RE: Control Charts for Alpha Counters

[Christoph_Hofmeyr/CNS1@cns.co.za]

Radsafers,
If one can be confident that the background is also Poisson distributed, it
is a big advantage.  The beauty of a Poisson distribution is of course that
the average is equal to the variance, which is just the square of the
standard deviation. However, it is defined in terms of events total, and
not event rate or other derivatives.  Therefore, it is theoretically
immaterial whether one takes many short measurements or one or a few long
ones to obtain an average background rate, provided the total measuring
time for the background is sufficient to accrue so many counts that the
reciprocal of the square root of the total number of counts ("events") is a
sufficiently small fraction.  This is a measure (SD) of how well one knows
the average background rate (the good news).  Further good news is that if
you now measure a sample, you are adding another Poisson distribution, and
the result is again a Poisson distribution.  The bad news is that the
"width" of the relevant background Poisson is relative to your sample
measuring time (variance in background component = average background rate
times sample measuring time), and not to all the effort you put into
determining the backgound (average) accurately. Further bad news,
particularly to compulsive background subtractors (who is not?), is that
unlike adding, subtracting Poisson distributions does not result in a
Poisson distribution.  By adding variances, you really put meaning into the
term uncertainty.
One further comment: the points on a Poisson distribution coincide rather
well with a normal distribution if one considers more than 20 to 30
"events".
Usual Disclaimer: My own view.
Chris Hofmeyr
CNS
Centurion
South Africa
chofmeyr@cns.co.za



Randy Redmond wrote:
Subject:  More on Statistics


I'd like opinions and definitely some references which justify the
following
practice or show that the following practice is not correct.

A laboratory performs a yearly calibration on its low level alpha counters.
During the yearly calibration, backgrounds are taken for various counting
times (10 each; average used for the background) - 60, 30, 20, 10, 5, 2, 1,
0.5 minutes.  The lab performs a daily background consisting of  10, 2
minute counts.  A control chart consisting of the daily 2 minute
backgrounds
versus the yearly 2 minute background +- 2 standard deviations is kept  (if
the daily background falls outside yearly +- 2 std.dev. something is
wrong).
The yearly backgrounds are used to document the MDAs of the instruments and
to determine the sample critical levels.  The daily background is
subtracted
from all sample results regardless of sample count time.

Randy Redmond
Lockheed Martin Energy Systems
P.O. Box 2009
Bldg.  9769,  MS 8081
Oak Ridge, TN  37831-8081
Email:  rxq@y12.doe.gov
Phone:  423-574-5640
Fax:  423-576-6047


In answer to Sandy Perle, Jay MacLellan wrote:


Subject:  RE: Control Charts for Alpha Counters



Sandy Perle wrote "In my opinion the lab should use a true Shewart Control
Chart, obtain
at least 30 independent data points, determine the true UCL and LCL,
based on the appropriate equations, and then use these Control Limits
to determine when the process is out of control. A true Shewart
Control Chart is based on normal tendency, which results in 99.97% of
true normal data falling within +/- 3 sigma."

This is a good plan if your routine count time is short enough to allow you
to
collect 30 background measurements.  If you are using a long routine count
time,
it isn't always practical.  Another caveat concerns the probability
distribution
for the counts.  If you are characterizing a low background system, the
distribution is Poisson, not normal.  And if you only collect a few counts
per
background measurement, you don't have a good estimate of the mean.  All
these
factors should be included in your control chart.

Jay A. MacLellan, CHP
Radiation and Health Technology
Pacific Northwest National Laboratory
Phone:  509-376-7247
Fax:      509-376-2906
Email:   jay.a.maclellan@pnl.gov

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