**5. Conclusions**

In this study, a new software reliability model was developed under the assumption that software failures occur in a dependent manner. We used three datasets for our evaluations. The first and second datasets showed the best fit, and the third dataset showed better results compared with many previously proposed models. The proposed model showed better results than DP1, DP2, and DPF, which are previously developed software-dependent failure occurrence models.

In addition, based on the proposed model, the optimal release time according to the change in the cost coefficient was suggested, and the total cost was analyzed accordingly. When the test cost was increased, the release time gradually increased, as did the overall cost; therefore, the optimal release time can be achieved when *C*1 is 20. In the proposed model, fault detection rate *b* was found to be the most important parameter for determining the optimal release time.

In the past, studies were conducted by assuming independence in the case of software failures; however, in a real environment, the software execution environment is extremely diverse and complex. Therefore, it is necessary to develop a model that assumes a dependent failure occurrence and propose a model that considers the actual operating environment. We plan to conduct a study using machine learning and deep learning for the proposed software-dependent failure occurrence in the future work.

**Author Contributions:** Conceptualization, H.P.; Funding acquisition, I.H.C., K.Y.S.; Software, Y.S.K.; Writing—original draft, Y.S.K.; Writing—review and editing, K.Y.S., I.H.C. and H.P. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research was supported by the Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education (NRF-2018R1D1A1B07045734, NRF-2021R1F1A1048592, and NRF-2021R1I1A1A01059842).

**Institutional Review Board Statement:** Not required.

**Informed Consent Statement:** Not applicable. **Data Availability Statement:** Data available in a publicly accessible repository.

**Acknowledgments:** This research was supported by the National Research Foundation of Korea. We are pleased to thank the Editor and the Referees for their useful suggestions.

**Conflicts of Interest:** The authors declare no conflict of interest.
