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2014 ICHLNRRA INTERCOMPARISON OF RADON

/

THORON GAS

AND RADON SHORT-LIVED DECAY PRODUCTS MEASURING

INSTRUMENTS IN THE NRPI PRAGUE

K. Jı´lek* and J. Timkova´

National Radiation Protection Institute, Prague, the Czech Republic *Corresponding author: karel.jilek@suro.cz

During the Eighth International Conference on High Levels of Natural Radiation and Radon Areas held in autumn 2014 at Prague, the third intercomparison of radon/thoron gas and radon short-lived decay products measurement instruments was orga-nised by and held at the Natural Radiation Division of the National Radiation Protection Institute (NRPI; SU´ RO v.v.i.) in Prague. The intercomparison was newly focussed also on continuous monitors with active sampling adapters capable to distin-guish radon/thoron gas in their mix field.

The results of radon gas measurements carried out in the big NRPI radon chamber indicated very well an average deviation of up to 5 % from the reference NRPI value for 80 % of all the exposed instruments. The results of equilibrium equivalent concen-tration continuous monitors indicated an average deviation of up to 5 % from the reference NRPI value for 40 % of all the exposed instruments and their∼8–10 % shift compared with the NRPI. The results of investigated ambient conditions upon response of exposed continuous monitors indicated influence of aerosol changes upon response of radon monitors with an active air sampling adapters through the filter, only. The exposures of both radon/thoron gas discriminative continuous monitors and passive detectors have been indicated inconsistent results: on one hand, their excellent agreement up to several per cent for both the gases, and on the other hand, systematic unsatisfactory differences up to 40 %. Additional radon/thoron exercises are recommended to improve both the instruments themselves and quality of their operators.

INTRODUCTION

Generally, it is well known that both radon and thoron gases and predominantly their short-lived decay products are the largest contributors to radi-ation dose from inhalradi-ation for members of the public. Hence, relevant action plans are currently under way in many European countries focussing on reduc-tion of indoor radon.

An inseparable part of these plans is also a QA/QC programme for used measurement instruments. International intercomparisons allowing an independ-ent control of used relevant measuremindepend-ent instrumindepend-ents or standards play a crucial role in the programme.

Whilst passive integral detectors are frequently used for a wide range of surveys of radon/thoron gas levels in houses, continuous monitors can be used for both special radon/thoron gas diagnostic measure-ments in houses(1)and as the key instruments for me-trology in the scope of relevant QA/QC programmes for radon/thoron gas and their short-lived progeny measurement instruments.

Currently, the National Radiation Protection Institute (NRPI) of Prague is accredited by the Czech National Accreditation body for radon measurements performed in a house. Its QA/QC programme and fa-cility enable to assure quality of measurements for all types of measurement instruments (spot, passive inte-gral, continuous) and quantities as follows:

– radon gas in air – thoron gas in air

– mix field of radon/thoron gas in air

– equilibrium equivalent concentration (EEC) for radon in air

– fpfor radon decay products in air

The programme is based on both traceability of its ref-erence instruments to measurement standards and in-dependent comparison of its reference instruments with measurement standards of worldwide renowned laboratories such as the PTB Braunschweig (D), the BfS Berlin (D) and the Czech Authorised Metrological Centre (SUJCHBO Kamenna). Both the big NRPI radon chamber and the small NRPI radon/thoron chamber(2–6)play a key role in the programme.

During the Eighth International Conference on High Levels of Natural Radiation and Radon Areas (ICHLNRRA), the third intercomparison of radon/ thoron gas and radon short-lived decay products measurement instruments was organised by and held at the Natural Radiation Division of the NRPI (SU´ RO v.v.i. in Czech) in Prague. Besides passive radon and radon/thoron discriminative integral detectors, radon gas and EEC continuous monitors, the intercomparison has also been newly focussed on continuous monitors with active sampling adapters capable to distinguish radon/thoron gas in their mix fields.

