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In this paper, we propose two general frameworks for deriving several software reliability growth models based on a non-homogeneous Poisson process (NHPP) in the presence of imperfect debugging and error generation. The proposed models are initially formulated for the case when there is no differentiation between failure observation and fault removal testing processes, and then extended for the case when there is a clear differentiation between failure observation and fault removal testing processes. During the last three decades, many software reliability growth models (SRGM) have been developed to describe software failures as a random process, and can be used to evaluate development status during testing. With SRGM, software engineers can easily measure (or forecast) the software reliability (or quality), and plot software reliability growth charts. It is not easy to select the best model from a plethora of models available. There are few SRGM in the literature of software engineering that differentiates between failure observation and fault removal processes. In real software development environments, the number of failures observed need not be the same as the number of faults removed. Due to the complexity of software systems, and an incomplete understanding of software, the testing team may not be able to remove the fault perfectly on observation of a failure, and the original fault may remain, resulting in a phenomenon known as imperfect debugging, or get replaced by another fault causing error generation. In the case of imperfect debugging, the fault content of the software remains the same; while in the case of error generation, the fault content increases as the testing progresses. Removal of observed faults may result in the introduction of new faults.