Re: Calculation of UCL/LCL for X Bar & R charts for n>>10*

[David Kerridge <dfkerridge@mac.com>]

> I have an automatic monitor that samples at 100%, so my
>  sample count (n) is very large (300-6000.  How to I
> calculate UCL and LCL for XBar and R charts.  I only have a
> table for sample sizes of 2-10, and I do not have the
> actual formula to allow me to scale to large sample sizes.
Dear kanedl@ldschurch.org,

      This is not as simple as it sounds. Although it would
be quite easy to tell you how to do the calculation, it would
almost certainly not help you.

       The main purpose of calculating control limits is to
help you to understand variation.

        The best way to do this is to study the variation in one
or more processes, and through that, the system to which the
processes contribute. The variation that you cannot measure,
and so cannot plot, is far more important than the variation
that you can measure. But to understand how variation works
you have to see it. When you have learned your lessons from
what you see, then apply it to the more important, but invisible
variation.

        If you apply the usual methods, designed for small
samples, to very large samples such as those you describe,
you may do actual harm.

        The usual "rules" will lead you to detect hundreds
of small and trivial special causes. Even if you remove
them, the actual product will not be noticeably better.
In fact, the constant changes in removing them may easily
make things worse. But the worst effect will be to waste
time when you should be moving on to more effective methods.

       So using such large samples will destroy one of the
main benefits of a control chart, which is to concentrate
attention where it does most good. Samples of 4 or five
seem by experience to strike about the right balance.

       There are three basic ways to improve a process.

1   Action on the whole system, for example by applying the 14 points
     and studying the System of Profound Knowledge.

2   Experiment, using the PDSA cycle

3   Removal of special causes.

These are in order of decreasing importance, though most people
start at the bottom, because the results are easy to get and the results
are visible. They may not last, because every time you make the
changes required by (2) or (1) new special causes arise, and others
disappear without specific action.

      It is a good idea to remove large special causes, because this
make the whole system more predictable, and makes it easier to see
what is happening. But as soon as practical, you want to get to
work on the more effective approaches. To do that you need the
the depth of understanding that you are unlikely to get without
studying control charts. So starting at (3) may be a good idea, though
not for the reasons (quick results) that many people suppose.

Best wishes
David
dfkerridge@mac.com