A packaging company operates a production line designed to fill each carton with 16.05 ounces of cereal. Based on extensive data from the production line the standard error of the mean for a sample of six boxes is found to be 0.04. If the process is under control, each time we take the mean of a sample of six boxes, we would expect to get a value within three standard errors of 16.05. In other words, we expect each sample mean to be between 16.05 - 3x(0.04) = 15.93 and 16.05 + 3x(0.04) = 16.17. In the chart below, these limits are marked as LCL ("Lower Control Limit") and UCL ("Upper Control Limit"). The red dots show the means of different 6-box samples. The light blue area between the LCL and UCL represents the region in which the process is under control.
Watch as a new sample is taken each period. From Period 1 to Period 6 in this simulation, the process is sampling from a distribution with a mean of 16.05 Starting at Period 7 (at the vertical dashed line), the process uses the mean specified by the slider under the graph. If this mean does not equal 16.05, the process is technically out of control. Use the slider to change the mean, click the Restart button, and see if you can tell that the process is out of control and at what period you know that.