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Most software reliability models assume independence of successive software runs. It is a strict assumption, and usually not valid in reality. Goseva-Popstojanova & Trivedi (2000) presented an interesting study on failure correlation among successive software runs. In this paper, by extending their results, a software reliability model is developed based on a Markov renewal process for the modeling of the dependence among successive software runs, where more than one type of failure is allowed in general formulation. Meanwhile, the cases of restarting with repair, and without repair, are considered. Although such a model is more complex than the traditional approach based on reliability growth, it incorporates more information about the failures, and system structure. A numerical example is also shown to illustrate the procedure, and provide some comparison.