# Software Reliability Growth Model with Dependent Failures and Uncertain Operating Environments
## 3 NHPP Software Reliability Growth Model (SRGM)
### Results  
The estimated parameters of the models are listed in Tables 5 and 6 using a least squares estimation (LSE). Tables 7 and 8 show the criteria obtained using the estimated parameters in Tables 5 and 6, the best value for each criteria is shown in bold. In Table 7, the proposed model shows the smallest MSE, the smallest PRR, the smallest PP, the smallest SAE, the largest R\({}^{2}\), the closest-to-zero Bias, the smallest PRV, the smallest RMSPE, the smallest MAE, the smallest MEOP and the closest-to-zero TS at 1.3805, 0.0772, 0.0763, 15.9817, 0.9948, \(-\)0.0021, 1.0832, 1.0832, 0.9401, 0.8879 and 3.9233. Though the AIC and BIC are not the smallest values among all models, the proposed model displays the third= smallest AIC at 78.0915. In particular, the PRR value of DPF2 is the second-smallest value at 0.3333, but the values of other criteria are not good. The overall criteria values of VTUB are not good. When looking at the values of the overall criteria, it can be seen that the goodness of fit of the proposed model is excellent. \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline  
In Table 8, the proposed model shows the smallest MSE and the smallest AIC at 2.7776 and 57.2427, respectively. Though other criteria are not the best values among all models, the proposed model shows the second-largest R\({}^{2}\), the second-smallest BIC, the second-closest-to-zero Bias, the second-smallest PRV, the second-smallest RMSPE, the second-closest-to-zero TS at 0.9920, 59.1823, \(-\)0.0070, 1.4213, 1.4213 and 3.6615, respectively. In particular, DPF1 shows the smallest PRR, the smallest PP, the smallest MAE and the smallest MEOP at 0.0276, 0.0270, 1.5924 and 1.4154, respectively. The VTUB shows the largest R\({}^{2}\), the smallest SAE, the smallest PRV, the smallest RMSPE and the closest-to-zero TS at 0.9925, 12.6030, 1.3688, 1.3704 and 3.5306, respectively. When looking at the values of the overall criteria, it can be seen that the goodness of fit of the proposed model is excellent. What is especially important about this result is that the fit of the proposed model is much better than DPF1, DPF2, and VTUB. In other words, DPF1 and DPF2 assume dependent failures, and VTUB assumes uncertain operating environments. It can be seen that the proposed model takes both assumptions into account and fits the dataset much better. Therefore, it is reasonable to predict the number of failures and conduct software reliability studies (reliability evaluation, release policy, etc.) based on the proposed model rather than DPF1, DPF2, or VTUB. Among the 13 criteria in this paper, the most classic and well used are the MSE, PRR, and PP. Figures 1 and 2 display the three criteria values of the top three models for each dataset. For the criteria--MSE, PRR, PP, AIC, and RMSPE--the smaller the value, the closer the predicted value of the model is to the actual value, relative to other models on the same dataset. For dataset 1 (See Figure 1), the proposed model displays the smallest MSE, the smallest PRR and the smallest PP at 1.3805, 0.0772, and 0.0763, respectively. For dataset 2 (see Figure 2), the proposed model displays the smallest MSE and the smallest AIC at 2.7776 and 57.2427, respectively. The VTUB displays the smallest RMSPE at 1.3704.