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In this paper, it is assumed that the mean of a normal process is monitored by a CUSUM control chart. When the control chart triggers a signal and declares that the process has gone out of control, a search process is started to find the time of change and the causes of going the process out of control. Several methods (plans) for finding the true (real) change point is proposed. It is shown that the plans which are based on the likelihood of the points in time perform better.