Various control charts are already developed for the problem of detecting any shift in the mean/median of a sequence of observations from a specified control value taken from some process. Some of them for detecting small shift(s) from the target values are Cumulative Sum (CUSUM), Cumulative Score (CuScore) and recently developed nonparametric charts. Various authors have already worked on CUSUM control charts and found suitable results. Another chart is Cuscore chart, which is also suitable for this situation. Another test is nonparametricCUSUM charts based on nonparametric test statistic. One of the efficient procedure is the Cumulative Sum Control chart (CSCC) originally introduced by Page [1]. The properties of CSCC procedure are usually derived under the assumption that the observations are independent and identically distributed normal random variables, another control chart based on Cumulative Scores developed by Munford [2]. The ARL of this scheme are simpler to compute than those of CSCC. Recently a new control chart is developed based on the nonparametric chart which is preferable from the robustness point of view. Few of the workers on nonparametric CSCC are Parent [3], Reynolds [4, 5], Mcgilchrist and Woodyer [6], Bakir and Reynolds [7] etc. In this paper we want to study the performance of CSCC, CuScore and Nonparametric CUSUM control Chart in detecting the mean/median shift from the specified (target) values. For this purpose we computed the ARL by the simulation method for both in control and under control situations of the process. Results obtained are displayed in various tables using different shift parameters and under different distributions. Results are also shown in graph for easy visual comparison.