It is very important to promptly detect the point-of-change of the behavior of a system. In this paper, two algorithms'- the algorithm of cumulative sums and median algorithm - are proposed for detecting the point. Unlike earlier algorithms, the schemes detect the point even when the distribution of the target process shifts before or after the point, and the detection is made in an interval of predefined length. We also develop analytical models predicting the probability of discord omission. The median algorithm allows simpler expression and easier use than the algorithm of cumulative sums. Moreover, it is proved to be applicable for a wide range of parameter values of the distribution. Computer simulation verifies the effectiveness of the proposed algorithms, and it reveals that the points are correctly detected with few false alarms for practical conditions. Also shifted distribution is of great advantage for finding discord.