RE: SPC - independent data

["Look, Alson" <alson.c.look@medtronic.com>]

Hi,
=20
Autocorrelation is a term from the area of Statistics called Time =
Series.  Autocorrelation can be thought of as a correlation coefficient. =
 The usual correlation coefficient is between two variables say X and Y. =
 If the correlation coefficient is high and you plot the data on a X Y =
scatter plot it may look like a "football" in shape.  If the correlation =
coefficient is random it will look more like a random scatter on a X Y =
plot.  Autocorrelation is the correlation between two values of the same =
variable.  For example, an autocorrelation of lag one implies the =
correlation of Xi and Xi-1.  If the autocorrelation is high you plot Xi =
vs. Xi-1 and the scatter plot may look like a "football."
Recently, I guess in the last ten years or so a large number of =
statisticians have indicated that if you have time series data (think =
SPC) and you have high autocorrelation you will underestimate your =
control limits and hence have more false alarms.  High positive =
autocorrelation has the effect of causing the variance (i.e. standard =
deviation) to be underestimated hence tighter control limits and more =
false alarms.  Many alternatives have been suggested.  One such that is =
popular is model the process, plot the residuals on a control chart and =
react to the out of control residuals.
Its not that simple.  Autocorrelation can be a natural part of the =
process or it can be induced.  In some processes if you sample at a high =
rate (i.e. you take your samples at say one a second) you may have =
autocorrelation.  Autocorrelation may also be a special cause.  It is =
important to think about your process before you try to time series =
model it.=20
It is also good to keep in mind that Shewhart's 1931 control chart ( I =
don't have his book in front of me but it is one of the charts in the =
first few chapters, the one where they are measuring resistance) has an =
autocorrelation of about .5 which is considered high by some.  Shewhart =
used the chart and found special causes.
Think about your process and how you are sampling.  Plot the Shewhart =
control chart.  If there are many out of control points ask why?  If you =
conclude that autocorrelation is a natural consequence of your process =
then adjust your control limits.  Don Wheeler's book on Advanced SPC has =
a nice example as well as an approximate correction factor for =
autocorrelation.
=20
Standard disclaimers
Alson
alook@pacbell.net
=20

Dirk, 

See "Understanding Statistical Process Control, Second Edition" by
Wheeler and Chambers, SPC press Knoxville, TN - pages 80 and 81. 

Also reference "Correlated Data and Control Charts" by Donald J.
Wheeler, 1989 from >> The Fifth Annual Forum of the British Deming
Association, Birmingham, England, April 28-30, 1992, Manuscript No. 37.
I believe reprints are available through SPC Press. 

See "Statistics for Experimenters, An Introduction to Design, Data
Analysis, and Model Building" by Box, Hunter, Hunter / John Wiley and
Sons, New York, New York -  Look at pages 62, 88, 104, 496, and 585.

Hope this helps.

Rgds, 
R K Bell