Radiation Protection Dosimetry (2015), Vol. 164, No. 4, pp. 556 – 562 Advance Access publication 19 May 2015
doi:10.1093/rpd/ncv311
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: [email protected]
INTRODUCTION Generally, it is well known that both radon and thoron gases and predominantly their short-lived decay products are the largest contributors to radiation dose from inhalation for members of the public. Hence, relevant action plans are currently under way in many European countries focussing on reduction of indoor radon. An inseparable part of these plans is also a QA/QC programme for used measurement instruments. International intercomparisons allowing an independent control of used relevant measurement instruments 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 measurements in houses(1) and as the key instruments for metrology 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 facility enable to assure quality of measurements for all types of measurement instruments (spot, passive integral, 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 fp for radon decay products in air
The programme is based on both traceability of its reference instruments to measurement standards and independent 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 ´ RO at the Natural Radiation Division of the NRPI (SU 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 countries took part in the intercomparison. They submitted
# The Author 2015. Published by Oxford University Press. All rights reserved. For Permissions, please email: [email protected]
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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´ RO v.v.i.) in nised by and held at the Natural Radiation Division of the National Radiation Protection Institute (NRPI; SU Prague. The intercomparison was newly focussed also on continuous monitors with active sampling adapters capable to distinguish 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 concentration 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.
HLNRRA INTERCOMPARISON
– – – –
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 intercomparison: –
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 detectors, 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 adapters with use of two defined pass flow sources 226 Ra and 228Th with well-known radon and thoron gas the source production.
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 Table 1.
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 deviation. 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 simultaneously exposed both passive integral detectors and continuous monitors in the big radon chamber investigated, 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
Exposure type A in the big radon chamber The big NRPI radon chamber is a 48-m3-type walkin with an airlock inside that allows the following quantities to be adjusted, held stable, monitored online 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 Centre de Recherche Nucle´aire d’Alger National Institute of Radiological Science, Chiba MI.AM Srl. ZVD Za´vod za Varstvo pro Delu D.D. Tracerlab GmbH., Ko¨ln Durridge Co. Inc., Boston Track Analysis System Ltd. NRPI, Prague
Country Algeria Japan Italy Slovenia Germany USA UK Czech Republic
A1
A2
A3 X
X X X X Ref
B
X
X X X
X Ref
X X/Ref
X X
C
X X X
Ref
Ref
X and Ref mean compared values and reference value, respectively; A1 means exposure of radon gas continuous monitors in the big radon chamber; A2 means exposure of EEC continuous monitors in the big radon chamber; A3 means 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.
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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), BWLMPlus25 (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.
K. JI´LEK AND J. TIMKOVA´
Exposure type B in the small Rn/Th chamber After deployment of all sets of investigated passive integral 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 continuous 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 B1 and 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 Table 3. 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 certified 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 productions 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 Exposure duration (h) av (Rn)/EEC (Bq m23) SD (Bq m23) SEM (Bq m23) ACH (h21) RH (%) T (8C) p (mbar) fp F Z (cm23) GM (nm)/GSD
A1/I
A1/II
A1/III
A1/IV
A2/I
A2/II
A2/III
A2/IV
20 6873 622 136 0.06 24.1 30.1 994 0.15 0.31 2876 101/2.5
23 6679 532 109 0.06 24.8 30.2 996 0.07 0.46 5586 135/2.2
23 6473 307 63 0.06 63.8 29.1 997 0.04 0.36 9756 154/2.0
68 6666 518 62 0.06 25.8 29.8 996 0.08 0.42 5076 192/2.1
20 2016 373 113 0.06 24.1 30.1 994 0.15 0.31 2876 101/2.5
23 2812 523 151 0.06 24.8 30.2 996 0.07 0.46 5586 135/2.2
23 3386 760 219 0.06 63.8 29.1 997 0.04 0.36 9756 154/2.0
68 2759 797 135 0.06 25.8 29.8 996 0.08 0.42 5076 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 fp means 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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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 fp were 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 atmosphere 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 conditions on response of tested continuous monitors, the relative humidity of ambient air, aerosol concentration, particle size distribution and ACH were properly changed within realistic indoor conditions, kept stable and monitored by means of the chamber accessories. That is why the exposures denoted as A1 and 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 took 1 d each, the fourth period denoted as IV corresponded in terms of time to total exposure A lasting for 3 d. The NRPI declares the overall uncertainty (K ¼1) of each calibration point of radon activity concentration better than 5 % and of EEC better than 10 %. Exposure conditions and magnitudes for all the investigated periods are given in Table 2.
