Software reliability growth modeling plays an important role in software reliability evaluation. To incorporate more information and provide more accurate analysis, modeling software fault detection and correction processes has attracted widespread research attention recently. However, the assumption of the stochastic fault correction time delay brings more difficulties in modeling and estimating the parameters. In practice, other than the grouped fault data, software test records often include some more detailed information, such as the rough time when one fault is detected or corrected. Such semi-grouped dataset contains more information about fault removal processes than commonly used grouped dataset. Using the semi-grouped datasets can improve the accuracy of time delayed models. In this paper, a fault removal modelling framework for software reliability with semi-grouped data is studied and extended into multi-released software. Also, the corresponding parameter estimation is carried out with Maximum Likelihood estimation method. One test dataset with three releases from a practical software project is applied with the proposed framework, which shows satisfactory performance with the results.