Multi-Objective X-bar Control Chart Design by Integrating NSGA- II and Data Envelopment Analysis

Abstract

Control charts are widely used in industry to establish and maintain statistical control of a process for quality improvement. Economic use of a control chart calls for designing the optimal parameters for sample size, sampling frequency, and the control limits for the chart. This paper investigates the X-bar control chart design through a twostage multi-objective optimization process. The multi-objective formulation reflects the multiple objective needs in designing an X-bar control chart. For example, these objectives may include average run length when in statistical control, the type-I error, and the detection power. The optimization process first searches the Pareto Frontiers using Non-dominated Sorting Generic Algorithm (NSGA-II), and then applies Data Envelopment Analyses (DEA) to reduce the Pareto optimal solutions to a workable size of efficient solutions for implementation. By performing trade-off analysis, guidelines are provided for choosing the appropriate design of an X-bar control chart. The proposed optimization method is applied in a case study, and the outcomes are compared with the literature results which reveal that the proposed model offers more practical design options in designing the X-bar control chart.

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