MINIMUM-LOSS DESIGN OF X-BAR CONTROL CHARTS FOR NON-NORMALLY CORRELATED DATA

ABSTRACT

When the [xbar] 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 charts, which is called the economic design of [xbar] 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 [xbar] 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