Since the early 1970's a number of models have been proposed for estimating software reliability. However, the realism of many of the underlying assumptions and the applicability of these models continue to be questioned. Our research work was motivated by the fact that although there are practical situations in which the assumption of independence among successive software failures could be easily violated, much of the published literature on software reliability modeling does not seriously address this issue. In this paper we present a modeling framework based on Markov renewal processes which naturally introduces dependence among successive software runs and enables the phenomena of failure correlation to be precisely characterized. Thus, incorporating failure correlation into dependability and performability predictions contributes toward more realistic modeling of software systems in operation.