Alpha Counting

["Albers, John P" <JPAd@pge.com>]

Radsafers,    I have a problem with alpha counting statistics.  I believe
that it is very difficult to "properly" detect 20 dpm/100cm2 alpha activity.
Your comments are appreciated

It began as a simple question...

I would like to report results for "detected" radioactivity with a range
that has a 95% probability of including the "true" result.

I would like to report results for "not detected" radioactivity with a range
(from zero to an upper limit) that has a 95% probability of including the
"true" result.
 
I would like to decide between "detected" and "not detected", so that I have
less than a 5% probability of a "False Positive" decision and less than a 5%
probability of a "False Negative" decision.

My application is low countrate measurements (alpha swipes for release).  I
observe an average background of 0.05 cpm and  I will count each swipe for
(an arbitrary) five minutes.

Since the Poisson distribution for background should produce 0 events with
about 77.9% probability, and produce either 0 or 1 events with about 97.4%
probability, I will consider that 2 or more events means radioactivity was
"detected".

By trial & error, I calculate that a gross countrate of 1.2592 cpm has
slightly less than a 5% probability of producing 0, 1 or 2 events.  Then,
for "not detected" radioactivity, the net countrate should be less than
1.2092 cpm, with 95% probability.

So, I observe and report the following:

Swipe #1 - 1 count in five minutes => Less than 1.209 cpm (net)

Swipe #2 - 2 counts in five minutes => 0.35 cpm (see below for uncertainty)

By trial & error, I calculate that a gross countrate of 1.445 cpm has
slightly less than a 2.5% probability of producing 2 or fewer events in 5
minutes, and that a gross countrate of 0.12372 cpm has slightly less than a
2.5% probability of producing 2 or more events in 5 minutes.

Therefore, swipe #2 should be reported as ranging from 0.07372 cpm (net) to
1.3950 cpm (net) or approximately 0.35 +1.04 -0.28 cpm (net).

Aside from being computationally intensive, is this approach mathematically
correct?  Thank you!
John P. Albers
Director, Radiation Protection
Humboldt Bay Power Plant
office 707-444-0877, pager 707-269-8547
JPAD@pge.com




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