HLNRRA INTERCOMPARISON 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) av (Rn)/av (Tn) (Bq m23) SD (Bq m23) SEM (Bq m23) RH (%) T (8C) p (mbar)
24 3780 437 89 12.1 24.1 994
24 7137 1107 226 12.1 24.1 994
24 4160 463 28 11.8 25.2 996
24 1690 736 151 11.8 25.2 996
2 4860 340 152 ,5 24.5 994
2 4119 309 138 ,5 24.5 994
2 8257 669 253 ,5 24.5 994
(a) (b) (c)
pure radon gas concentration, denoted as C0 pure thoron gas concentration, denoted as C1 mix radon/thoron concentration, denoted as C2
following formula:
in the sources output airstream calculated as Pi/F with overall uncertainty up to 5 % (K ¼1). Pi is the relevant well-known radon/thoron source production, F is the flow rate of a carrier gas through the source and K is 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 adapters of tested monitors to the source output airstream. Since sampled gas concentrations were under influence of flow rate of used carrier gas only during whole exercise, the flow rate through used sources was monitored 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 Table 3.
X Y ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi t ¼ s 2 S 2 S pXffiffiffi þ pYffiffiffiffi n m
ð1Þ
where X and Y are mean values reported by participants and the NRPI reference mean value, respectively. SX and SY are sample standard deviations given from participants and from the NRPI, respectively. n and m are 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. if p-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 comparing instrument, both ratio R and the per cent difference D% (denoted PD as for per cent difference in %) were defined as follows:
RESULTS To evaluate participants data and compare them with the NRPI reference values, the following two approaches were used with respect to statistical character of the observed data: (a)
Welch’s t-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 compared instruments are not significantly different. Welch’s t-test defines the statistic t by the
X Y
ð2Þ
D% ¼ abs (R 1Þ 100
ð3Þ
R¼
where all symbols have the same meanings as in Equation (1). An approximate 95 % confidence interval for ratio R denoted as (RL, RU) can be calculated by means of
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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 Table 2.
K. JI´LEK AND J. TIMKOVA´
Fieller’s theorem ðRL ; RU Þ ¼
(8, 9)
1 1g
as follows:
X + t0:975 ðn þ mÞ Y sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 1 X2 s2X þ 2 s2Y g s2X Y Y
ð4Þ
(a) (b)
Figure 3. Proportions of instruments by achieved rank for each exposure and the PD. Exposure A2.
exposures type A1 and A2 exposures type A3, B and C
and p-values ,0.05 and .0.05, respectively, for all the investigated exposures, the proportions of instruments by achieved relevant rank for each exposure are then illustrated in Figures 1 –6.
Figure 4. Proportions of instruments by achieved rank for each exposure and p-value. Exposure A2.
Figure 1. Proportions of instruments by achieved rank for each exposure and the PD. Exposure A1.
Figure 5. Proportions of instruments by achieved rank for each exposure and the PD. Exposures A3, B and C. a)
Figure 2. Proportions of instruments by achieved rank for each exposure and p-value. Exposure A1.
PD 5 % 5 % , PD 10 % 10 % , PD 20 % PD . 20 %
b)
PD 10 % 10 % , PD 20 % PD . 20 %
The overall results of observed ratios R and p-values represented with relevant medians and mean values accompanied with their range for relevant exposures are given in Table 4.
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The notation where g ¼ t0:975 ðn þ mÞs2X =Y 2. t0;975 ðn þ mÞ stands for 97.5 % quantile of t-distribution with n þ m degrees of freedom. Based on both practically ranked values of PD defined in the following for:
HLNRRA INTERCOMPARISON
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 B1 and B2 and one-batterypowered instrument discharged during exposures A2/II and A2/III. Based on the results given in Table 4 and Figures 1– 6, it can be concluded for the following.
