To meet highly competitive market challenges along with technological upgrades and changing user requirements, software firms offer newer versions of their products by adding new features and new functionalities. But this also results in increase in the fault content of software. In this paper we propose a discrete software reliability growth model (SRGM) for fault removal process incorporating the effect of up-gradations on the subsequent releases of the software. It is further assumed that faults present in the software are not of the same type and may be classified as simple and hard faults depending upon the effort and time consumed for their removal. The proposed model has been validated on a real life dataset for software with four releases. The results obtained are encouraging and fairly accurate.