Synthetic-X¯ control charts optimized for in-control and out-of-control regions

There are real industrial cases where small shifts in the quality of a productive process do not need to be detected, but, at the same time, it is necessary to maintain the performance of the control chart to detect large shifts which are considered important. In this paper the optimization, zero- and steady-state cases, of the synthetic-X¯ control chart is studied (standard, side-sensitive, group runs and side-sensitive group runs versions) with the aim of not detecting shifts in a region of admissible shifts (in-control region) and, at the same time, being able to detect shifts considered important (out-of-control region). Genetic algorithms have been employed to solve this optimization problem and user-friendly software has been developed with the objective of helping users to select the best synthetic-X¯ chart for the process. On the other hand, a comparison is made with the optimized EWMA chart for this in-control and out-of-control optimization problem.