SPC - Independent Data

[Jonathan Siegel <jmsiegel@yahoo.com>]

It's worth mentioning that in Deming's view there is
no such thing as truly independent data. This belief
underlay Deming's objections to the chi-squared test
(which tests for independence). According to Deming,
everything is at least slightly dependent on
everything else if we observe it enough. For all we
know this could be caused by the act of measuring.
Roll a die enough times, and the act of rolling it
will nick it in ways that favor certain spots.
Interviewees can give one age to female interviewers,
another to male interviewers. If a test shows
independence, all it tells us is that we haven't
collected enough data yet. 

This is also true of data from sequential industrial
processes. The question is, does the dependence enough
to affect our purpose?

Shewhart's original approach didn't include all the
tests for out-of-control conditions sometimes used, in
part because some later tests depend on normal theory
and Shewhart wasn't willing to assume that data even
came from a probability distribution. 

I'll also point out that whether to adjust for a trend
or not depends on ones purpose and knowledge about the
particular process. Sometimes the trend itself signals
a problem. Other times a trend is part of the intended
underlying process and one is simply interested in
variation around that process. One should only adjust
for trends in the latter case.

Jonathan Siegel