A multi-objective optimization of the synthetic T2 control chart for solving the problem of in-control and out-of-control regions

In some real applications of Statistical Process Control it is necessary to design a control chart to not detect small shifts, but keeping a good performance to detect moderate and large shifts (designing for In-control and Out-of-control regions). In this work we show how the new synthetic T 2 control chart can be designed to cope with this objective. A multi-objective optimization is carried out employing Genetic Algorithms, finding the Pareto-optimal front of non-dominated solutions for this problem.