RE: Six Sigma and The Empirical Rule

[Steven_S_Prevette@rl.gov]

Does the term "Six Sigma" refer to a total data dispersion range of 6 sigma
centered about the mean on a normally distributed sample? Or does "Six
Sigma" refer to a one-sided data spread (either to the right or left of the
mean) for a total of 12 sigma data dispersion range?

SSP - Generally it is 6 sigma from the average.  Most examples I have seen
are two-sided data.  One one-sided data, they still only go to 6 sigma from
the average.

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.

SSP - I have not heard the phrase "empirical rule" before.  99.73% does come
from the Normal (or Gaussian) distribution.  Please note that control
charting does not rely upon the Normal distribution, nor the 99.73% (nor,
for that matter, the central limit theorem).  Control charting is
distribution-free, relying upon the Tchebychev Inequality.

If "Six Sigma" refers to a dispersion range of 12 sigma, what does the
Empirical Rule state at 6 standard deviations? 

SSP:  The article by Bill Latzko in the DEN archives does give a way to
calculate it.  In addition, you can use formulae in Excel spreadsheet to
calculate it.  By the way, the 6 sigma aficionados subtract 1.5 sigma from
any calculation, supposedly because data can "drift" by 1.5 sigma.

Does anyone have a reference
for the application of the Empirical Rule past 3 standard deviations?

SSP:  See http://deming.ces.clemson.edu/pub/den/six_sig.pdf 

Steve Prevette
Site Technical Authority for Statistical Trending
Environment, Safety and Health
Fluor Hanford, A Fluor Global Services Company
ASQ Certified Quality Engineer
steven_s_prevette@rl.gov
509-373-9371