Bias Correction Factors
The bias correction factors, d2, d3, and d4, are a set of numeric constants with values that change with respect to subgroup size, n. They are used to calculate the within-subgroup measures of dispersion Sigma(X) and Sigma(R). When using the average range (R-bar) to calculate the within-subgroup measure of dispersion Sigma(X), the average range is divided by the bias correction factor d2. When using the median range (R-tilde) to calculate Sigma(X), the median range is divided by the bias correction factor d4.
When calculating Sigma(R), the bias correction factor d3 is multiplied by Sigma(X). Thus, Sigma(R) can be expressed in terms of the average range or the median range as follows:
Why were they created?
Estimating the measure of dispersion using the range of a small subgroup underestimates the true population standard deviation. This underestimation is called small-sample bias. Without correcting for this bias, the process limits that are calculated using Sigma(X) will be too narrow, leading to false alarms. The bias correction factors were created to avoid this. The were created as a practical method for calculating process limits without concern of calculating limits that were too narrow.