(1) Exposure A1: The results of about 80 % of exposed instruments indicated very good average agreement with the NRPI reference value represented with the average PD of up to 5 %. The instruments also appeared to be independent of
Figure 6. Proportions of instruments by achieved rank for each exposure and p-value. Exposures A3, B and C.
Table 4. The results from all the exposures. Exposure type
A1/I A1/II A1/III A1/IV A2/I A2/II A2/III A2/IV A3 B1/Rn B1/Tn B2/Rn B2/Tn C1 C2/Rn C2/Tn
Ratio R
p-Value
Median
Mean (range)
Median
Mean (range)
0.97 0.98 0.97 0.98 1.04 1.16 1.07 1.11 0.92 0.96 1.08 0.97 1.41 0.74 1.00 0.83
0.96 (0.83–1.10) 0.96 (0.85–1.02) 0.92 (0.70–1.04) 0.95 (0.79–1.02) 1.03 (0.88–1.16) 1.12 (1.02–1.19) 1.06 (0.96–1.13) 1.08 (0.98–1.13) 1.04 (0.76–1.45) 1.08 (0.87–1.42) 0.88 (0.31–1.24) 1.10 (0.94–1.38) 1.25 (0.91–1.43) 0.74 (0.46–1.01) 1.05 (0.93–1.26) 0.89 (0.42–1.47)
0.17 0.41 0.05 0.13 0.11 , 0.05 0.41 0.075 , 0.05 0.09 0.23 0.47 0.28 0.38 0.40 , 0.05
0.38 (, 0.05–0.98) 0.39 (, 0.05–0.93) 0.26 (, 0.05–0.99) 0.15 (, 0.05–0.36) 0.19 (, 0.05–0.65) 0.20 (, 0.05–0.73) 0.45 (0.14– 0.93) 0.31 (, 0.05–0.86) , 0.05 (, 0.05– , 0.05) 0.27 (, 0.05–0.71) 0.23 (, 0.05–0.45) 0.42 (0.11– 0.67) 0.42 (0.25– 0.74) 0.38 (, 0.05–0.76) 0.38 (, 0.05–0.73) 0.19 (, 0.05–0.71)
N means the number of exposed continuous monitors or sets of passive detectors.
561
N
9 9 9 9 9 8 8 8 3 3 3 3 3 2 4 4
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Exposure in the big radon chamber
changes in investigated ambient conditions. Only 20 % of the monitors systematically underestimated 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 different ways, it was treated as the two instruments. Statistically significant differences of this monitor were also indicated by Welch’s t-tests by means of the p-values reaching , 0.05 during all the investigated time periods. (2) Exposure A2: The results of about 40 % of exposed monitors indicated a very good agreement with the reference value represented with the average PD of up to 5 % during the whole exposure. The rest of monitors exhibited slight overestimation 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’s t-test during investigated period III. None of the compared monitors was statistically rejected by the test.
K. JI´LEK AND J. TIMKOVA´
Exposure C2: Four Rn/Tn gas discriminative continuous 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 %, respectively, but unsatisfactory results for thoron gas represented 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.
Exposure in the small Rn/Tn chamber Four sets of different paired Rn/Tn gas discriminative passive detectors have been exposed. However, the participants 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’s t-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 provided again unsatisfactory 25 % overestimation of the reference value for both investigated cases. Nevertheless, none of the monitors was rejected by Welch’s t-tests due to the small number of measurements 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’s t-test with p-value , 0.05.
FUNDING The present work has been partially funded by the Grant from the Technological Agency of the Czech ˇ R) under Contract No. TA02010881. Republic (TAC REFERENCES 1. Fronˇka, A., Jı´lek, K. and Moucˇka, L. Significance of independent radon entry rate and air Exchange rate assessment 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 monitors. 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. Nukleonika 55(4), 433–437 (2010). 7. Welch, B. L. The generalization of "Student’s" problem when several different population variances are involved. Biometrica 34(1– 2), 28–35 (1947). 8. Fieller, E. C. The distribution of the index in a bivariate Normal distribution. Biometrica 24(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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(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’s t-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 detectors and their influence on absolute humidity with respect to the high number of observed outliers. Interestingly, the only one exposed set of detectors based on SSNTD diverged from the reference value by ,10 %, nevertheless, was rejected by Welch’s t-test due to the small variance of the results (i.e. the detector gave results with a relatively small but certain deviation).
