Endress+Hauser PROFIBUS Gammapilot M FMG60 Operating Instructions Manual page 92

Technical Data
Statistical fluctuation of the
radioactive decay
!
92
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:
I
N
σ =
τ
The required parameters are:
• I : the pulse rate
N
• 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.
I
N
95% of the displayed measuring values are within the 2σ confidence limit.
In order to calcutae the relative error (percentage), the standard deviation must be divided by the
pulse rate:
σ
2 2
σ
2 = =
rel
τ
I
I
N
N
Example
• I = 1000/s
N
• τ = 10 s
2σ = 0,02 = 2%
rel
Note!
As a general rule, the statistical fluctuations can be reduced by enlarging the output damping
(integration time).
Gammapilot M FMG 60 - PROFIBUS PA
2σ
t
L00-FMG60xxx-05-00-00-xx-045