MATERIALS AND METHODS

Participants

In total, seven laboratories from seven different coun-tries took part in the intercomparison. They submitted

Radiation Protection Dosimetry (2015), pp. 1–7 doi:10.1093/rpd/ncv311

Radiation Protection Dosimetry Advance Access published May 19, 2015

at National Radiation Protection Institute on June 3, 2015

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– nine radon gas continuous monitors type— AlphaGUARD (2x), RAD7 (2x), Canary Pro (2x), Radon MAPPER (1x), ERS/RDM 25 (2x) – two passive radon gas integral systems based on

low sensitivity—E-perms electrets and SSNTD – nine continuous monitors for measurements

of EEC type—Doseman Pro (5x), BWLM-Plus25 (2x), ERS/RDM 25 (2x)

– four discriminative Rn/Tn gas continuous monitors with an active adapter type—RAD7 (2x), Alpha GUARD (1x), Radon/Thoron MAPPER (1x) – four passive integral systems (E-perm and RM-1

Rn/Tn based on electrets, and RADUET and PADC based on SSNTD) capable to distinguish radon and thoron gas in their mix field.

Each submitted passive integral system included more than one pair of Rn/Tn discriminative detectors based on both SSNTDs and electrets.

A list of all participants is given in Table1.

Logistical arrangement

Each participant was asked to return his results in terms of all measured records from used relevant continuous monitors and in terms of average value of relevant measured quantity from each exposed passive detector including corresponding standard de-viation. ID of each monitor and a passive detector was required. To avoid problems with differently adjusted sampling times for continuous monitors and to facilitate the comparison of the results from simul-taneously exposed both passive integral detectors and continuous monitors in the big radon chamber inves-tigated, exposure periods have been chosen properly. Each participant was also informed in advance about dynamic range of compared quantity. Immediately, after the end of the intercomparison, all monitors and detectors including passive transit detectors were

returned to the originating laboratories for evaluation of their results. Deadline for the results has been fixed.

Exposures

Based on all the submitted instruments, following types of exposures were carried out during the inter-comparison:

– Type A: Common in terms of time exposure in the big NRPI radon chamber comprising: (a) exposure of radon gas continuous monitors,

denoted as A1

(b) exposure of short-lived radon decay product continuous monitors, denoted as A2

(c) exposure of radon gas passive integral detec-tors, denoted as A3

– Type B: Exposures of passive integral radon/ thoron (Rn/Tn) gas discriminative detectors in the small Rn/Tn chamber for two different ratios of activity concentration Rn/Tn gas.

– Type C: Exposure of Rn/Tn gas discriminative continuous monitors with active sampling adap-ters with use of two defined pass flow sources226 Ra and228Th with well-known radon and thoron gas the source production.

Exposure type A in the big radon chamber

The big NRPI radon chamber is a 48-m3-type walk-in with an airlock walk-inside that allows the followwalk-ing quantities to be adjusted, held stable, monitored on-line and recorded(3):

– radon concentration

– EEC, including its unattached fraction (fp) – air exchange rate (ACH)

– temperature and relative humidity – generated spherical aerosols

Table 1. List of participants and submitted exposures.

Institution Country A1 A2 A3 B C

Centre de Recherche Nucle´aire d’Alger Algeria X X

National Institute of Radiological Science, Chiba Japan X

MI.AM Srl. Italy X X X X

ZVD Za´vod za Varstvo pro Delu D.D. Slovenia X X X

Tracerlab GmbH., Ko¨ln Germany X X

Durridge Co. Inc., Boston USA X X

Track Analysis System Ltd. UK X X

NRPI, Prague Czech Republic Ref Ref Ref X/Ref Ref

X and Ref mean compared values and reference value, respectively; A1means exposure of radon gas continuous monitors in

the big radon chamber; A2means exposure of EEC continuous monitors in the big radon chamber; A3means exposure sets

of a passive radon gas detectors in the big radon chamber; B means exposure sets of a passive Rn/Tn discriminative detectors in the small Rn/Tn chamber; C means active samplings of Rn/Tn gas discriminative continuous monitors.

K. JI´LEK AND J. TIMKOVA´

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Prior to installing all the instruments, a desired steady-state radon concentration of about 7 kBq m23 was set up in the chamber. Radon concentration inside the chamber was continuously monitored on-line by means of the NRPI reference monitor AlphaGUARD on an hourly basis, and additionally, twice a day, inner atmosphere of the chamber was sampled into the NRPI reference scintillation cells type NY. Simultaneously, every 2 h, values of EEC and fpwere also continuously monitored on-line in the chamber by means of the NRPI reference continuous monitor Fritra 4.

Besides on-line monitoring of EEC and fp, inner at-mosphere of the chamber was also sampled twice a day by means of the one-grab samplings through the diffusion screen on the Millipore AA 0.8-mm filter placed behind the screen to estimate unattached and attached activities of each short-lived radon decay product.