doi:10.1093/rpd/ncv311
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: [email protected]
INTRODUCTION Generally, it is well known that both radon and thoron gases and predominantly their short-lived decay products are the largest contributors to radiation dose from inhalation for members of the public. Hence, relevant action plans are currently under way in many European countries focussing on reduction of indoor radon. An inseparable part of these plans is also a QA/QC programme for used measurement instruments. International intercomparisons allowing an independent control of used relevant measurement instruments 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 measurements in houses(1) and as the key instruments for metrology 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 facility enable to assure quality of measurements for all types of measurement instruments (spot, passive integral, 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 fp for radon decay products in air
The programme is based on both traceability of its reference instruments to measurement standards and independent 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 ´ RO at the Natural Radiation Division of the NRPI (SU 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 countries took part in the intercomparison. They submitted
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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´ RO v.v.i.) in nised by and held at the Natural Radiation Division of the National Radiation Protection Institute (NRPI; SU Prague. The intercomparison was newly focussed also on continuous monitors with active sampling adapters capable to distinguish 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 concentration 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.
HLNRRA INTERCOMPARISON
– – – –
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 intercomparison: –
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 detectors, 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 adapters with use of two defined pass flow sources 226 Ra and 228Th with well-known radon and thoron gas the source production.
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 Table 1.
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 deviation. 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 simultaneously exposed both passive integral detectors and continuous monitors in the big radon chamber investigated, 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
Exposure type A in the big radon chamber The big NRPI radon chamber is a 48-m3-type walkin with an airlock inside that allows the following quantities to be adjusted, held stable, monitored online 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 Centre de Recherche Nucle´aire d’Alger National Institute of Radiological Science, Chiba MI.AM Srl. ZVD Za´vod za Varstvo pro Delu D.D. Tracerlab GmbH., Ko¨ln Durridge Co. Inc., Boston Track Analysis System Ltd. NRPI, Prague
Country Algeria Japan Italy Slovenia Germany USA UK Czech Republic
A1
A2
A3 X
X X X X Ref
B
X
X X X
X Ref
X X/Ref
X X
C
X X X
Ref
Ref
X and Ref mean compared values and reference value, respectively; A1 means exposure of radon gas continuous monitors in the big radon chamber; A2 means exposure of EEC continuous monitors in the big radon chamber; A3 means 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.
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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), BWLMPlus25 (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.
K. JI´LEK AND J. TIMKOVA´
Exposure type B in the small Rn/Th chamber After deployment of all sets of investigated passive integral 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 continuous 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 B1 and 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 Table 3. 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 certified 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 productions 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 Exposure duration (h) av (Rn)/EEC (Bq m23) SD (Bq m23) SEM (Bq m23) ACH (h21) RH (%) T (8C) p (mbar) fp F Z (cm23) GM (nm)/GSD
A1/I
A1/II
A1/III
A1/IV
A2/I
A2/II
A2/III
A2/IV
20 6873 622 136 0.06 24.1 30.1 994 0.15 0.31 2876 101/2.5
23 6679 532 109 0.06 24.8 30.2 996 0.07 0.46 5586 135/2.2
23 6473 307 63 0.06 63.8 29.1 997 0.04 0.36 9756 154/2.0
68 6666 518 62 0.06 25.8 29.8 996 0.08 0.42 5076 192/2.1
20 2016 373 113 0.06 24.1 30.1 994 0.15 0.31 2876 101/2.5
23 2812 523 151 0.06 24.8 30.2 996 0.07 0.46 5586 135/2.2
23 3386 760 219 0.06 63.8 29.1 997 0.04 0.36 9756 154/2.0
68 2759 797 135 0.06 25.8 29.8 996 0.08 0.42 5076 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 fp means 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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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 fp were 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 atmosphere 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 conditions on response of tested continuous monitors, the relative humidity of ambient air, aerosol concentration, particle size distribution and ACH were properly changed within realistic indoor conditions, kept stable and monitored by means of the chamber accessories. That is why the exposures denoted as A1 and 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 took 1 d each, the fourth period denoted as IV corresponded in terms of time to total exposure A lasting for 3 d. The NRPI declares the overall uncertainty (K ¼1) of each calibration point of radon activity concentration better than 5 % and of EEC better than 10 %. Exposure conditions and magnitudes for all the investigated periods are given in Table 2.
