Economic Design of Averages Control Charts for Monitoring a Process with Correlated Samples

When an x control chart is used to monitor a manufacturing process, three parameters should be determined: the sample size, the 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. Traditionally, when designing a x chart, it is assumed that the measurements within a sample are independently distributed; however, this assumption may not be tenable. In this paper, we develop the economic design of x charts for correlated measurements within a sample. An example is presented to illustrate the solution procedure. From the results of the sensitivity analyses of this example, we find that if the measurements in the sample are positively correlated, highly correlated data result in a smaller sample size, a frequent sampling interval and narrower control limits; however, if the measurements in the sample are negatively correlated, highly correlated data yield a smaller sample size and narrower control limits.