Statistical design of the percentile-based depth-based multivariate control chart

We introduce a method for the statistical design of a depth-based control chart, using the percentile-based approach. The proposed control chart is affine invariant and is asymptotically distribution-free. Generally, the performance of a control chart is evaluated with the average run length metric. The average run length metric has a geometric distribution skewed to the right with a large standard deviation and may not be a proper measure for evaluating the control chart. Therefore, we use the statistical design method of control charts with the PL approach, which is an improvement and development on classical statistical design. By employing constraints on average run length, the length of in-control and out-of-control performances are guaranteed with predetermined probabilities and we can ensure that the in-control run length exceeds the desired value and the out-of-control run length is less than the desired value. Simulation studies show that the proposed control chart is more efficient than the average run length approach.