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Open source software which serve as key components of critical infrastructures in the social life are still ever-expanding now. We focus on the quality problems of open source software developed under open source project. In case of considering the effect of the debugging process 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 reporters, and so on. Considering from a point of view of the software reliability growth model, it is difficult to cover the software fault-report phenomena on the bug tracking system of open source software. We propose a new approach to software reliability assessment based on deterministic chaos theory. Also, we analyze actual software fault count data to show numerical examples of software reliability assessment for the open source software.