RE: R-Bar/d2

["alson look" <alson.look@megapathdsl.net>]

Hi,


A quick note: 

Shewhart's book (1931) Economic Control of Quality on pp 184+, and p 312
uses c2 as a correction factor for his control charts.  The sigma Shewhart
used was not the standard deviation we commonly use today.  Shewhart used a
sigma that divides the sum of squares by n rather than n-1.
Grant's 1946 Statistical Quality Control book (one of the first SQC books)
uses d2 and c2.  D2 for the Xbar and Range Chart and c2 for the Xbar and
Sigma Chart.

ASTM Manual on Presentation of Data and Control Chart Analysis STP 15D pp
136+ has a discussion of how d2 is derived.  Essentially it comes down to
using what I believe we call today Order Statistics (area of Mathematical
Statistics) in order to determine d2.  It involves triple integrals of the
normal distribution.

Irving Burr's Statistical Quality Control book pp 98-105 has a similar
discussion.

It is interesting to note that the ASTM points out that d2, d3, and c4 (we
use c4 rather than c2 today due to the fact that most people use a sigma
that divides by n-1 rather than n.) "may for most practical purposes be
considered satisfactory for use in control chart work even though the
universe is not Normal."

Alson C H Look
Alson.look@megapathdsl.net