## Statistical Process Control

Read this chapter on the basics of statistical process control (SPC). SPC is a standard tool for monitoring whether a process is performing as expected and, if not, where problems occur. While reading, consider how this kind of tool factors in process capacity management.

### Control Chart Background

A process may either be classified as in control or out of control. The boundaries for these classifications are set by calculating the mean, standard deviation, and range of a set of process data collected when the process is under stable operation. Then, subsequent data can be compared to this already calculated mean, standard deviation and range to determine whether the new data fall within acceptable bounds. For good and safe control, subsequent data collected should fall within three standard deviations of the mean. Control charts build on this basic idea of statistical analysis by plotting the mean or range of subsequent data against time. For example, if an engineer knows the mean (grand average) value, standard deviation, and range of a process, this information can be displayed as a bell curve, or population density function (PDF). The image below shows the control chart for a data set with the PDF overlay.

Figure I. Control chart showing PDF for a data set

The centerline is the mean value of the data set and the green, blue and red lines represent one, two, and three standard deviations from the mean value. In generalized terms, if data points fall within three standard deviations of the mean (within the red lines), the process is considered to be in control. These rules are discussed in greater detail later in this section.

Control Charts are commonly used in six sigma control today, as a means of overall process improvement. For more on six-sigma control, see six sigma.