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In current software reliability modeling research, the main concern is how to develop general prediction models. In this paper, we propose several improvements on the conventional software reliability growth models (SRGMs) to describe actual software development process by eliminating some unrealistic assumptions. Most of these models have focused on the failure detection process and not given equal priority to modeling the fault correction process. But, most latent software errors may remain uncorrected for a long time even after they are detected, which increases their impact. The remaining software faults are often one of the most unreliable reasons for software quality. Therefore, we develop a general framework of the modeling of the failure detection and fault correction processes. Furthermore, we apply neural network with back-propagation to match the histories of software failure data. We will also illustrate how to construct the neural networks from the mathematical viewpoints of software reliability modeling in detail. Finally, numerical examples are shown to illustrate the results of the integration of the detection and correction process in terms of predictive ability and some other standard criteria.