Range Estimation of Standard Deviation

The estimator of standard deviation based on range is the control chart factor known as d2.

The factor d2 is the mean of a random variable (r.v.) "W" known as the relative range.  (Montgomery "Introduction to Statistical Quality Control 5th Ed" section 5-2).  Because d2 is the expected value (mean) of a r.v. it is actually not a constant, but is rather a point estimate of the mean of a distribution. 

The file "range_vs_stddev.R.txt" attached at the bottom of this page contains R code for running a Monte Carlo simulation to demonstrate the properties of the Range method of estimating Standard Deviation.  It is based on the Montgomery text "Introduction to Statistical Quality Control 5e" page 198.

The file "Simulation of d2 and R-bar vs S chart" (also attached at the bottom of this page) shows some of the more interesting results of the R code simulation.