Many software reliability growth models (SRGMs) have been developed in the past three decades to estimate software reliability measures such as the number of remaining faults and software reliability. The underlying common assumption of many existing models is that the operating environment and the developing environment are the same. This is often not the case in practice because the operating environments are usually unknown due to the uncertainty of environments in the field. In this paper, we develop a generalized software reliability model incorporating the uncertainty of fault-detection rate per unit of time in the operating environments. A logistic fault-detection software reliability model is derived. Examples are included to illustrate the goodness of fit of the proposed model and existing nonhomogeneous Poisson process (NHPP) models based on a set of failure data. Three goodness-of-fit criteria, such as mean square error, predictive power, and predictive ratio risk are used as an example to illustrate model comparisons. The results show that the proposed logistic fault-detection model fit significantly better than other existing NHPP models based on all three goodness-of-fit criteria.