## 5 Conclusions  
This study introduced a new type of NHPP software reliability model that simultaneously assumes uncertainty in the operating environment and dependent failure occurrence. Unlike previous studies, this study extends the range of failures that can occur in complex and diverse software by presenting a model that can predict the probability of occurrence in various environments. In addition, to demonstrate the effectiveness of the developed software reliability model, an \(MCDM\) using the maximum value, which can be interpreted in various manners. This method evaluates the effectiveness of a model through a comprehensive interpretation because when assessing the effectiveness of a model based on each criterion, it is particularly useful when multiple models perform well across individual criteria. In an analysis with 15 models across two datasets, it was showed that in Dataset 1, the proposed model performed best on all criteria, and in Dataset 2, the existing \(MCDM\) showed the third-best result, whereas the newly proposed \(MCDM\) showed the best result. Therefore, the \(MCDM\), which improves the existing \(MCDM\) method, can increase the level of comparison by considering both quantitative and qualitative evaluations. The sensitivity analysis was conducted to compare the changes in the mean value function \(m(t)\) due to changes in the parameters for the two datasets. The changes for \(N\) showed a trend of increasing variation as the value increases, \(\alpha\) showed a relatively small variation compared to other parameters, and \(\beta\) showed a trend of decreasing variation as the value increases. The changes in the mean value function \(m(t)\), that is, the impact on software  
Figure 7: Results of sensitivity analysis for changes in parameters in dataset 2. (**a**) parameter \(N\); (**b**) parameter \(\alpha\); (**c**) parameter \(\beta\); (**d**) parameter \(\gamma\).  
failure prediction owing to changes in the parameters included in the model, varied per parameter and showed changes with common characteristics.  
With the development of the software industry, the complexity and diversity of software have led to various software failures. Research on assumptions such as dependent failures and operating environment uncertainties is underway to predict these failures. Further research should be conducted based on additional assumptions to extend these studies. This study proposes a model with multiple assumptions, and there is a possibility of errors when these assumptions are changed. Therefore, additional research is required on generalizable software reliability models to predict software failure.  
Conceptualization, H.P.; Funding acquisition, Y.S.K. and K.Y.S.; Software, Y.S.K.; Writing--original draft, Y.S.K. and K.Y.S.; 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.  
This research was supported by the Global-Learning & Academic Research Institution for Master's and Ph.D. students and a Postdocs (LAMP) Program of the National Research Foundation of Korea (NRF) grant funded by the Ministry of Education (No. RS-2023-00285353).  
Not applicable.  
Data Availability Statement: Data are available in a publicly accessible repository.  
This study was supported by the National Research Foundation of Korea.  
The authors declare no conflicts of interest.