PCM-2 Manual.pdf - Voss Associates

ackground, would be selected. The total count rate on which to alarm is derived by dividing 10
counts by the length of the count time interval.
The Poisson Distribution Function can be cumbersome to use because the p(x) and P(x) values are not
directly obtained by a single calculation. Rather, chains of calculations or the use of a look up table
are required.
2. High Count Rates and/or Long Counting Intervals
When 20 or more background counts are expected per count cycle, the Gaussian Distribution
Function can be invoked with acceptable results. In terms of count rate, background will be
annotated with the symbol R B , R representing a count rate and B signifying background. The data
must be first standardized, then normalized to the function as follows:
Because the function is "standardized", i.e., centered about zero, so average background is subtracted
from the data so as to reference to zero instead of average background. Thus, the alarm set point is
expressed as a net count rate -- or count rate above background.
Regardless of the level of R B , it is normalized, or scaled to the Gaussian function, by its standard
deviation. Because Table 2 operates on (J (standard deviation) the entire distribution of R B is known
in terms of its (J. An alarm setpoint would then be selected as being an appropriate number of (J
above the average background count rate for a given false alarm rate. An appropriate name for the
constant that would multiply (J is SIGMA FACTOR, abbreviated as "SF."
Eq. 35 illustrates how simply the alarm setpoint is selected where RA(MIN) symbolizes the net count
rate on which to alarm. Note that the alarm set point is expressed as a minimum since lower count
rates would result in higher false alarm probabilities. Higher values are permissible since they would
serve to reduce the false alarm rate. Figure 6 is a graphic interpretation of Eq. 35.
RA(MIN)
'"' ~' - -',!"'" /'
- ~ ! - /T
= SF J --j
'J. '8 '
r-
~ Eq. 35
I
i
\
-+- R
A( ,",,'n)
Figure 6
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