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The conducted simulation study gives the evidence that the Hotelling's T-square control chart performs well for any shift of mean for identifying the out of control signal. Meanwhile, the Shewhart x-bar control chart performs well only for a large shift of mean. In addition, it needs large subgroup size to truly identify the detection rate of out of control signal, whereas the Hotelling's T-square control chart does not depend on subgroup size to correctly perform.