The metrological traceability, performance and precision of european radon calibration facilities

International Journal of Environmental Research and Public Health Article The Metrological Traceability, Performance and Precision of European Radon Calibration Facilities Thomas R. Beck 1,* , Andrei Antohe 2, Francesco Cardellini 3, Alexandra Cuco¸s 4, Eliska Fialova 5, Claudia Grossi 6, Kinga Hening 4, Jens Jensen 7, Dejan Kastratovi´c 8, Matej Krivošík9, Patrick Lobner 10, Aurelian Luca 2, Franz Josef Maringer 10 , Nathalie Michielsen 11, Petr P. S. Otahal 5, Luis Quindós12, Daniel Rábago 12 , Carlos Sainz 12 , LászlóSz˝ucs 13, Constantin Teodorescu 2, Cathrin Tolinsson 7, Cornel Liviu Tugulan 2, Tuukka Turtiainen 14, Arturo Vargas 6, Josef Vosahlik 5, Goran Vukoslavovic 8, Hannah Wiedner 10 and Katarzyna Wołoszczuk 15   Citation: Beck, T.R.; Antohe, A.; Cardellini, F.; Cuco¸s, A.; Fialova, E.; Grossi, C.; Hening, K.; Jensen, J.; Kastratovi´c, D.; Krivošík, M.; et al. The Metrological Traceability, Performance and Precision of European Radon Calibration Facilities. Int. J. Environ. Res. Public Health 2021,18, 12150. https:// doi.org/10.3390/ijerph182212150 Academic Editor: Miroslaw Janik Received: 7 October 2021 Accepted: 11 November 2021 Published: 19 November 2021 Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations. Copyright: © 2021 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/). 1Federal Office for Radiation Protection, 10318 Berlin, Germany 2Institutul National de Cercetare-Dezvoltare Pentru Fizica si Inginerie Nucleara “Horia Hulubei”, 077125 Ilfov County, Romania; [email protected] (A.A.); [email protected]o (A.L.); [email protected]o (C.T.); [email protected]o (C.L.T.) 3ENEA-INMRI, 00123 Roma, Italy; [email protected] 4“CONSTANTIN COSMA” Radon Laboratory, Faculty of Environmental Science and Engineering, Babes—Bolyai University, 400294 Cluj-Napoca, Romania; [email protected] (A.C.); [email protected] (K.H.) 5Státní Ústav Jaderné, Chemickéa BiologickéOchrany, 262 31 Milin, Czech Republic; [email protected] (E.F.); [email protected] (P.P.S.O.); [email protected] (J.V.) 6Laboratory of 222Rn Studies, Institut de Tècniques Energètiques, Universitat Politècnica de Catalunya, 08028 Barcelona, Spain; claudia.gr[email protected] (C.G.); arturo.var[email protected] (A.V.) 7SwedishRadiation Safety Authority, 171 16 Stockholm, Sweden; [email protected] (J.J.); [email protected] (C.T.) 8Bureau of Metrology, Podgorica 81000, Montenegro; [email protected] (D.K.); [email protected].me (G.V.) 9Slovak Institute of Metrology, Department of Ionizing Radiation, 842 55 Bratislava, Slovakia; [email protected].sk 10 Physikalisch-Technischer Prüfdienst, Bundesamt für Eichund Vermessungswesen, 1160 Vienna, Austria; [email protected] (P.L.); [email protected] (F.J.M.); [email protected].at (H.W.) 11 Institut de Radioprotection et de SûretéNucléaire, 92262 Paris, France; [email protected] 12 Radon Group, Laboratory of Environmental Radioactivity of the University of Cantabria, 39011 Santander, Spain; [email protected] (L.Q.); [email protected] (D.R.); [email protected] (C.S.) 13 Budapest F˝ováros Kormányhivatala, 1024 Budapest, Hungary; [email protected].hu 14 Radiation and Nuclear Safety Authority, 00880 Helsinki, Finland; [email protected] 15 Central Laboratory for Radiological Protection, 03-194 Warsaw, Poland; [email protected] *Correspondence: [email protected] Abstract: An interlaboratory comparison for European radon calibration facilities was conducted to evaluate the establishment of a harmonized quality level for the activity concentration of radon in air and to demonstrate the performance of the facilities when calibrating measurement instruments for radon. Fifteen calibration facilities from 13 different European countries participated. They represented different levels in the metrological hierarchy: national metrology institutes and designated institutes, national authorities for radiation protection and participants from universities. The interlaboratory comparison was conducted by the German Federal Office for Radiation Protection (BfS) and took place from 2018 to 2020. Participants were requested to measure radon in atmospheres of their own facilities according to their own procedures and requirements for metrological traceability. A measurement device with suitable properties was used to determine the comparison values. The results of the comparison showed that the radon activity concentrations that were determined by European calibration facilities complying with