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In this thesis, we discuss the problem of change point estimation in quality control. When the control chart makes a signal which shows that the process is out of control, and the process mean has been changed if we can find a good estimate of the change point, the main cause of disturbances can be identified more quickly. Last studies usually assume that the change in the process mean is a step change, and under this assumption, using Bayesian and Classical methods, the change point is estimated. In this thesis it is assumed that the change. In the process mean has a linear trend. Under this condition the change point is estimated. In addition, a new criteria for evaluating the estimate of the change point is introduced. Then, using this criteria, the efficiency of the estimators is evaluated in different conditions.