The control chart is a graph used to study how a process changes over time. Data are plotted in time order. A control chart always has a central line for the average, an upper line for the upper control limit, and a lower line for the lower control limit. These lines are determined from historical data.
- Points representing a statistic (e.g., a mean, range, proportion) of measurements of a quality characteristic in samples taken from the process at different times (i.e., the data)
- The mean of this statistic using all the samples is calculated (e.g., the mean of the means, mean of the ranges, mean of the proportions) - or for a reference period against which change can be assessed. Similarly a median can be used instead.
- A centre line is drawn at the value of the mean or median of the statistic
- The standard deviation (e.g., sqrt(variance) of the mean) of the statistic is calculated using all the samples - or again for a reference period against which change can be assessed. in the case of XmR charts, strictly it is an approximation of standard deviation, the[clarification needed] does not make the assumption of homogeneity of process over time that the standard deviation makes.
- Upper and lower control limits (sometimes called "natural process limits") that indicate the threshold at which the process output is considered statistically 'unlikely' and are drawn typically at 3 standard deviations from the center line
