In this thesis we discuss existing software reliability models and then derive the relationships between them in prticular, between Jelinski-Moranda model (J-M model) and Goel-Okumoto model (G-O model), typicals of TBF (time between failures) models and FC (fault count) models, respectively, from Shanthiumer model and conditional Shanthiumer model. Also we will see that Littlewood model is obtained as a special case of conditional Shanthiumer model in terms of Miller``s EOS method, and hence we will derive a relationship between Littlewood model and Shanthikumar model.