The Robust Economic Statistical Design of the Hotelling’s T^2 Chart

Economic statistical designs aim at minimizing the cost of process monitoring when a specific scenario or a set of estimated process and cost parameters is given. However, in practical situations the process may be affected by more than one scenario which may lead to severe cost penalties for upsetting the true scenario. This paper presents the robust economic statistical design (RESD) of the T^2 chart to reduce the monetary losses when there are multiple distinct scenarios. The genetic algorithm optimization method is employed here to minimize the total expected monitoring cost across all distinct scenarios. Through two numerical examples the proposed method is illustrated. Simulation studies indicate that the robust economic statistical designs should be encouraged in practice.