Software has become a vital factor in the fourth industrial revolution. Owing to the increase in demand for software products in various fields (big data, artificial intelligence, the Internet of Things, etc.), the software industry has expanded more than ever before. Therefore, software reliability has become very important, and efforts are being made to increase it. One of these efforts is the development of software reliability models (SRMs). SRMs have been studied for a long time as a model that predicts software reliability by using the number of software faults. Software failures can occur for several reasons, including independent software faults such as code errors and software hangs, as well as dependent cases where code errors lead to other software faults. Recently, due to the diversity of software operating environments, software faults are more likely to occur in a dependent manner, and, for this reason, they are likely to increase rapidly from the beginning and progress slowly to the maximum number thereafter. In addition, many large companies have focused on open-source software (OSS) development, and OSS is being developed by many users. In this study, we propose a new SRM that considers the number of finite faults and dependent faults, and examine the goodness-of-fit of a new SRM and other existing non-homogeneous Poisson process models based on the OSS datasets. Through numerical examples, the proposed model demonstrated a significantly better goodness-of-fit when compared to other existing models, and it also exhibited better results on the newly proposed integrated criteria.