Multiple-objective design of an $$\overline{{\user2{X}}} $$ control chart with multiple assignable causes.

Control charts are widely implemented in firms to establish and maintain statistical control of a process which leads to the improved quality and productivity. Therefore, designs of control charts have gained particular attention from the outset. 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. Subsequently, optimal design of control charts is formulated as a multiple-objective decision-making problem. Moreover, the cost function is extended from single to multiple assignable causes because there exist multiple assignable causes in real practice. An algorithm using data envelopment analysis is applied to solve the multiple-objective decision-making (MODM) model. Some numerical and experimental analyses are provided to illustrate the algorithm procedure. Sensitivity analysis is carried out to investigate the robustness of the model, and comparisons with other related published papers are made. It is shown that the proposed MODM model can overcome some drawbacks attached to the previous models and approaches. [ABSTRACT FROM AUTHOR]