In order to check the influence of ambient condi-tions on response of tested continuous monitors, the relative humidity of ambient air, aerosol concentra-tion, particle size distribution and ACH were proper-ly changed within realistic indoor conditions, kept stable and monitored by means of the chamber accessories.

That is why the exposures denoted as A1and A2 were additionally divided for evaluation into four partial investigated time periods differing in ambient conditions. Whilst partial periods denoted as I, II and III took1 d each, the fourth period denoted as IV corresponded in terms of time to total exposure A lasting for3 d.

The NRPI declares the overall uncertainty (K¼1) of each calibration point of radon activity concentra-tion better than 5 % and of EEC better than 10 %.

Exposure conditions and magnitudes for all the investigated periods are given in Table2.

Exposure type B in the small Rn/Th chamber

After deployment of all sets of investigated passive in-tegral detectors on the floor of the stainless steel shell inside the chamber, the chamber (150 dm3) was closed. Afterwards, used Rn/Tn gas pass flow source, stable pump, precise flow meter calibrator Defender M 530 (Bios, USA) and the reference NRPI continu-ous monitor RAD7 were properly connected to the chamber in a short loop. Desired and stable ratios of Rn/Tn activity concentrations were achieved by means of properly chosen both magnitude of flow rates through the used source and a proper option of “delay” volume for thoron gas, which was also part of the loop.

In order to check the influence of different ratios of Rn/Tn gas on response of investigated detectors, two exposures differing in Rn/Tn gas ratios were carried out, lasting for 24 h and each denoted as B1and B2 stepwise. The NRPI declares the overall uncertainty (K ¼1) of each calibration point of radon/thoron activity concentration better than 10 %. Exposure conditions and magnitudes for all the investigated periods are given in Table3.

Exposure type C of continuous monitors with an active sampling adapters

The NRPI is equipped with stable pumps, the precise flow meter calibrators Defender type M 530 and certi-fied both radon gas source (type RF, producer CMIIZ Prague, CZ) and thoron gas source (type Th 1025, producer Pylon, CND) type flow pass through with well-known radon/thoron gas source produc-tions P.

The proper connection and combination of the sources allowed to set up stable and well-known: Table 2. Exposure conditions and magnitudes during exposures in the big radon chamber.

Exposure type A1/I A1/II A1/III A1/IV A2/I A2/II A2/III A2/IV

Exposure duration (h) 20 23 23 68 20 23 23 68 av(Rn)/EEC (Bq m 23 ) 6873 6679 6473 6666 2016 2812 3386 2759 SD (Bq m23) 622 532 307 518 373 523 760 797 SEM (Bq m23) 136 109 63 62 113 151 219 135 ACH (h21) 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 RH (%) 24.1 24.8 63.8 25.8 24.1 24.8 63.8 25.8 T (8C) 30.1 30.2 29.1 29.8 30.1 30.2 29.1 29.8 p (mbar) 994 996 997 996 994 996 997 996 fp 0.15 0.07 0.04 0.08 0.15 0.07 0.04 0.08 F 0.31 0.46 0.36 0.42 0.31 0.46 0.36 0.42 Z (cm23) 2876 5586 9756 5076 2876 5586 9756 5076 GM (nm)/GSD 101/2.5 135/2.2 154/2.0 192/2.1 101/2.5 135/2.2 154/2.0 192/2.1 av(Rn)/EEC means mean radon concentration and EEC, respectively; SD means standard deviation; SEM means standard

error of the mean; RH, T and p means relative air humidity, air temperature and atmospheric pressure, respectively; ACH means air exchange rate; F and fpmeans equilibrium factor and unattached part of EEC, respectively; GM/GSD means

geometrical mean and geometrical standard deviation of measured aerosol size distribution.

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(a) pure radon gas concentration, denoted as C0 (b) pure thoron gas concentration, denoted as C1

(c) mix radon/thoron concentration, denoted as C2 in the sources output airstream calculated as Pi/F with overall uncertainty up to 5 % (K¼1).Piis the relevant well-known radon/thoron source produc-tion,F is the flow rate of a carrier gas through the source andKis the coverage factor.

The experimental setup in the present study allowed by means of using a proper splitter to connect at the same time one or two sampling adap-ters of tested monitors to the source output airstream. Since sampled gas concentrations were under influ-ence of flow rate of used carrier gas only during whole exercise, the flow rate through used sources was moni-tored on a minutely basis. Dry outdoor air was used as carrier gas with neglected content of radon/thoron gas in comparison with investigated concentrations of the order kBq m23.