metrological traceability requirements were consistent with each other and had common mean values. The deviations from these values were normally distributed. The range of variation of the common mean value was a measure of the degree of agreement between the participants. For exposures above 1000 Bq/m 3 , the variation was about 4% Int. J. Environ. Res. Public Health 2021,18, 12150. https://doi.org/10.3390/ijerph182212150 https://www.mdpi.com/journal/ijerph Int. J. Environ. Res. Public Health 2021,18, 12150 2 of 15 for a level of confidence of approximately 95% (k=2) . For lower exposure levels, the variation increased to about 6%. Keywords: radon; interlaboratory comparison; radon activity concentration; calibration; metrological traceability 1. Introduction The European Council Directive 2013/59/EURATOM requires that the EU member states introduce regulations for protection against radon exposure in homes and at workplaces [ 1 ]. In this context, the European metrology institutes are required to create a harmonized quality level for radon activity concentrations. The realization of the measurement quantity with a high degree of agreement between calibration bodies ensures that measurements are comparable and results are mutually recognized in the EU member states. The term radon used in the EU legal act, as well as in this work, refers to the radionuclide 222Rn. In the framework of the European Metrology Programme for Innovation and Research (EMPIR), the project Metrology for Radon Monitoring (MetroRADON) was initiated, which included an interlaboratory comparison to evaluate the metrological traceability of European radon calibration facilities and to demonstrate their performance and precision when calibrating measurement instruments for radon in the range from 300 to 10,000 Bq/m3. Calibration services from the different EU member states, which preferably represent the respective national reference for the quantity of radon activity concentration in air, were encouraged to participate in the comparison. The interlaboratory comparison was conducted by the German Federal Office for Radiation Protection (BfS, coordinator) and took place from 2018 to 2020. The participants were requested to measure the atmospheres of their own facilities according to their own procedures and requirements for metrological traceability. The comparison value was determined with a measurement device that had appropriate metrological characteristics and was made available to the participants in turn. Differences in the comparison values demonstrated the differences of the participants in the measurement of the radon activity concentration. The measure of precision was considered to be the degree of agreement between participants in the determination of the quantity. The interlaboratory comparison also showed the uncertainties when passing on the quantity to third parties through the calibration of devices. In total, 15 calibration facilities from 12 different countries of the European Union and one from Montenegro participated in the interlaboratory comparison. Table 1presents the calibration facilities that were involved in the comparison. The pool of participants encompassed seven national metrology institutes and designated institutes (BEV-PTP, STUK, BFKH, ENEA, IFIN-HH, MNE, SMI), five national authorities for radiation protection (BfS, SUJCHBO, IRSN, CLOR, SSM) and three participants from universities (UBB, LaRUC, UPC). The considerable number of participants from various European countries with different positions in the metrological hierarchy and thus different positions in the metrological traceability chain allowed for a representative evaluation of the performance and precision in the calibration of measurement instruments for radon. Int. J. Environ. Res. Public Health 2021,18, 12150 3 of 15 Table 1. Calibration facilities participating in the interlaboratory comparison (sorted alphabetically by country). Short Name Affiliation Country BEV-PTP Physikalisch-technischer Prüfdienst, Bundesamt für Eichund Vermessungswesen Arltgasse 35, 1160 Wien Austria SUJCHBO Státní ústav jaderné, chemickéa biologickéochrany Kamenna 71, 262 31 Milin Czech Republic STUK Radiation and Nuclear Safety Authority Laippatie 4, 00880 Helsinki Finland IRSN Institut de Radioprotection et de SûretéNucléaire 31 avenue de la Division Leclerc, 92262 Fontenay-aux-Roses France BfS (Coordinator) German Federal Office for Radiation Protection Köpenicker Allee 120–130, 10318 Berlin Germany BFKH Budapest F˝ováros Kormányhivatala