RE: R-Bar/d2

["Prevette, Steven S" <Steven_S_Prevette@rl.gov>]

Where does d2 come from?  (as used in R-Bar/d2 to 
estimate sigma for the population)  

My suggested answer - Acheson Duncan provides a derivation of d2 in his
Quality Control and Industrial Statistics in Chapter 6, section 2.  It is
based upon knowing the standard deviation of sigma for small samples, which
comes from the chi square.  Duncan also references page 184 of Economic
Control of Quality of Manufactured Product (Shewhart).  I have to admit it
is quite complex, and both books provide the formula for the c4 correction
which is:

Sqrt(2 / (n-1) ) x ((n-2)/2)! / ((n-3)/2)!  

The d series of factors are then derived from this.

Yes, the derivation is based upon the Normal distribution.  Personally, this
is why I prefer to use the sample standard deviation of the individuals,
which does not rely on the normal distribution.  But this has been a
controversial thought, and generally not supported by Wheeler.

Steve Prevette
Occupational Safety and Health
Fluor Hanford, A Fluor Government Group Project
ASQ Certified Quality Engineer
steven_s_prevette@rl.gov
509-373-9371