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In general, the software reliability models based on the nonhomogeneous Poisson processes (NHPPs) are quite popular to assess quantitatively the software reliability and its related dependability measures. Nevertheless, it is not so easy to select the best model from a huge number of candidates in the software testing phase, because the predictive performance of software reliability models strongly depends on the fault-detection data. The asymptotic trend of software fault-detection data can be explained by two kinds of NHPP models; finite fault model and infinite fault model. In other words, one needs to make a hypothesis whether the software contains a finite or infinite number of faults, in selecting the software reliability model in advance. In this article, we present an approach to treat both finite and infinite fault models in a unified modeling framework. By introducing an infinite server queueing model to describe the software debugging behavior, we show that it can involve representative NHPP models with a finite and an infinite number of faults. Further, we provide two parameter estimation methods for the unified NHPP based software reliability models from both standpoints of Bayesian and nonBayesian statistics. Numerical examples with real fault-detection data are devoted to compare the infinite server queueing model with the existing one under the same probability circumstance.