In order to avoid any problems during sampling with dilution of sampled concentrations, proper flow rates were used, which were much higher than those used for samplings. Based on common agreement with participants, exposures types C1 and C2 have been carried out.

Relevant exposure conditions and magnitudes are summarised in Table3.

RESULTS

To evaluate participants data and compare them with the NRPI reference values, the following two ap-proaches were used with respect to statistical character of the observed data:

(a) Welch’st-test(7)as a two-sample location test to check the null hypothesis that two populations with unequal variances have equal means, i.e. responses of the reference instrument and com-pared instruments are not significantly differ-ent. Welch’st-test defines the statistictby the

following formula: t¼ ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiXY SX ffiffiffi n p 2 þ SYffiffiffiffi m p 2 s ð1Þ

whereX andY are mean values reported by partici-pants and the NRPI reference mean value, respective-ly. SX and SYare sample standard deviations given from participants and from the NRPI, respectively.n andmare the corresponding sample sizes.

Generally, application of the two-tailed Welch’s t-test yields a p-value. If the p-value is less than the adopted significance level of 5 %, i.e. ifp-value

,0.05, then the null hypothesis of equality of means is rejected. The significance level of 5 % means that on average in 5 cases out of 100 cases, the null hypothesis is rejected even when the null hypothesis holds. One needs to be conscious of this trait of statistical testing especially when many tests are carried out.

(b) In order to quantify the observed difference between mean values of reference and compar-ing instrument, both ratioRand the per cent differenceD%(denoted PD as for per cent dif-ference in %) were defined as follows:

R¼X

Y ð2Þ

D%¼abs (R1Þ 100 ð3Þ

where all symbols have the same meanings as in Equation (1).

An approximate 95 % confidence interval for ratio Rdenoted as (RL,RU) can be calculated by means of Table 3. Exposure conditions and magnitudes during exposures in the small Tn/Rn chamber and type C.

Exposure type B1/Rn B1/Tn B2/Rn B2/Tn C1/Tn C2/Tn C2/Rn Exposure duration (h) 24 24 24 24 2 2 2 av(Rn)/av(Tn) (Bq m23) 3780 7137 4160 1690 4860 4119 8257 SD (Bq m23) 437 1107 463 736 340 309 669 SEM (Bq m23) 89 226 28 151 152 138 253 RH (%) 12.1 12.1 11.8 11.8 ,5 ,5 ,5 T (8C) 24.1 24.1 25.2 25.2 24.5 24.5 24.5 p (mbar) 994 994 996 996 994 994 994

av(Rn)/av(Tn) means mean values of radon gas and thoron gas activity concentration, respectively.

Meanings of all rest of the parameters are the same as in Table2.

K. JI´LEK AND J. TIMKOVA´

at National Radiation Protection Institute on June 3, 2015

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Fieller’s theorem(8,9)as follows: ðRL;RUÞ ¼ 1 1g X Y+t0:975ðnþmÞ 1 Y ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi s2 Xþ X2 Y2s 2 Yg s2X s ð4Þ

where g¼t0:975ðnþmÞs2X=Y2. The notation t0;975ðnþmÞstands for 97.5 % quantile oft

-distribu-tion withnþmdegrees of freedom.

Based on both practically ranked values of PD defined in the following for:

(a) exposures type A1and A2 (b) exposures type A3, B and C

and p-values,0.05 and .0.05, respectively, for all the investigated exposures, the proportions of instru-ments by achieved relevant rank for each exposure are then illustrated in Figures1–6.

a) PD5 % b) PD10 %

5 %,PD10 % 10 %,PD20 % 10 %,PD20 % PD.20 % PD.20 %

The overall results of observed ratiosRandp-values represented with relevant medians and mean values accompanied with their range for relevant exposures are given in Table4.

Figure 1. Proportions of instruments by achieved rank for each exposure and the PD. Exposure A1.

Figure 2. Proportions of instruments by achieved rank for each exposure andp-value. Exposure A1.

Figure 3. Proportions of instruments by achieved rank for each exposure and the PD. Exposure A2.

Figure 4. Proportions of instruments by achieved rank for each exposure andp-value. Exposure A2.

Figure 5. Proportions of instruments by achieved rank for each exposure and the PD. Exposures A3, B and C.

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CONCLUSIONS

The participants submitted measurement results from all the exposed instruments besides one complete set of passive Rn/Tn discriminative SSNTD detectors exposed within exposures B1and B2and one-battery-powered instrument discharged during exposures A2/II and A2/III.

