X-bar/R chart
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2008-07-05T19:34:53Z
Jay1279
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{{Unreferenced|date=June 2007}}
An '''X-bar/R chart''' is a specific member of a family of [[control chart]]s. 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 [[telephone]]s.
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 [[Cartesian coordinate system|horizontal axis]] denoting the sample number.
The [[Cartesian coordinate system|vertical axis]] on the top chart depicts the [[Sample (statistics)|sample]] [[Arithmetic mean|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 deviation]]s (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 [[variance|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, [http://www.aiag.org A.I.A.G.], 2006.
[[Category:Quality control tools]]
[[Category:Statistical charts and diagrams]]