PM-7 Operating Manua.. - Voss Associates

Algorithms
Statistical Theory
N A could be converted to a count rate, RA, by dividing it by T, the count
time. The right hand side of Eq. 2.6 would, of course, have to be divided by
T also. If the denominator, T, is placed under the radical it would become
T 2 , but N B(avg) divided by time is also a count rate which will be defined as
RB which is equal to the average background count rate. Thus, Eq. 2.6 can
be expressed in terms of count rates by Eq. 2.7:
N A = SF R -----
B Eq. 2.7
T
The PM-7 uses Eq. 2.7 to determine the alarm setpoints (above
background) for the individual detector channels. The analogy of the above
example can be applied to a combined count rate produced in a detector
channel by background plus source activity. With RDA being the level of
source activity of interest, the total count rate produced in the detector
channel would be R B + RDA x eff where eff is the 4-pi efficiency of the
detector. The average count rate produced above average background is
RDA x eff (average). For a given probability of detection, or confidence
level, an alarm setpoint must be selected the appropriate number of “sigma”
below RDA x eff. The multiplier of this sigma is called “z”, and by analysis
can produce Eq. 2.8:
R
R A RDA × eff z B + RDA × eff
= – ------------------------------------- Eq. 2.8
T
The individual detector channels in the PM-7 calculate their RDA using Eq.
2.9 and compare that value to MAX RDA to verify that the former is the
lower of the two. If this is not true, the instrument is placed out of service
due to a high background condition. Eq. 2.9 is derived by setting Eq. 2.7
equal to Eq. 2.8 and solving for RDA. Note that Eq. 2.9 is iterative in that
RDA exists on both sides of the equal sign.
RDA
=
SF
R B R
----- z B + RDA × eff
+ --------------------------------------
T
T
----------------------------------------------------------------------
eff
Eq. 2.9
Thermo Fisher Scientific
Personnel Monitor -7 Techical Guide_4-5_