## 4 Conclusions  
In this paper, the problem of modeling software fault-detection processes and fault-correction processes together with imperfect debugging and testing coverage has been investigated. From the viewpoint of fault amount instead of fault correction time delay, a new SRGT model addressing the fault re-introduction and testing coverage is put forward by introducing the relationship function between the MVF of detected faults and corrected faults. The proposed model is applied to two kinds of data sets: one that contains information not only of detected fault numbers but also corrected fault numbers, and another that contains only detected fault numbers. No matter what kind of data sets, the proposed model gives significantly better goodness-of-fit and prediction results comparing with other existing NHPP models for three real data sets according to four criteria. It should be noted that, though adding more parameters makes the software reliability model  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Model No.**} & \multirow{2}{*}{**Model Name**} & \multicolumn{1}{c}{**80\% OF DS-1**} & \multicolumn{1}{c}{**80\% OF DS-2**} & \multicolumn{1}{c}{**80\% OF DS-3**} \\ \cline{3-5}  & & **SSE** & **SSE** & **SSE** \\ \hline
1 & G-O model(also called \(m_{1}(f)\)) & 823.0713 & 6.7713 \(\times\) 10\({}^{4}\) & 147.2964 \\
2 & \(m_{2}(t)\) & 119.7111 & 7.3709 \(\times\) 10\({}^{3}\) & 356.5743 \\
3 & \(m_{3}(t)\) & 69.0496 & 5.3543 \(\times\) 10\({}^{3}\) & **6.9655** \\
4 & Inflection S-shaped & 750.1803 & 2.7742 \(\times\) 10\({}^{3}\) & 356.5814 \\
5 & Yamada exponential & 401.7862 & 6.0381 \(\times\) 10\({}^{4}\) & 377.2231 \\
6 & Yamada Rayleigh & 197.3302 & 3.4667 \(\times\) 10\({}^{5}\) & 73.4246 \\
7 & Yamada Weibull & 553.6076 & 3.4596 \(\times\) 10\({}^{3}\) & 676.6515 \\
8 & Delayed S-shaped & 69.0496 & 3.5343 \(\times\) 10\({}^{3}\) & **6.9655** \\
9 & HD/G-O & 823.0713 & 6.7713 \(\times\) 10\({}^{4}\) & 356.5818 \\
10 & Yamada imperfect(1) & 823.0770 & 6.7713 \(\times\) 10\({}^{4}\) & 356.5837 \\
11 & Yamada imperfect(2) & 823.0724 & 5.7234 \(\times\) 10\({}^{4}\) & 356.5827 \\
12 & P-Z (1997) model & 595.6770 & 2.8149 \(\times\) 10\({}^{3}\) & 334.1059 \\
13 & Fault removal model (2003) & 286.2138 & 1.9332 \(\times\) 10\({}^{4}\) & 345.1824 \\
14 & P-Z coverage model (2003) & 69.0496 & 3.5343 \(\times\) 10\({}^{3}\) & 1.5362 \(\times\) 10\({}^{3}\) \\
15 & SRGM-3 model (2011) & 549.9081 & 1.1495 \(\times\) 10\({}^{4}\) & 1.2792 \(\times\) 10\({}^{4}\) \\
16 & proposed model & **37.0169** & **236.0253** & 23.0348 \\ \hline \hline \end{tabular}  
* Notes: The bold number means the result of the best SRGM in this column.  
\end{table}
Table 9: Comparison of SRGMs’ predictive power for DS-1, DS-2 and DS-3.  
more complicated and the task of parameter estimation more difficult, by automating the calculations using software tools it is not a critical problem.  
Conceptualization, Q.L. and H.P.; Data Curation, Q.L.; Formal Analysis, Q.L.; Funding Acquisition, Q.L.; Investigation, Q.L.; Methodology, Q.L. and H.P.; Project Administration, Q.L.; Resources, Q.L. and H.P.; Supervision, H.P.; Writing--Review and Editing, H.P. All authors have read and agreed to the published version of the manuscript.  
This research was partly funded by \"National Key Laboratory of Science and Technology on Reliability and Environmental Engineering of China\", grant number \"WDZC2019601A303\".  
Not applicable.  
The authors declare no conflict of interest.