This is about the motivation for the R chart and its math. We shouldn’t ask manufacturing professionals to apply a technical tool without explaining its purpose and its theory.
However, without doing either, the SPC literature promotes the use of the R chart to detect changes in the fluctuations of measured variables, along with \bar{X} charts for changes in their means. The books provide recipes for using these charts, but no explanation.
Harold Dodge introduced the R chart 100 years ago to overcome shop floor pushback against calculating sample standard deviations with paper, pencil, and slide rules. While easier to understand and to use daily, sample ranges are mathematically more complex and more sensitive to extreme values than standard deviations.
Like all control charts, the R chart uses limits calculated for the Gaussian distribution. As no simple formula is available for the R chart, setting control limits for it requires numerical approximations that must have consumed months for human computers in 1924.
Today, you can replicate them instantaneously with software. These calculations reveal that the \pm 3\sigma limits in the books for the range chart do not actually encompass the 99.73% of the distribution that they do in \bar{X} charts.
The R chart was an ingenious workaround to technical and human constraints of the 1920s that no longer exist. Today, rather than blindly applying these tools, we must draw inspiration from their inventors and develop solutions to meet the process capability challenges we are actually facing.
Nov 7 2025
The Lowdown on the Range Chart
This is about the motivation for the R chart and its math. We shouldn’t ask manufacturing professionals to apply a technical tool without explaining its purpose and its theory.
However, without doing either, the SPC literature promotes the use of the R chart to detect changes in the fluctuations of measured variables, along with \bar{X} charts for changes in their means. The books provide recipes for using these charts, but no explanation.
Harold Dodge introduced the R chart 100 years ago to overcome shop floor pushback against calculating sample standard deviations with paper, pencil, and slide rules. While easier to understand and to use daily, sample ranges are mathematically more complex and more sensitive to extreme values than standard deviations.
Like all control charts, the R chart uses limits calculated for the Gaussian distribution. As no simple formula is available for the R chart, setting control limits for it requires numerical approximations that must have consumed months for human computers in 1924.
Today, you can replicate them instantaneously with software. These calculations reveal that the \pm 3\sigma limits in the books for the range chart do not actually encompass the 99.73% of the distribution that they do in \bar{X} charts.
The R chart was an ingenious workaround to technical and human constraints of the 1920s that no longer exist. Today, rather than blindly applying these tools, we must draw inspiration from their inventors and develop solutions to meet the process capability challenges we are actually facing.
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By Michel Baudin • Quality 0 • Tags: Control Charts, Quality, Range Chart, SPC, Xbar-R chart