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In this paper, both fault detection and correction processes are considered in software reliability growth modeling. The dependency of the two processes is first studied from the viewpoint of the fault number in two ways. One is the ratio of corrected fault number to detected fault number, which appears S-shaped. And the other is the difference between the detected fault number and corrected fault number, which appears Bell-shaped. Then based on the ratio and difference functions, two software reliability models are proposed for both fault detection and correction processes. The proposed models are evaluated by a data set of software testing. The experimental results show that the new models fit the data set of fault detection and correction processes very well.