Performance of Multivariate Control Chart over Shewhart Control Chart

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.