Appendix A Algorithms
286
The net count rate for an occupant is obtained by subtracting the current effective
background average from the measured gross count rate:
Equation 24 Net Rate
( )
FactorShieldSelfRateBackgroundRateGrossRateNet ×−=
(24)
The greatest component of statistical error is usually in the gross count rate due to the
relatively short counting time; the error in the background average rate is usually less
significant due to the longer averaging period. However this might not be the case in
unusually high background conditions or if the background averaging period is short,
for example following a step change in background. The program considers the
statistical error in the background average during alarm set point and counting time
calculations (see the term
in Equation 25 on to Equation 28 in the
following section.
Alarm Trip Points
The Used Trip Point (UTP) is the value that is compared with the Net Rate to make
the Clean / Contaminated decision. It can be the Lowest Level Of Detection (LLD),
the Contaminated Trip Point (CTP), or the Alarm Trip Point (ATP), depending on the
circumstances. These terms are now explained.
The Lowest Level of Detection (LLD) is the minimum count rate above background
that will not trigger a false alarm due to statistical fluctuations. It corrects for the
statistical uncertainty in the background rate. This relationship is shown in the
following equation.
Equation 25 Lowest Limit of Detection
)s(T
)cps(R
)s(T
)cps(R
K)cps(LLD
b
b
m
b
+×=
α
(25)
…where
is the effective average background count rate (for the individual zone),
i.e. the average background count rate
multiplied by the Self Shield Factor,
is the monitoring time and
is the time over which the background count rate is
averaged (Background Average Period default = 300 s). The Self Shield Factor is
described under the F2 – (Zone) Settings screen. The term K Alpha, is a statistical
term related to the false alarm rate.
The Alarm Level Set point (ALS) is the release level specified by the facility at
which the unit is monitoring.