X-bar/R chart

An X-bar/R chart is a specific member of a family of control charts. A control chart is a tool used in quality control, specifically SPC or statistical process control, as originally developed by Walter A. Shewhart at Western Electric in 1924 to improve the quality of telephones.

A control chart is a plot of measurements of a product on two special scales, usually located above and below each other and running horizontally. X-Bar/R charts consist of two charts, both with the same horizontal axis denoting the sample number.

The vertical axis on the top chart depicts the sample means (X-Bar) for a series of lots or subgroup samples. It has a centerline represented by Xdoublebar, which is simply the overall process average, as well as two horizontal lines, one above and one below the centerline, known as the upper control limit or UCL and lower control limit or LCL, respectively. These lines are drawn at a distance of plus and minus three standard deviations (that is, standard deviations of the sampling distribution of sample means) from the process average. In practice, tabulated constants are available to determine the control limits, or they are automatically calculated by the SPC software used.

The bottom chart has the range (R) of each subgroup plotted on the vertical axis. Like an X-Bar chart, R charts have a centerline and two control limits. However, for sample sizes below 7, the LCL is zero.

The purpose of any control chart is to help determine if variations in measurements of a product are caused by small, normal variations that cannot be acted upon ("common causes"), or by some larger "special cause" that can be acted upon or fixed. The type of chart to be used is based on the nature of the data.

The X-bar/R chart is normally used for numerical data that is captured in subgroups in some logical manner – for example 3 production parts measured every hour. A special cause such as a broken tool will then show up as an abnormal pattern of points on the chart.

Literature
QS9000 manual "Fundamental Statistical Process Control", 2nd edition, A.I.A.G., 2006.