PCM-2 Manual.pdf - Voss Associates

Controlling Sensitivity
Qualitative counting exercises frequently seek to alarm with high reliability on some predetermined
level of activity. The activity of interest is herein labelled RELIABLY DETECTABLE ACTIVITY,
or RDA. In a detector channel, the average count rate produced by RDA in the presence of
background is RDA x Eff + R B
where Eff is the detector 47f efficiency, counts/disintegration. The
net count rate produced by the source (RDA), and identified as R s , is expressed in Eq. 39.
Eq. 39
The obvious redundance of R B
in Eq. 39 is stated for a purpose that will be developed here. The
term inside the square brackets represents Rs + R B
which is measured in an interval which will be
identified as Ts + B' From the resultant count rate, R B , the assumed background count rate average, is
subtracted to produce Rs. R B , being previously determined, has a different time base identified as TB'
Therefore, the standard deviation of Rs, determined by invoking Eq. 4, shown below.
(Js
RDA x Eff + RB +
RB Eq.40
Ts + B
T B
It is common practice to maintain a long-term background average such that TB is much greater than
Ts + B' The result of this is that the right hand term under the radical becomes negligibly small
compared to the left hand term and is usually ignored as will be the case throughout the rest of this
discussion. The reader is cautioned, however, that in a counting exercise where T B is approximately
equal to Ts + B (or worse, less than the composite count time), the identity of Eq. 40 should be used
instead of Eq. 41. In Eq. 41 the "S + B" subscript is dropped since the need to differentiate between
two counting intervals goes away.
a ~ JRnA X /;1f ' R, Eq.41
s
T
If an alarm set point is made equal to Rs' there would be a 50 % likelihood that RDA would cause an
alarm since Rs is its associated average count rate. Being an average, it is expected to exceed its
average half of the time and be less than that value the remaining half of the time. By inspecting
Figure 8, the reader can envision that for significant (> > 0.50) probabilities of detection, the alarm
setpoint must be lower than Rs. In a manner analogous to selecting RA(MIN), a maximum permissible
alarm set point is expressed in terms of (Js. The multiplier of (Js is called "z" in this document. The
desired probability of detection (also called Confidence Level) determines the value of z which is
selected from Table 2. A 90% confidence level (probability of RDA producing an alarm) is
accomplished with z = 1.28 and a 95% confidence level results from z = 1.65.
PCM2.MAN