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Open source software development and their uses becoming more popular and increasing rapidly due to tremendous growth in the field of internet and network technologies. Since the mid 1990s, there has been a surge of interest among academics and practitioner in open source software. It has been always a challenging and interesting to know the dynamics of bug in the software. In software different types of bugs are laying which are not similar in nature. Some of them may be complex from the user's point of view while others may be complex from the developer's point of view. In this paper, we proposed a generalized reliability growth model to determine different category of bugs lying in open source software. The failure intensity of the proposed model is not only dependent upon residual bug content but also on power function of testing time. The proposed model also caters the huge user growth in case of open source software. The model is validated using several real software failure data sets collected from open source software development websites. We have also shown goodness of fit curve along with comparison criteria like MSE, R2, Bias, Variation and Root mean squared error to validate the proposed model.