Software reliability is the major dynamic attribute of the software quality, so gaining reliability of software product is a vital issue for software products. Due to intense competition the software companies are coming with multiple add-ons to survive in the pure competitive environment by keeping an eye on existing system i.e. system in operational phase. Software reliability engineering is focused on engineering techniques for timely add-ons/Up-gradations and maintaining software systems whose reliability can be quantitatively evaluated. In order to estimate as well as to predict the reliability of software systems, failure data need to be properly measured by various means during software development and operational phases. Although software reliability has remained an active research subject over the past 35 years, challenges and open questions still exist. This paper presents a discrete software reliability growth modeling framework for multi-up gradations including the concept of two types of imperfect debugging during software fault removal phenomenon. The Proposed model has been validated on real data set and provides fairly good results.