Re: sample size vs error

"Dies Deambulo" <[EMAIL PROTECTED]> wrote in message
news:[EMAIL PROTECTED]
> I've gotten email that asked me to explain this clearer.  Here goes.
>   We are making a measurment of a circuit on a wafer as it is being
> processed.  We are actually making several hundred different
> measurments in our fab for various things.  (like the width of an etch
> line.)
> All the calculations are made using only the last 60 data points.
> This includes the standard deviation and mean.  (this is why I'm
> worried.)
> What I mean by trend is the use of the WECO rules (Western EleCtric
> Operations, I believe) they
> look for different "trends" in the data.  like a point greater than
> three sigma or 5 data points in a row
> above the mean.   There are 7 or 8 of these rules.
> What I want to know is if 60 data points of measured data are enough
> to believe the mean, standard deviation and trends in this data.
> If not, how can I calculate the number needed for resonable accuracy?
>
> again, I apologize if I'm not to clear on this.
>
> Oh, I understand that some news groups prefer adding at the top and
> others seem to prefer adding to the bottom.  I wasn't sure what the
> protocol was for this group.
>
> Robert
>
> On Wed, 19 Nov 2003 03:38:12 GMT, Dies Deambulo <[EMAIL PROTECTED]>
> wrote:
>
> >I apologize but it has been several years since college statistics.
> >Here's the problem.  I'm worried that we aren't using enough data
> >points in the trend charts we have to make accurate conclusions.
> >We make a measurement and record the value.  We use the last 60
> >points to determine the mean and standard deviation.  Then we graph
> >these points using plus/minus three sigma as the control limits.
> >What concerns me is the one over the square root of the number
> >of samples indicated that the error is about 13%.  That's seems a bit
> >high.  I don't even know if that rule of thumb applies in this case.
> >I've also found an equation that gives the number of samples to
> >obtain a confidence of say 99% that the error is a certain percent.
> >N = z^2 * p * (1-p)/e^2   where z is from the normal distribution and
> >for 99% is 2.5758, e is the error that we want.  But I'm not sure how
> >to figure p for a trend chart.  Maybe there's a different equation for
> >this kind of data use?
> >So to recap, is 60 data points enough to assure that my analysis of
> >the trend is good?  If someone could recommend a resource for this,
> >that too would be much appreciated.
> >
> >Thanks,
> >
> >Robert
>

I think what you are doing, correct me if I'm wrong, is equivalent to applying
a quality control procedure to, say, the diameter of bolts coming off a line.
Every so often you take a sample of 60 bolts and see if their diameters are
too wide or too thin according to some control charts that have been set up.
And you want to know if 60 is enough. Is that right?

I'm not sure. Here are some general observations that may be helpful.

1. 60 is well beyond the usual sample size in quality control procedures. So
in that sense it is probably plenty.

2. If you want to get more comfortable with the sample size, divide the
standard deviation you calculated by the square root of 59 (60 -1) and then
multiply by 2.58. You are 99% confident that the true mean - from which you
took a sample of 60 - is between the mean you calculate + or - this number.

3. I'm not familiar with the formula for N that you cite. Often in quality
control "p" is used for the fraction of items defective in a batch.

Hope this helps.

Bill