HLNRRA INTERCOMPARISON 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) av (Rn)/av (Tn) (Bq m23) SD (Bq m23) SEM (Bq m23) RH (%) T (8C) p (mbar)
24 3780 437 89 12.1 24.1 994
24 7137 1107 226 12.1 24.1 994
24 4160 463 28 11.8 25.2 996
24 1690 736 151 11.8 25.2 996
2 4860 340 152 ,5 24.5 994
2 4119 309 138 ,5 24.5 994
2 8257 669 253 ,5 24.5 994
(a) (b) (c)
pure radon gas concentration, denoted as C0 pure thoron gas concentration, denoted as C1 mix radon/thoron concentration, denoted as C2
following formula:
in the sources output airstream calculated as Pi/F with overall uncertainty up to 5 % (K ¼1). Pi is the relevant well-known radon/thoron source production, F is the flow rate of a carrier gas through the source and K is 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 adapters of tested monitors to the source output airstream. Since sampled gas concentrations were under influence of flow rate of used carrier gas only during whole exercise, the flow rate through used sources was monitored 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 Table 3.
X Y ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi t ¼ s 2 S 2 S pXffiffiffi þ pYffiffiffiffi n m
ð1Þ
where X and Y are mean values reported by participants and the NRPI reference mean value, respectively. SX and SY are sample standard deviations given from participants and from the NRPI, respectively. n and m are 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. if p-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 comparing instrument, both ratio R and the per cent difference D% (denoted PD as for per cent difference in %) were defined as follows:
RESULTS To evaluate participants data and compare them with the NRPI reference values, the following two approaches were used with respect to statistical character of the observed data: (a)
Welch’s t-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 compared instruments are not significantly different. Welch’s t-test defines the statistic t by the
X Y
ð2Þ
D% ¼ abs (R 1Þ 100
ð3Þ
R¼
where all symbols have the same meanings as in Equation (1). An approximate 95 % confidence interval for ratio R denoted as (RL, RU) can be calculated by means of
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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 Table 2.
K. JI´LEK AND J. TIMKOVA´
Fieller’s theorem ðRL ; RU Þ ¼
(8, 9)
1 1g
as follows:
X + t0:975 ðn þ mÞ Y sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 1 X2 s2X þ 2 s2Y g s2X Y Y
ð4Þ
(a) (b)
Figure 3. Proportions of instruments by achieved rank for each exposure and the PD. Exposure A2.
exposures type A1 and A2 exposures type A3, B and C
and p-values ,0.05 and .0.05, respectively, for all the investigated exposures, the proportions of instruments by achieved relevant rank for each exposure are then illustrated in Figures 1 –6.
Figure 4. Proportions of instruments by achieved rank for each exposure and p-value. Exposure A2.
Figure 1. Proportions of instruments by achieved rank for each exposure and the PD. Exposure A1.
Figure 5. Proportions of instruments by achieved rank for each exposure and the PD. Exposures A3, B and C. a)
Figure 2. Proportions of instruments by achieved rank for each exposure and p-value. Exposure A1.
PD 5 % 5 % , PD 10 % 10 % , PD 20 % PD . 20 %
b)
PD 10 % 10 % , PD 20 % PD . 20 %
The overall results of observed ratios R and p-values represented with relevant medians and mean values accompanied with their range for relevant exposures are given in Table 4.
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The notation where g ¼ t0:975 ðn þ mÞs2X =Y 2. t0;975 ðn þ mÞ stands for 97.5 % quantile of t-distribution with n þ m degrees of freedom. Based on both practically ranked values of PD defined in the following for:
HLNRRA INTERCOMPARISON
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 B1 and B2 and one-batterypowered instrument discharged during exposures A2/II and A2/III. Based on the results given in Table 4 and Figures 1– 6, it can be concluded for the following.
(1) Exposure A1: The results of about 80 % of exposed instruments indicated very good average agreement with the NRPI reference value represented with the average PD of up to 5 %. The instruments also appeared to be independent of
Figure 6. Proportions of instruments by achieved rank for each exposure and p-value. Exposures A3, B and C.
