Endress+Hauser Gammapilot M FMG60 - Page 100

Technical data Gammapilot M FMG60 with FOUNDATION Fieldbus
100 Endress+Hauser
Statistical fluctuation of the
radioactive decay
The radioactive decay is subject to statistical fluctuations. Therefore, the pulse rate fluctuates about
its average value. The standard deviation σ is a measure for these fluctuations. It can be calculated
in the following way:
where:
•I
N
: the pulse rate
• τ: the output damping (integration time) as defined by the user
The standard deviation can be used to calculate various confidence limits. For the planning of
radiometric measuring points, the 2σ− confidence limit is generally used. Approx. 95% of the
indicated pulse rates have got a deviation of less than 2σ from the average value. Only for approx.
5% is the deviation larger than 2σ.
L00-FMG60xxx-05-00-00-xx-045
95% of the displayed measuring values are within the 2σ confidence limit.
In order to calculate the relative error (percentage), the standard deviation must be divided by the
pulse rate:
Example
•I
N
= 1000/s
• τ = 10 s
⇒ 2σ
rel
= 0.02 = 2%
!
Note!
As a general rule, the statistical fluctuations can be reduced by enlarging the output damping
(integration time).
s =
N
I
t
2s
t
I
N
s
t
rel
=
N
I
2
s
N
I
=
2
2