Joint X- and S2 Control Charts Optimal Design Using Genetic Algorithm

A simple and flexible model for economic statistical design of joint X- and S2 control charts was proposed. The design problem was approached by constrained fuzzy multiobjective modeling for three objectives: joint power, joint Type I error, and joint total control cost. Fuzzy membership functions were created to measure the satisfaction levels of the objectives, and the overall satisfaction level of the design was calculated using a weighted-average method. A genetic algorithm was designed to solve this model. The strength of this model lies in its effectiveness in detecting the assignable causes through the joint design and in its simplicity and flexibility in dealing with uncertainties in the design.