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Dealing
with Non-Normality
by Paul
A. Keller, CQE CQA
Tom Pyzdek's article Non-Normal
Distributions in the Real World provides many examples and sound reasoning
for the existence of Non-normal data. Tom elaborates on the implications
of non-normality, particularly as they relate to capability calculations.
As Tom suggests, when processes are sufficiently non-normal we'll need
to estimate the shape of the distribution to calculate process capability
or control limits for individuals data. Quality America's SPC products,
including SPC-PC IV, SPC-PC IV Starter Kit, and QA-Shop Floor, allow users
to fit curves to data using the Johnson family of distributions. A key
requirement for defining distributions is that the data be from a controlled
process. This makes sense, as the lack of statistical control indicates
the presence of multiple distributions. When rational
subgroups of size greater than one can be formed, an X-Bar
chart can be used to evaluate process control. When rational subgroups
are limited to single observations, Individual-X
charts would seem the natural choice for evaluating process control.
However, we need to define the distribution in order to calculate the
proper control limits for these individual data values. This is a problem,
since we cannot define the distribution unless the process is in control.
It seems we are in a "Catch 22" scenario.
Fortunately, there are
other charts for individuals data. The EWMA
chart is a popular choice for this situation. Since the plotted statistic
is an average (an exponentially weighted average), the Normal distribution
is used to define control limits. We can establish control using the EWMA
chart, then define the distribution using the Johnson methods. This fitted
curve can be used to calculate process capability and control limits for
the Individuals chart.
More information on this
topic can be found in these links:
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