How we calculate Minimum Detectable Activity (MDA)
The Minimum Detectable Activity, or MDA, represents the smallest quantity of a radioisotope which can be detected with 95% confidence in one of our systems (rainwater, or the various air sampling systems). It is fundamentally based on the statistical variation of detector counts in the region where a peak from the isotope would appear. If the statistical variation is greater than the counts from an actual amount of radioactivity of that isotope, it is not statistically significant and it is not detected.
We start with a background spectrum from the setup, which shows what we would see if there is no source present. We look at a region of the histogram within the FWHM (full width at half maximum) of our detector resolution (FWHM is 1.15 keV at 364 keV, and 2 keV at 1460 keV), at the most significant gamma energy for each radioisotope. Specifically, that is 229 keV for Te-132, 364 keV for I-131, 604 keV for Cs-134, 662 keV for Cs-137, and 667 keV for I-132. We sum the counts in the energy spectrum within the FWHM, which represents the variance of the counting statistics. Then the standard deviation, or "sigma," of the counts in this region is the square root of the variance. A detectable activity must produce enough counts to be at least 2 times sigma within the FWHM. (Only 76.1% of the counts in a gaussian-shaped peak fall within the FWHM.) Two sigma means that there is only a 5% chance that such a detection results from random fluctuations in the background countrate.
To be more explicit, a detectable activity must produce at least a number of counts that is approximately 2*sqrt[sum(counts in FWHM of peak)] / 0.761.
This number of counts must then be converted into an activity concentration in the sample, in Bq/L or equivalent. This follows the same analysis chain that is used for converting the counts measured from a sample into a measured activity. Basically, the detector efficiency, initial sample size, and branching ratio of the gamma transition are taken into account. The resulting activity concentration calculated is the MDA for that isotope.