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 chart, 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 from the process average.
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. Unlike an X-Bar chart, the control limits on an R chart are not symetric about the centerline, and for small subgroups 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, 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 Xbar/R chart is normally used for numerical data that is grouped in subgroups in some logical manner, for example 3 games of bowling that occur on one night. This allows the night to be considered as a unit, so a special cause such as a slippery floor or a sick bowler will be more obvious as a point on the chart.
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