A DEA Based MODM Model for Designing X Control Chart

Control charts are widely implemented in firms to establish and maintain statistical control of a process which leads to the improved quality and productivity. Design of control charts requires that the engineer selects a sample size, a sampling frequency and the control limits for the chart. In this paper, a possible combination of design parameters is considered as a decision making unit which is identified by three attributes: hourly expected cost, detection power of the chart and in-control average run length. Optimal design of control charts can be formulated as multiple objective decision making (MODM). The cost function is extended from single to multiple assignable causes because there exist multiple assignable causes in real practice. An algorithm using DEA is applied to solve the MODM model. A numerical example is used to illustrate the algorithm procedure. Finally, sensitivity analysis has been carried out to investigate the robustness of the model Index Terms Control chart design, Data envelopment analysis, X control chart, Multiple-objective decision making (MODM)