Department of Industrial Engineering and Management
National Yunlin University of Science and Technology
123, Section 3, University Road, Touliu, Yunlin, Taiwan, 640, R.O.C.
Department of Industrial Management
National Huwei Institute of Technology
Department of Industrial Management
Southern Taiwan University of Technology
When the X-bar chart is applied to monitor a production process, three parameters should be determined: the sample size, the sampling interval between successive subgroups, and the control limits for the chart. In 1956, Duncan [5] presented the first cost model to determine the three parameters for the X-bar charts, which is called the economic design of X-bar charts. Alexander et al. [1] combined Duncan’s cost model with the Taguchi loss function to present a loss model for determining the three parameters. Traditionally, when conducting the design of control charts, one usually assumes the measurements within a subgroup are independently and normally distributed. However, this assumption may not be tenable. In this paper, we develop the minimum-loss design of X-bar charts for non-normally correlated data, where Alexander’s loss model is used as the objective function. An example is provided to illustrate the solution procedure. A sensitivity analysis is performed to investigate the effects of non-normality and correlation coefficient on the optimal design of the chart.
Keywords: control chart, loss function, non-normality, correlation
(*Contact: E-mail choucy@cim.yuntech.edu.tw )
Cite this article as: Chao-Yu Chou, Chun-Lang Chang and Chung-Ho Chen, "Minimum-Loss Design of X-Bar Control Charts for Non-Normally Correlated Data," Journal of the Chinese Institute of Industrial Engineers, 19, 16-24 (2002).