Németvölgyi út 37-39, 1024 Budapest Hungary ENEA ENEA-INMRI, via Anguillarese, 301 - 00123 Roma Italy MNE Bureau of Metrology Arsenija Boljevi´ca bb, 81000 Podgorica Montenegro CLOR Central Laboratory for Radiological Protection Konwaliowa 7, 03-194 Warsaw Poland IFIN-HH Institutul National de Cercetare-Dezvoltare pentru Fizica si Inginerie Nucleara “Horia Hulubei” 30 Reactorului St., 077125 Magurele, Ilfov County, POB MG-6 Romania UBB “CONSTANTIN COSMA” Radon Laboratory, Babes—Bolyai University, Faculty of Environmental Science and Engineering Fantanele 30, 400294 Cluj-Napoca Romania SMU Slovak Institute of Metrology, Department of Ionizing Radiation Karloveská63, 842 55 Bratislava Slovak Republic LaRUC Radon Group, Laboratory of Environmental Radioactivity of the University of Cantabria (LaRUC) C/Cardenal Herrera Oria S/N, 39011 Santander, Cantabria Spain UPC Laboratory of 222Rn studies (LER) of the Institut de Tècniques Energètiques (INTE) of the Universitat Politècnica de Catalunya (UPC), Campus Diagonal Sud, Edificio PC (PavellóC) Av. Diagonal, 647, 08028 Barcelona Spain SSM Swedish Radiation Safety Authority Solna strandväg 96, 171 16 Stockholm Sweden 2. Organization and Methodology 2.1. Procedure of Interlaboratory Comparison The basic design of the interlaboratory comparison was developed in consultation with the members of the advisory group, which consisted of the EMPIR project collaborators. An agreed protocol for the comparison was handed out to each participant in advance. It informed about the procedure of the comparison, as well as the handover and handling of the comparison device. The comparison device was sent to each participant in turn. It was made available to the participant for a predefined duration in order to perform the exposure measurements. After completing the exposure measurements, the device had to be returned to the coordinator. In addition to the exposure data, participants were asked to report data on the temperature, air humidity and air pressures that prevailed during the exposure measurements. 2.2. Comparison Device The comparison device was used to transfer the comparison value for the measurements at different locations and levels. The device did not embody the comparison reference value. Int. J. Environ. Res. Public Health 2021,18, 12150 4 of 15 The coordinator selected an electronic instrument of type AlphaGUARD PQ 2000 PRO TTL. This type of device is a standard instrument for the measurement of radon activity concentrations. The instrument is robust and reliable under various environmental conditions and is easy to use. Measurement results are stored safe from manipulation in its internal memory with sufficient capacity for the comparison exercises. The instrument was operated in the diffusion mode with an integration time of 10 min. The comparison device was calibrated in the facilities of the coordinator at different radon activity concentrations in the range between 300 and 12,000 Bq/m 3 . Calibrations were performed before, during and after the interlaboratory comparison [ 2 ]. Taking the uncertainty into account, a constant calibration factor was obtained over the whole investigated range, which pointed to the linear relationship between the indicated value and the radon activity concentration in air. Similarly, no change in the calibration factor was observed over the comparison period, implying that the measurement characteristics of the instrument were constant, allowing for equal conditions for each participant. The calibrations were flanked by regular background measurements. For this purpose, the device was enclosed in a volume that was flushed with low-radon air. Low-radon air was obtained from pressurized cylinders in which the air had previously been stored for a longer period. The resulting radon concentration in the volume was considered to be negligible (zero) and the device indicated the datum error for zero value of radon activity concentration. The background of the comparison device was measured before each run. It was constant throughout the comparison period and was determined to be 4 ± 5 Bq/m 3 , which had a negligible effect on the measurement results. The attributed uncertainty was the standard uncertainty. The AlphaGUARD operates with automatic background correction. Due to stochastic measurement effects that are not taken into account in the automatic background correction, the device provides measured values for the background that can also be negative. Visual inspections of the comparison device for damage, including