Identification of a real time of a change in a process, when an out-of-control signal is present is significant. This may reduce costs of defective products as well as the time of exploring and fixing the cause of defects. Another popular topic in the Statistical Process Control (SPC) is profile monitoring, where knowing the distribution of one or more quality characteristics may not be appropriate for discussing the quality of processes or products. One, rather, uses a relationship between a response variable and one or more explanatory variable for this purpose. In this paper, the concept of Maximum Likelihood Estimator (MLE) applied to estimate of the change point in binary profiles, when the type of change is drift. Simulation studies are provided to evaluate the effectiveness of the change point estimator.