Minimum-loss design of X-bar control charts for non-normally correlated data

Chao-Yu Chou*

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.

Chun-Lang Chang

Department of Industrial Management

National Huwei Institute of Technology

Chung-Ho Chen

Department of Industrial Management

Southern Taiwan University of Technology

ABSTRACT

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).