Economic design of autoregressive moving average control chart using genetic algorithms

  • Authors:

  • Sung-Nung Lin;Chao-Yu Chou;Shu-Ling Wang;Hui-Rong Liu

  • Affiliations:

  • Department of Industrial Engineering and Management, National Yunlin University of Science and Technology, Douliu 640, Taiwan;Department of Finance, National Taichung Institute of Technology, Taichung 404, Taiwan;Department of Information Management, National Taichung Institute of Technology, Taichung 404, Taiwan;Department of Leisure and Recreation Management, National Taichung Institute of Technology, Taichung 404, Taiwan

  • Venue:
  • Expert Systems with Applications: An International Journal
  • Year:
  • 2012

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Abstract

When designing control charts, it is usually assumed that the observations from the process at different time points are independent. However, this assumption may not be true for some production processes, e.g., the continuous chemical processes. The presence of autocorrelation in the process data can result in significant effect on the statistical performance of control charts. Jiang, Tsui, and Woodall (2000) developed a control chart, called the autoregressive moving average (ARMA) control chart, which has been shown suitable for monitoring a series of autocorrelated data. In the present paper, we develop the economic design of ARMA control chart to determine the optimal values of the test and chart parameters of the chart such that the expected total cost per hour is minimized. An illustrative example is provided and the genetic algorithm is applied to obtain the optimal solution of the economic design. A sensitivity analysis shows that the expected total cost associated with the control chart operation is positively affected by the occurrence frequency of the assignable cause, the time required to discover the assignable cause or to correct the process, and the quality cost per hour while producing in control or out of control, and is negatively influenced by the shift magnitude in process mean.