Economic design of X charts for non-normally correlated data

When the X chart is applied to monitor a manufacturing process, three parameters should be determined: sample size, sampling interval between successive samples, and the control limits for the chart. In 1956, Duncan presented the first cost model to determine the three parameters for the X charts, which is called the economic design of X charts. This paper develops the economic design of X charts for non-normally correlated data. An example of juice production process is presented to illustrate the solution procedure. A sensitivity analysis is performed to show the effects of non-normality and correlation coefficient on the optimal design of the chart.