Multiobjective genetic algorithm approach to the economic statistical design of control charts with an application to X ̄ bar and S ² charts

Control charts are the primary tools of statistical process control. These charts may be designed by using a simple rule suggested by Shewhart, a statistical criterion, an economic criterion, or a joint economic statistical criterion. Each method has its strengths and weaknesses. One weakness of the methods of design listed is their lack of flexibility and adaptability, a primary objective of practical mathematical models. In this article, we explore multiobjective models as an alternative for the methods listed. These provide a set of optimal solutions rather than a single optimal solution and thus allow the user to tailor their solution to the temporal imperative of a specific industrial situation. We present a solution to a well-known industrial problem and compare optimal multiobjective designs with economic designs, statistical designs, economic statistical designs, and heuristic designs.