Statistical Error (For Non-Mathematicians); Error Prediction - SARAD RTM 1688-2 Manual

RTM 1688-2
Valid register addresses are:
Register Register content
Address
0x0000 Radon concentration [Bq/m³]
0x0002 Statistical error of Radon concentration [%]
0x0004 Average Radon concentration since last start [Bq/m³]
0x0006 Battery voltage [V]
0x0008 Temperature [°C]
0x000A Relative humidity [%]
0x000C barometric pressure [mbar]
0x000E Thoron concentration [Bq/m³]
0x0010 Statistical error of Thoron concentration [%]
0x0012 Average Thoron concentration since last start [Bq/m³]
IEEE 745 float values (4 Byte) are transmitted as two sequential 16 bit registers. The number of
registers to be read must be two. That means, only one value can be transmitted per frame. Other
values and not stated register addresses will cause an exception response.
Bus Settings:

Address by INIT software

Transfer protocol by push button menu at instrument

Statistical Error (for non-mathematicians)

The radioactive decay is a statistical process. That means, even if the Radon concentration is
constant over the time, the number of decays N counted within several intervals of the same
period will be different. N will vary around the mean value of all considered intervals.
Considering an infinite number of intervals would lead to an average which one indicates the
"true" result of N. For a single interval, the value of N will be either below or above the "true"
value. This observed deviation is covered by the term "Statistical Error".
Therefore, each serious measurement contains beside the calculated Radon value the error
band for a stated confidence interval. The commonly used confidence intervals are 1, 2 or 3
Sigma () which refer to a likelihood of 68.3%, 95.45% and 99.73%.
For example, the correct interpretation of a measured Radon concentration of 780 Bq/m³ with
a statistical 1error of ±15% is:
The real "true" Radon concentration lies with a likelihood of 68.3% within the range from 663
Bq/m³ (780 Bq/m³ - 15%) to 897 Bq/m³ (780 Bq/m³ + 15%).

Error Prediction

The relative statistical error E for a chosen confidence interval of k-Sigma can be predicted
from the number of detected counts N by the equation:
E[%] = 100% * k * (N) / N
14 Manual_RTM1688-2_EN_24-02-2023.docx
Number of Format
registers
2 Float
2 Float
2 Float
2 Float
2 Float
2 Float
2 Float
2 Float
2 Float
2 Float
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