Re: R-Bar/d2

[John <jsdwd@ispwest.com>]

> Imagine sampling from a purely normal distribution that has a mean of 0 and
> a standard deviation of one. If you sampled 250 subgroups of size 5 from
> this distribution, what would it's average range be? What would the standar=
> d
> deviation of the range be?
> 
> d2 is the mean range when sampling from 250 subgroups of size 5 (we see
> 2.378 above, pretty close to what=B9s in the tables). d3 is the standard
> deviation of the range (0.823 in the simulator).
> 
> Wayne J. Levin, M.A.Sc., P.Eng

Interesting.  I had ( mistakenly) always thought this was where d2 came from
(i.e. A sampling distribution).  I was interested to note in discusions with
Don Wheeler that it had been derived.

It turns out that the first attempt was by Tippet in 1925 followed by an
effort by Pearson (Egon) in the 30s.  These were N of 2 and 3 (at least).

The computer made the work easier.  In 1960 factors were carried out to 10
decimal places.  Irving Burr in the late 60s showed that d2 was very robust
with mound shaped distributions.  Don Wheeler has a book, "Normality and
Process Behavior Charts", that covers this in more detail.

John Dowd
jsdwd@ispwest.com