This paper presents a software reliability model that is based on a nonhomogeneous poisson process. The major contribution of this model is combining multiple failure types with imperfect debugging by use of S-shaped mean value function. The software reliability model allows for three different types of errors: Critical errors are the most difficult to detect and the most expensive to remove. Major errors are moderately difficult to detect and fairly expensive to remove. Minor errors are easy to detect and inexpensive to remove. The model also allows for the introduction of any of these types of errors during the removal of an error. A numerical example is provided to illustrate the above techniques.