Most of the models for software reliability analysis are based on reliability growth models which deal with the fault detection process only. In this paper, some useful approaches to the modeling of both software fault detection and fault correction processes are discussed. Since the estimation of model parameters in software testing is essential to give accurate prediction and help make the right decision about software release, the problem of estimating the parameters is addressed here. Taking into account the dependency between the fault correction process and the fault detection process, a new explicit formula for the likelihood function is derived and the maximum likelihood estimates are obtained under various time delay assumptions. An actual set of data from a software development project is used as an illustrative example. A Monte Carlo simulation is carried out to compare the predictive capability between the LSE method and the MLE method.