Based on the results given in Table 4 and Figures1–6, it can be concluded for the following.

Exposure in the big radon chamber

(1) Exposure A1: The results of about 80 % of exposed instruments indicated very good average agreement with the NRPI reference value repre-sented with the average PD of up to 5 %. The instruments also appeared to be independent of

changes in investigated ambient conditions. Only 20 % of the monitors systematically underesti-mated the NRPI reference values on average from 15 % (during investigated periods I and II) up to 25 % during investigated period III. In fact, those 20 % of monitors were represented with only one monitor using active air samplings through filter. Since it was providing results by means of two dif-ferent ways, it was treated as the two instruments. Statistically significant differences of this monitor were also indicated by Welch’st-tests by means of thep-values reaching,0.05 during all the inves-tigated time periods.

(2) Exposure A2: The results of about 40 % of exposed monitors indicated a very good agree-ment with the reference value represented with the average PD of up to 5 % during the whole ex-posure. The rest of monitors exhibited slight over-estimation with the average PD of about 11 %. None of them exceeded 13 %. Generally, the results within investigated partial periods I – III indicated that the average PD of about 50 % of exposed monitors ranged from 4 % to 15 %. Additionally, there was no any observed influence of ambient conditions upon behaviour of the monitors. None of the compared instruments exceeded the acceptable PD of 20 %. A systematic shift in the PD of about 10 % of all the compared instruments was observed. The best parity between the NRPI reference value and results from the compared instruments was indicated by Welch’st-test during investigated period III. None of the compared monitors was statistically rejected by the test.

Figure 6. Proportions of instruments by achieved rank for each exposure andp-value. Exposures A3, B and C.

Table 4. The results from all the exposures.

Exposure type RatioR p-Value N

Median Mean (range) Median Mean (range)

A1/I 0.97 0.96 (0.83 – 1.10) 0.17 0.38 (,0.05 – 0.98) 9 A1/II 0.98 0.96 (0.85 – 1.02) 0.41 0.39 (,0.05 – 0.93) 9 A1/III 0.97 0.92 (0.70 – 1.04) 0.05 0.26 (,0.05 – 0.99) 9 A1/IV 0.98 0.95 (0.79 – 1.02) 0.13 0.15 (,0.05 – 0.36) 9 A2/I 1.04 1.03 (0.88 – 1.16) 0.11 0.19 (,0.05 – 0.65) 9 A2/II 1.16 1.12 (1.02 – 1.19) ,0.05 0.20 (,0.05 – 0.73) 8 A2/III 1.07 1.06 (0.96 – 1.13) 0.41 0.45 (0.14 – 0.93) 8 A2/IV 1.11 1.08 (0.98 – 1.13) 0.075 0.31 (,0.05 – 0.86) 8 A3 0.92 1.04 (0.76 – 1.45) ,0.05 ,0.05 (,0.05 –,0.05) 3 B1/Rn 0.96 1.08 (0.87 – 1.42) 0.09 0.27 (,0.05 – 0.71) 3 B1/Tn 1.08 0.88 (0.31 – 1.24) 0.23 0.23 (,0.05 – 0.45) 3 B2/Rn 0.97 1.10 (0.94 – 1.38) 0.47 0.42 (0.11 – 0.67) 3 B2/Tn 1.41 1.25 (0.91 – 1.43) 0.28 0.42 (0.25 – 0.74) 3 C1 0.74 0.74 (0.46 – 1.01) 0.38 0.38 (,0.05 – 0.76) 2 C2/Rn 1.00 1.05 (0.93 – 1.26) 0.40 0.38 (,0.05 – 0.73) 4 C2/Tn 0.83 0.89 (0.42 – 1.47) ,0.05 0.19 (,0.05 – 0.71) 4 Nmeans the number of exposed continuous monitors or sets of passive detectors.

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(3) Exposure A3: The results from radon gas passive integral detectors exposed simultaneously with the radon gas continuous monitors varied greatly from the NRPI reference value with PD over 20 %. Welch’st-test rejected the null hypothesis of equality of the means of all the instruments in comparison with the reference value. The reason of the rejection probably consisted in an improper option of low-sensitivity exposed electret detec-tors and their influence on absolute humidity with respect to the high number of observed out-liers. Interestingly, the only one exposed set of detectors based on SSNTD diverged from the ref-erence value by,10 %, nevertheless, was rejected by Welch’st-test due to the small variance of the results (i.e. the detector gave results with a rela-tively small but certain deviation).

