Explaining the constant, d2

In an MSA, d2 is a constant used when calculating an estimate of the process standard deviation from the average range (R-bar) of subgroups. It represents the expected value of the sample range when the underlying distribution is normal with a standard deviation of 1.

The primary use of the d2 constant is to convert the average range (R-bar) of measurements taken within a subgroup into an estimate of the process standard deviation (sigma, σ). This is particularly helpful in process capability analysis and control chart construction when the subgroup size (n) is known.

The formula for estimating sigma (standard deviation) is: σ = R-bar / d2 (aka Study Variation in this case). This standard deviation is often referred to as a measure of "within subgroup variation".

The value of d2 depends on the subgroup size (n) and can be found in tables such as shown below. Most statistical software will have these constants as well. 

d2 is often used in conjunction with other control chart constants like d3 and d4. d3 is used to calculate the UCL for range charts and d4 is used to calculate the UCL for X-bar charts.

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