SECTION 12.2 Summary

• Standard three-sigma control charts plot the values of some statistic for regular samples from the process against the time order of the samples. The center line is set at the mean of the plotted statistic. The control limits lie three standard deviations of the plotted statistic above and below the center line. A point outside the control limits is an out-of-control signal.
• When we measure some quantitative characteristic of the process and gather samples of two or more observations, we use and charts for process control. The chart monitors variation within individual samples. If the chart is in control, the chart monitors variation from sample to sample. To interpret the charts, always look first at the chart. For larger subgroups, the chart can be replaced by an chart.
• The chart and chart are used for monitoring a process of individual observations. The chart does not benefit from the central limit theorem effect. As a result, it is important to check if the individual observations follow the Normal distribution before constructing the chart.
• Capability indices measure process variability () or process center and variability () against the standard provided by external specifications for the output of the process. Larger values indicate higher capability.
• Interpretation of and requires that measurements on the process output have a roughly Normal distribution. These indices are not meaningful unless the process is in control so that its center and variability are stable.
• Estimates of and can be quite inaccurate when based on small numbers of observations, due to sampling variability. It is generally recommended that capability index estimates be based on at least 50 measurements.