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 ˉx and R charts for process control. The R chart monitors variation within individual samples. If the R chart is in control, the ˉx chart monitors variation from sample to sample. To interpret the charts, always look first at the R chart. For larger subgroups, the R chart can be replaced by an s chart.
The I chart and MR chart are used for monitoring a process of individual observations. The I 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 I chart.
Capability indices measure process variability (Cp) or process center and variability (Cpk) against the standard provided by external specifications for the output of the process. Larger values indicate higher capability.
Interpretation of Cp and Cpk 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 Cp and Cpk 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.