Control Chart

A control chart is a graphical tool that provides the ability to monitor a process for changes that occur, and can be used to identify and characterize different sources of variation that act on a process. Most commonly, control charts plot the values of some characteristic of a process over time. In addition to the individual points, a control chart also displays three other (vertical) lines: a center line at the process average, an upper control limit (UCL) located three standard deviations above the center line, and a lower control limit (LCL) located three standard deviations below the center line. This chart provides the ability to distinguish random variation that is inherent to the process (called common cause variation) from sporadic variation that is not part of the normal process and produces a localized change to the process (called special cause variation). Special cause variation can be identified by applying rules that seek to distinguish it from common cause variation. Most commonly, any point that occurs more than three standard deviations away from the mean is identified as stemming from a special cause. Other rules seek to identify process shifts (such as a series of seven or more points all on the same side of the center line), or process trends (a series of seven or more points where each point is greater or less than the immediately preceding point).

Various kinds of control charts have been developed to handle different types of data and different methods of data collection. Attributes data describe data that are based on counts. The p chart is a type of control chart that plots the proportion, p, of items that possess a certain attribute (for example, the proportion of patients in a hospital that contract a particular kind of infection each month). The c chart and the u chart display either the count or the rate of occurrence of attributes that occur in a fixed period of time (or space), such as the number of inspection violations per week (or room).

Variables data describe quantitative measurements (such as length of time, dollars spent, or physical measurements). If data are collected in small subgroups over time, the X-bar [Page 106]chart displays the averages of the values in each subgroup, and the R chart displays the ranges of the values in each subgroup. Thus, the process can be monitored for both changes in average, and changes in variation. As an example, the emergency room at a hospital could select (at random) five individuals who present themselves for treatment and measure the amount of time until they have been seen by a physician. This could be done daily for a month, with the averages plotted in the X-bar chart, and the ranges plotted in the R Chart.

If the data cannot be aggregated in subgroups, but rather individual measurements occur over time, then these can be plotted using an X chart (also called an individuals chart). An example might be the number of prescriptions filled in a pharmacy each day.

Control charts have proven themselves to be extremely useful tools for better understanding the dynamics of processes.

...