# Method Evaluation and Validation

In the following, two selected procedures are evaluated with respect to LLD, MDA and uncertainty budget.

226Ra through 222Rn ingrowth (method 2.2.1.4., 24 h storage)

Lower Limit of Detection

The Minimum Detectable Activity MDA is calculated through LLD and the background without considering the uncertainties for analysis by

where fv represents the volume factor, ft1 the daughter ingrowth factor and ft2 the decay factor between Rn extraction and mean measuring time. The following experimental parameters have to be considered for the calculation of MDA for the procedure of 226Ra determination through Radon ingrowth with 24 h ingrowth storage:

R0        0.5 count / hour

t           1 hour (measurement of sample and background)

ε          300 %

fv         8/7 x 1000/12

ft1        1 / (1- exp-(24/92.16) * ln 2)

ft2        1 / exp-(3/92.16) * ln 2

V          12 mL

LLD = 2 * 1.645 * (2 * 0.5 / 602 * 602)1/2

LLD = 0.00091 sec-1 per sample

Minimum Detectable Activity:

MDA [Bq/L] =  0.00091/3 * 95.2 * 6.06 * 1.02

MDA = 0.178 Bq/L

Analysis of uncertainty

Several parameters influence the variability of the analysis.  The list of parameters and its relative standard uncertainty are:

The uncertainty parameters are assumed to be independent from each other; therefore the calculation of the analysis uncertainty U or u(y) is done by the law of propagation of errors (sum of errors in square)

Total analysis uncertainty:    U = 6.5 %

226Ra by RAD Disk filter (method 2.2.1.5.)

(a) Gel measurement of the EDTA eluate:

Lower Limit of Detection

LLD = 2 * 1.645 * (2 * 120 / 602 * 602)½ = 0.014 sec-1    per sample

Minimum Detectable Activity:

MDA [Bq/L] = (LLD / e * V) * ft = (0.014 / (0.9 * 3) * 1.02

MDA           = 5.3 mBq/L

Analysis uncertainties

The following uncertainty parameters influence the analysis:

Total analysis uncertainty:           U = 6.3 %

Remark: No influence by other radionuclides in absence of 224Ra

(b) Extraction of 222Rn from EDTA eluate after equilibration (storage >25 days):

Lower Limit of Detection (LLD)

After equilibration with 222Rn (> 25 days, <1 % error), the LLD is calculated according to:

LLD = 0.00091 sec-1 (see 226Ra)  per sample

Minimum Detectable Activity

MDA [Bq/L] = (LLD / e * V) * f= (0.00091 / (3 * 3) * 1 * 1.02

MDA           = 0.1 mBq/L

The additional uncertainties of this method through Rn losses by emanation (4 %) and durig equilibration are compensated by a lower uncertainty for calibration of organic phases (no quenching and better PSD).