Economic design of variable parameters X̄ control charts for processes with fuzzy mean shifts

Abstract

Modern studies have shown that the X̄ control charts with variable parameters (VPs) detect process shifts faster than the traditional X̄ control charts. This article developed the economic design of the VP X̄ control chart to determine the values of the design parameters of the chart. However, this study, different from previous studies, was focused on the process that is subject to a disturbing cause, and the occurrence of the cause can result in a fuzzy mean shift (ie the magnitude of the mean shift could not be recognized exactly). The issue of economically selecting the design parameters for the chart was firstly formulated as a mathematical programming model with a fuzzy objective function that could cope with fuzzy number type of mean shift. A fuzzy-simulation-based genetic algorithm was then employed to search for the optimal values of the design parameters from the model. An industrial example was provided to illustrate the solution procedure, and was used for comparison between the VP and the traditional X̄ chart. Effects of model parameters on the solution of the economic design were also discussed.

Keywords:

• economic design
• fuzzy-simulation-based genetic algorithm
• variable parameters
• control chart