In this paper, we propose a new model that incorporates both the fault-detection process and the fault-correction process. In addition, the faultcorrection process is modeled as a delayed faultdetection process. Significant improvements on the conventional software reliability growth models (SRGMs) to better describe the actual software development have been achieved by eliminating an unrealistic assumption that detected errors are immediately corrected. This can especially be seen when some latent software errors are hard to detect and they even exist in the software product for a long time after they are detected. Therefore, the time delayed by the correction process is not negligible. The objective here is to remove this assumption in order to make the SRGMs more realistic and accurate. Finally, two real data sets have been performed, and the results show that the proposed new model performs much better in estimating the number of initial faults.