Table 4. The results from all the exposures. Exposure type
A1/I A1/II A1/III A1/IV A2/I A2/II A2/III A2/IV A3 B1/Rn B1/Tn B2/Rn B2/Tn C1 C2/Rn C2/Tn
Ratio R
p-Value
Median
Mean (range)
Median
Mean (range)
0.97 0.98 0.97 0.98 1.04 1.16 1.07 1.11 0.92 0.96 1.08 0.97 1.41 0.74 1.00 0.83
0.96 (0.83–1.10) 0.96 (0.85–1.02) 0.92 (0.70–1.04) 0.95 (0.79–1.02) 1.03 (0.88–1.16) 1.12 (1.02–1.19) 1.06 (0.96–1.13) 1.08 (0.98–1.13) 1.04 (0.76–1.45) 1.08 (0.87–1.42) 0.88 (0.31–1.24) 1.10 (0.94–1.38) 1.25 (0.91–1.43) 0.74 (0.46–1.01) 1.05 (0.93–1.26) 0.89 (0.42–1.47)
0.17 0.41 0.05 0.13 0.11 , 0.05 0.41 0.075 , 0.05 0.09 0.23 0.47 0.28 0.38 0.40 , 0.05
0.38 (, 0.05–0.98) 0.39 (, 0.05–0.93) 0.26 (, 0.05–0.99) 0.15 (, 0.05–0.36) 0.19 (, 0.05–0.65) 0.20 (, 0.05–0.73) 0.45 (0.14– 0.93) 0.31 (, 0.05–0.86) , 0.05 (, 0.05– , 0.05) 0.27 (, 0.05–0.71) 0.23 (, 0.05–0.45) 0.42 (0.11– 0.67) 0.42 (0.25– 0.74) 0.38 (, 0.05–0.76) 0.38 (, 0.05–0.73) 0.19 (, 0.05–0.71)
N means the number of exposed continuous monitors or sets of passive detectors.
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N
9 9 9 9 9 8 8 8 3 3 3 3 3 2 4 4
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Exposure in the big radon chamber
changes in investigated ambient conditions. Only 20 % of the monitors systematically underestimated 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 different ways, it was treated as the two instruments. Statistically significant differences of this monitor were also indicated by Welch’s t-tests by means of the p-values reaching , 0.05 during all the investigated time periods. (2) Exposure A2: The results of about 40 % of exposed monitors indicated a very good agreement with the reference value represented with the average PD of up to 5 % during the whole exposure. The rest of monitors exhibited slight overestimation 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’s t-test during investigated period III. None of the compared monitors was statistically rejected by the test.
K. JI´LEK AND J. TIMKOVA´
Exposure C2: Four Rn/Tn gas discriminative continuous 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 %, respectively, but unsatisfactory results for thoron gas represented 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.
Exposure in the small Rn/Tn chamber Four sets of different paired Rn/Tn gas discriminative passive detectors have been exposed. However, the participants 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’s t-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 provided again unsatisfactory 25 % overestimation of the reference value for both investigated cases. Nevertheless, none of the monitors was rejected by Welch’s t-tests due to the small number of measurements 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’s t-test with p-value , 0.05.
FUNDING The present work has been partially funded by the Grant from the Technological Agency of the Czech ˇ R) under Contract No. TA02010881. Republic (TAC REFERENCES 1. Fronˇka, A., Jı´lek, K. and Moucˇka, L. Significance of independent radon entry rate and air Exchange rate assessment 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 monitors. 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. Nukleonika 55(4), 433–437 (2010). 7. Welch, B. L. The generalization of "Student’s" problem when several different population variances are involved. Biometrica 34(1– 2), 28–35 (1947). 8. Fieller, E. C. The distribution of the index in a bivariate Normal distribution. Biometrica 24(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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(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’s t-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 detectors and their influence on absolute humidity with respect to the high number of observed outliers. Interestingly, the only one exposed set of detectors based on SSNTD diverged from the reference value by ,10 %, nevertheless, was rejected by Welch’s t-test due to the small variance of the results (i.e. the detector gave results with a relatively small but certain deviation).
