A new approach for multicriteria design of an X control chart

This paper proposes to design an Xmacr control chart through a data envelopment analysis (DEA) based multicriteria branch and bound algorithm. The proposed multicriteria model avoids the difficulty of estimating costs associated with false alarm and operation under out-of-control status, and reduces the need for the decision maker to specify the statistical bounds on two types of errors and to provide preference information during the control chart design process. Through appropriate branching and bounding procedures, the DEA-based multicriteria branch and bound algorithm can quickly target the solution region where Pareto optimal solutions exist. Instead of involving the decision makers during the whole design process, few Pareto optimal solutions with useful trade off information can be presented to decision makers.