Error Prediction - SARAD RTM1688-2 User Manual

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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

The simple consequence is: The higher the number of counts the higher is the accuracy of

the measurement. From the opposite point of view one could ask: How many counts I have

to detect to achieve a predefined uncertainty?

Two items will affect the number of counted decays: The sensitivity of the instrument at the

one hand side and the time period used for counting process (integration interval) on the

other hand.

While the sensitivity is an instrument specific constant, the integration interval may be

expanded to the maximum acceptable value for the desired time resolution of a

measurement series.

The relationship between the measured Radon concentration C

and the number of counts

N within an integration interval T is:

= N / (T * S)

whereby S represents the Sensitivity of the instrument, given in the unit [cts/(min*kBq/m³)].

The sensitivity using the slow mode is double as high as in the fast mode (see chapter

"Theory of Operation") and whenever the required response time is more than 2 hours the

slow mode should be selected.

For the following examples a fast mode sensitivity of 4 cts/(min*kBq/m³) shall assumed

while the slow mode sensitivity shall be 8 cts/(min*kBq/m³).

The first question could be: Which integration interval T has to set to get a statistical

uncertainty less than 10% at a confidence level of 1if the expected Radon concentration is

200 Bq/m³?

A 1error of 10% requires 100 counts (100%* 1 * (100) / 100 = 10%). Using the fast mode,

the integration interval can be calculated by

T(fast) = N / (C

* S) = 100 cts / (0.2 kBq/m³ * 4 cts/(min*kBq/m³) = 125 min.

Because the required interval is longer than 2 hours, the slow mode is the better choice,

leading to the following result:

User Manual RTM1688-2 06-02-2019.docx

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