Re: Six Sigma and The Empirical Rule

[John <jsdwd@ispwest.com>]

On 3/6/03 12:57 AM, "Van Putten, Dirk" <Dvanputten@lodanwest.com> wrote:


> 
> The Empirical Rule states that at 3 standard deviations (sigma for a sample)
> to the right and left (total dispersion range of 6 sigma), 99.73% of all
> data should fall within that range.
> 

This is incorrect.  Citing "Understanding Statistical Process Control" by
Donald Wheeler (where I believe 'Empirical Rule' was coined) the following
pertains:

The Empirical Rule:  Given a homogeneous set of data:

Part One:  Roughly 60% to 75% of the data will be located within a distance
of one sigma unit on either side of the average.

Part Two:  Usually 90% to 98% of the data will be located within a distance
of two sigma units on either side of the average.

Part Three:  Approximately 99$ to 100% of the data will be located within a
a distance of three sigma units on either side of the average.

The above is copied directly from the book (a copyright problem?...I don't
Don would mind).

The 99.73% figure cited by Mr. Van Putten is from a Normal Distribution and
is not applicable to real life.  It is a theoretical model.  For example the
Normal Distribution is asymptotic.  That would indicate that even in a state
of statistical control, there is some probability (albeit small) of drilling
a 3/8" hole with a 1/4" bit.  Of course this does not happen when there are
no special causes.

John Dowd
jsdwd@ispwest.com