Exposure in the small Rn/Tn chamber

Four sets of different paired Rn/Tn gas discriminative passive detectors have been exposed. However, the par-ticipants provided results from the three sets, only. Exposure B1: The results indicated that the only one set

of paired Rn/Tn discriminative detectors provided acceptable results with PD ,10 % for radon and with acceptable PD ,15 % for thoron. Remaining two sets of detectors provided unsatisfactory results. One of them achieved an acceptable PD of,5 % for radon but enormous underestimation by more than 50 % for thoron gas. The last set indicated PD higher than 20 % for both radon and thoron. Its results were rejected also by Welch’st-test.

Exposure B2: The most successful set of detectors from the previous exposure B1 provided excellent results represented by the PD of ,5 % for both radon and thoron. One of the remaining sets of the same detectors as in the previous exposure B1 also here provided acceptable results for radon gas only represented with PD ,10 % but enormous 40 % overestimation of the reference value for thoron. The other remaining set of detectors pro-vided again unsatisfactory 25 % overestimation of the reference value for both investigated cases. Nevertheless, none of the monitors was rejected by Welch’st-tests due to the small number of measure-ments and their great variance.

Exposure of monitors with an active sampling adapters

Exposure C1: Only two Rn/Tn gas discriminative continuous monitors were exposed in a pure thoron gas atmosphere. Whilst the results of one of them were in a perfect agreement with the NRPI reference value and represented by the PD of smaller than 5 %, the other monitor drastically underestimated the NRPI reference value by more than 50 % and was rejected also by Welch’st-test withp-value,0.05.

Exposure C2: Four Rn/Tn gas discriminative continu-ous monitors have been exposed in the mix field of Rn/Tn gas. The first one, the same and excellent as in the previous exposure C1, provided again accurate results represented with the PD of below 5 % for both cases. The two of three remaining monitors provided acceptable results for radon gas represented with the PD of better than 5 % and 10 %, respective-ly, but unsatisfactory results for thoron gas repre-sented with the PD of higher than 40 %. The fourth monitor provided unsatisfactory results for both radon and thoron with the PD of.25 %.

ACKNOWLEDGEMENTS

The authors would like to gratefully acknowledge all the participants and Dr. J. Thomas for his valuable comments helping to improve the text.

FUNDING

The present work has been partially funded by the Grant from the Technological Agency of the Czech Republic (TACˇ R) under Contract No. TA02010881. REFERENCES

1. Fronˇka, A., Jı´lek, K. and Moucˇka, L.Significance of in-dependent radon entry rate and air Exchange rate assess-ment for the purpose of radon mitigation effectiveness proper evaluation: Case studies. Radiat. Protect. Dosim. 145(2 – 3), 133 – 137 (2011).

2. Jilek, K., Thomas, J. and Brabec, M.Quality assurance programme for radon and its short-lived progeny measuring instruments in NRPI Prague. Rad. Protect. Dosim. 130(1), 43 – 47 (2008).

3. Thomas, J. and Jı´lek, K.Evaluation and comparison of measurements of unattached and attached radon progeny in the radon chamber of the PTB Braunschweig (Germany) with the NRPI Praha (Czech Republic). Radiat. Protect. Dosim.145(2– 3), 316 – 319 (2011). 4. Jı´lek, K. and Marusiakova, M. Results of the 2010

National Radiation Protection Institute intercomparison of radon and its short-lived decay product continuous moni-tors. Radiat. Protect. Dosim.145(2 – 3), 273 – 279 (2011). 5. Jilek, K.et al.International intercomparison of measuring

instruments for radon/thoron gas and radon short-lived daughter products in the NRPI Prague. Radiat Protect. Dosim.160(1 – 3), 154 – 159 (2014).

6. Thomas, J., Jı´lek, K. and Brabec, M. Inversion of the Jacobi-Porstendo¨rfer room model for the radon progeny. Nukleonika55(4), 433 – 437 (2010).

7. Welch, B. L. The generalization of "Student’s" problem when several different population variances are involved. Biometrica34(1 – 2), 28 – 35 (1947).

8. Fieller, E. C. The distribution of the index in a bivariate Normal distribution. Biometrica24(3–4), 428–440 (1932). 9. Fieller, E. C.A fundamental formula in the statistics of

biological assay, and some applications. Q. J. Pharm. Pharmacol.17, 117 – 123 (1944).

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References

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