Appendix A Algorithms
278
Dividing through by
yields:
, and hence the variance ratio is zero.
Thus the closer the Variance Ratio is to zero the closer the average is to a Poisson
distribution. Values larger than one imply that a noise source such as low gas flow,
electronic noise, or a fluctuating background, is affecting the background rate.
The background rate, variance and variance ratio can be viewed on the F3 –
Background History screen for each detection zone.
Background Rate Reset
At every background update the new instantaneous background rate
is compared
to the current upper and lower background rate reset limits. If
is outside either
limit (over two background count intervals) then the running average for that detector
is discarded (reset) and a new average is computed using only the latest value. For a
smaller background level change that is within the upper and lower reset limits, the
background average will change gradually to the new level within the Background
Average Period. On Alpha/Beta units, the background reset for the Alpha and Beta
channels function independently.
The Background Reset Upper and Lower Reset Limits are defined in Equation 22 and
Equation 23.
Equation 22 Background Reset Upper Limit
b
B
B
T
R
KRUpperLimit ×+=
∆
(22)
Equation 23 Background Reset Lower Limit
b
B
B
T
R
KRLowerLimit ×−=
∆
(23)
...where
is the current (Average) Background Count Rate and
is the
Background Collect Time (default = 5 s). Note that a longer Background Collect
Time (
) results in tighter limits, i.e. the unit is more responsive to real changes in
background.
Special Cases:
• If
, then the
term is removed from the UpperLimit in Equation 22
above.
• If
, then the
term is removed and the second occurrence of
changes to
from the LowerLimit in Equation 23.