Reliability models for hardware described by the nonhomogeneous Poisson process are examined. Quantitative measures useful in determining software reliability are explored, and their estimation is discussed. The failure occurrence process is examined from the viewpoint of reliability growth in the software error detection process. The two reliability models discussed are most suitable when the detected errors in the observed data follow an S-shaped growth curve, which reflects well the learning process. Here, the personnel testing the software adapt to the testing environment and improve their testing skills. The asymptotic property of the maximum-likelihood estimation of the parameters in each model is used to present point and interval estimations for the remaining software errors and software reliability, which serve as the measures for the reliability. Applying the reliability models to the actual software error data, fitness to the observed data is verified, together with the evaluation for the reliability measures.