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Network technologies have made rapid progress with the dissemination of computer systems in all areas. The current software development environment has been changing into new development paradigms such as concurrent distributed development environment and the so-called open source project by using network computing technologies. Especially, OSS (Open Source Software) systems which serve as key components of critical infrastructures in the society are still ever-expanding now. We focus on OSS developed under open source project. In case of considering the effect of the debugging process on an entire system in the development of a method of reliability assessment for open source project, it is necessary to grasp the deeply-intertwined factors, such as programming path, size of each component, skill of fault reporter, and so on. In order to consider the effect of each software component on the reliability of an entire system under such open source software development, we propose a new approach to software reliability assessment by creating a fusion of neural networks and a software reliability growth model. Also, it has been necessary to manage the software development process in terms of reliability, effort, and version-upgrade time. In this paper, we find the optimal total version-upgrade time based on the total expected software maintenance effort.