\ \hline
9 & DPF & \(\hat{a}=322.915\), \(\hat{b}=0.00018\), \(\hat{a}=994.419\), \(\hat{b}=0.00005\), \(\hat{c}=0.33127\), \(\hat{h}=6.4475\) & \(\hat{c}=0.57131\), \(\hat{h}=10.012\) \\ \hline
10 & UDPF & \(\hat{b}=652.600\), \(\hat{a}=21497.41\), \(\hat{b}=13.526\), \(\hat{a}=2439.458\), \(\hat{b}=8.9936\), \(\hat{b}=1804.06\) & \(\hat{b}=10.564\), \(\hat{b}=192350.3\) \\ \hline
11 & DNN & \(\alpha=0.000001\Table 6 shows the result values of the criteria using 80% of Dataset 2. The values of MSE, MAE, PRV, RMSPE, MEOP, TS, and PC in GRU were the lowest at 4.5494, 2.0688, 0.5218, 2.1336, 2.0489, 2.2311, and 79.0128, respectively, and R\({}^{2}\) of 0.9988 in GRU and LSTM appeared the highest. PRR showed the lowest value of 1.5342 in DNN, and PP showed the smallest value of 1.7716 in TP. In GRU, 8 out of 10 criteria showed good results. Among the software reliability models assuming NHPP, the model with the lowest result was the Vtub model, with a preSSE value of 159,551.23. In contrast, most software reliability models using deep learning showed smaller values than the existing software reliability models; among them, the RNN model showed the smallest value of 71.06. Table 7 shows the result values for the criteria using 90% of Dataset 2. MSE, PRV, RMSPE, TS, and PC showed the smallest values of 8.8655, 0.9189, 2.9787, 2.3336, and 1237.5573, respectively, in GRU, and R\({}^{2}\) showed the largest value of 0.9988 in the same model. MAE and MEOP had the smallest values of 2.8168 and 2.7928, respectively, in RNN. PRR was 1.6236 in DNN, and PP was the smallest at 1.4301 in Vtub. In GRU, 6 out of 10 criteria showed good results. Regarding the preSSE value, the GRU model showed the smallest value of 468.03 among the software reliability models using deep learning. Figures 3 and 4 are graphs that combine the estimated and trained values for 80% and 90% of the data above with the predicted values for the remaining 20% and 10%. The points