In general, software reliability models have focused on modeling and predicting the failure detection process and have not given equal priority to modeling the fault correction process. However, it is important to address the fault correction process in order to identify the need for process improvements. Process improvements, in turn, will contribute to achieving software reliability goals. We introduce the concept of a fault correction profile -- a set of functions that predict fault correction events as a function of failure detection events. The fault correction profile identifies the need for process improvements and provides information for developing fault correction strategies. Related to the fault correction profile is the goal fault correction profile. This profile represents the fault correction goal against which the achieved fault correction profile can be compared. This comparison motivates the concept of fault correction process instability, and the attributes of instability. Applying these concepts to the NASA Goddard Space Flight Center fault correction process and its data, we demonstrate that the need for process improvement can be identified, and that improvements in process would contribute to meeting product reliability goals.