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An open source software serves as key components of critical infrastructures in the social life. We focus on the quality problems of open source software developed under the 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 the open source project, it is necessary to grasp the deeply-intertwined factors, such as programming path, size of each component, skill of fault reporters, etc. We propose a new approach to reliability assessment for open source software. Also, we analyze actual software fault-count data to show numerical examples of software reliability assessment for the open source software. Moreover, we compare the proposed method based on chaos theory with the conventional software reliability growth models for open source software by using several comparison criteria of goodness-of-fit.