Re: xBar-R versus X-chart control charts

["John McConnell" <wysowl@msn.com.au>]

I would like to solicit the knowledge and experience of others on this
subject.

If the data are stable, the difference between control limits based on sigma
and those developed from R-bar is indeed insignificant.

My own experience, particularly in manufacturing, is that the creation of a
reasonably stable process is an early priority.  This means that the data
are unstable to begin with in most cases.

Because of this, usually the initial data show more than a few special
causes as well as shifts in the process mean.  In turn, I find that using
sigma (Root Mean Square Deviation) as an estimate from which to develop
control limits regularly produces limits beyond which no points fall, and
which is commonly mis-interpreted as a fairly stable system.   Providing the
data are at least reasonably continuous, this is to be expected.

This can be a critical error, because folks are likely to attempt to
determine causal relationships (especially with plant trials etc.) whilst
the process is in fact in a state of chaos.

However, using R -bar as the basis for my estimates produces a much more
easily interpreted chart, with the control limits being much tighter than
was the case using sigma, providing the special causes have been removed
from the calculations for R-bar.  Special causes and shifts in the process
mean then become much more obvious and it is easier to galvanise some sort
of corrective action.

Sometimes, both approaches can be used to good effect when we are trying to
convince managers to take action to stabilise the plant processes.  For
instance, for any given measure, calculate the sigma of a series of data.
Then calculate the R-bar of the same series, being careful to use only one
system of data if shifts in the average occur, as well as being careful to
remove special causes from the calculations.  What you now have is an
estimate of what R-bar would be, if only we could hold the process in a
stable state.  Now convert R-bar to sigma using the d2 factor (from memory,
sigma = R-bar/d2, I am on the road and don't have a text handy, and you
would be wise not to trust my memory).

You now have two estimates of the standard deviation.  One is the usual Root
Mean Square Deviation calculation that includes all the specials and shifts
in process average, and one is an estimate from R-bar that tells us what
might be achieved if stability was the norm.  Regularly, the RMS Deviation
estimate will be two to four times larger than the R-bar estimate.  This is
turn can be used to estimate the likely improvements that would follow if
the process were to be stabilised.

Is this making any sense?  I would like to hear what your experiences are,
especially if they differ from mine.

John McConnell
Wysowl Pty Ltd
Brisbane, Australia
wysowl@msn.com.au
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