PCM-2 Manual.pdf - Voss Associates

can only assume a single value, determined by the first (n - 1) points -- hence zero degrees of
freedom exist for the n the data point.
QUALITATIVE MEASUREMENTS
A typical qualitative measurement in a radiation monitoring system is a "go/no-go" determination.
For such a measurement an instrument is set up to alarm when a pre-determined count rate is
exceededo Two primary constraints control the appropriate count rate on which to alarm. The first
of these is the background count rate and what is deemed an associated false alarm rate, or probability
that background alone will randomly exceed the alarm set point. This determines the lower limit for
an alarm set point. The second constraint is the upper limit on the alarm set point which ultimately,
determines the minimum activity (above background) that will cause an alarm with an associated
probability or confidence level. Each constraint will be considered individually and then in
combination with each other.
Controlling False Alarm Rates
What will be called a TYPE I false alarm herein is an alarm caused by background alone. Because
the background count rate is random, during anyone counting interval the background count rate
could assume any non-negative value. Thus, even with a high alarm set point, there will exist a finite
probability that a TYPE I false alarm will occur. Accepting that false alarms will not be entirely
eliminated, the first step is to establish an acceptable probability of false alarm. For a single
measurement, that small probability will be labelled "p." For multiple measurements, be they
sequential or simultaneous by way of multiple detector channels operating simultaneously, the overall
false alarm probability of false alarm for "N" measurements (P N ) is defined by Eq. 33.
Eq. 33
Once an overall false alarm rate is established, the false alarm rate per individual channel or
measurement is derived from Eq. 33 as illustrated by Eq. 34.
Nr----
p=I--V I - PN
Eq. 34
1. Low Count Rates and/or Short Counting Intervals
Counting exercises whose product of count rate and count time result in 20 or less counts per interval
(average), as stated earlier, are appropriately modelled by the Poisson Distribution Function. By
using the numbers from the example on page 7, Table 1 can be invoked for an example of false alarm
rate control. In that example, 2.5 counts was the average expected number of counts per count
interval. If a false alarm rate of 0.001 or less is desired, it is noted from Table 1 that, based on A =
2.5, P(lO) = 0.000277 satisfies the requirement whereas P(9) = 0.00114 exceeds the maximum
acceptable false alarm rate Thus, an alarm setpoint of 10 counts per count time interval. including
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