RE: R-Bar/d2

[Rip Stauffer <rstauffer@bluefirepartners.com>]

Steve Prevette said, "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."

As I understand it, the reason for using average dispersion statistics
instead of overall dispersion statistics is that the former will enable us
to turn up the signal-noise ratio, thus rendering charts that are more
sensitive in finding special causes. If we include all the data in the
calculation (including data related to process shifts), we stand a good
chance of inflating the limits and masking special causes. This generally
applies more to initial calculations of limits. If Rbar/d2 yields about the
same value as the sample standard deviation, then you could say that the
data don't contain any special causes. Either statistic should provide about
the same sensitivity going forward. If the sample standard deviation is
significantly larger than Rbar/d2, you would use Rbar/d2.

Normality or the lack thereof doesn't really matter; as someone (Jonathan
Siegel or David Kerridge, maybe) said a few years ago: "it's not as though
the standard deviation is some true measure of dispersion and all the others
are just approximations. All dispersion statistics are the results of the
arithmetic." I'm probably horribly paraphrasing at least two other people
and Wheeler in that statement, but it makes sense. Control charts based on
Rbar/d2 have long been proven very robust to departures from normality,
despite the assumptions inherent in the arithmetic. Shewhart spent a lot of
time proving that normality is neither necessary nor sufficient in assessing
a state of statistical control.

Best regards,

Rip

Rip Stauffer
BlueFire Partners
612-916-0197
rstauffer@bluefirepartners.com