Multi-objective Efficient Design of np Control Chart Using Data Envelopment Analysis

Control charts are the most important tools of statistical process control used to discriminate between assignable and common causes of variation and to improve the quality of a process. To design a control chart, three parameters including sample size, sampling interval, and control limits should be determined. The objectives are hourly expected cost, in-control average run length, power of the control chart, and average time to signal. Different approaches such as statistical design, economic design, and economic-statistical design of control charts have been considered by many researchers. Recently, multi-objective design of control chart has been investigated in the literature. In this paper we propose a multi-objective economic-statistical design of np control chart (np-MOESD). To solve the multi-objective model, a method is used to find the Pareto optimal solution and then a combined method based on Data Envelopment Analysis (DEA) is proposed to determine the most efficient design parameters. A numerical example of Duncan [1] illustrates the proposed approach. Sensitivity analysis is performed to evaluate the proposed model. In addition, the proposed model is compared with pure economic design (Duncan’s model) as well as another model in the literature. Results show that the proposed np-MOESD model improves statistical properties of np control charts.