the diffusion filter, verification of functionality and checking of the set measurement parameters (e.g., calibration factor) supplemented the regular checks before the instrument was used for the next run. 2.3. Exposure Levels Within the specified study range between 300 and 10,000 Bq/m 3 , 3 different exposure levels with low, medium and high radon activity concentrations were defined for the comparison. The nominal values of the radon activity concentrations are given in Table 2. Table 2. Nominal levels of the radon activity concentrations for the exposure of the comparison device. No. Nominal Value (Bq/m3) Range of Accepted Deviation (Bq/m3) 1 400 350–450 2 1000 900–1100 3 6000 5500–6500 The value of 1000 Bq/m 3 was already included in a previous comparison of calibration facilities for radon activity concentrations, which was carried out within the framework of the Euromet Project 657 [3]. In practice, the participants could not exactly adhere to the specified nominal values. Therefore, deviations from the nominal values were accepted within which the respective activity concentrations were expected. With the exception of a few participants, most of the participants were able to meet these requirements. The main reasons for not achieving the nominal radon activity concentrations within their accepted deviations were generally: Int. J. Environ. Res. Public Health 2021,18, 12150 5 of 15 1. The participants were not able to keep the activity concentration constant over the duration of exposure, as the activity concentration decreased over time, mainly due to radioactive decay; 2. The radon sources that were available in the participant’s laboratories and/or the methods used to create the radon atmosphere were not suitable for reaching the predetermined concentrations. The assessment of the degree of agreement between participants was carried out only for the results that were obtained at exposures that were within the accepted deviations. However, the results of measurements outside the accepted deviations from the nominal values were not excluded from consideration and are referred to in the following as singular exposures. They complemented the conclusions of this study by supporting its extension to the entire range of radon concentrations from low to high levels. 2.4. Methods for Processing the Results The investigated quantity, which made the participant’s performance comparable, was the ratio R of the radon activity concentration CRefLab , which was reported by the participant as the mean value for the relevant exposure period and the mean radon activity concentration CCD , which was measured during the same period with the comparison device: R=CRefLab CCD (1) The standard uncertainty ∆R=u(R) was calculated from the propagation of uncertainty from Equation (1). The relative uncertainty is given by ∆R R=s∆CRefLab CRefLab 2 +∆CCD CCD 2 (2) ∆CRefLab =u(CRefLab) represents the standard uncertainty as reported by the participant and was determined according to its own procedure. The reported uncertainty included the statistical variation from repeated observations (type A evaluation of standard uncertainty) and contributions from other sources, in particular from data provided in the calibration and other certificates (type B evaluation of standard uncertainty) [ 4 ]. However, the procedure that was used by participants to calculate the measurement uncertainties was not evaluated as part of this interlaboratory comparison. ∆CCD is the uncertainty of the mean radon activity concentration, which was determined by the comparison device. Since the comparison device did not embody the comparison reference value, only the type A uncertainty given by the standard deviation of the mean, namely, s (CCD) , was considered: ∆CCD =s(CCD)=v u u t ∑CCD,j−CCD2 n(n−1)(3) CCD,j is the jth of nmeasurements that were taken with the comparison device. Other contributions to the uncertainty, particularly from calibration factors, were not included. This was due to the essential requirement for the comparison device to provide an indication that depended linearly on the value of the radon activity concentration. The initial investigations of the comparison device showed that the linearity could be assumed over the entire range up to a radon activity concentration of 10,000 Bq/m3. It should be noted that the simple averaging of the measurements performed with the comparison device and the use of Equation (3) was valid if the activity concentration was kept constant during the relevant exposure period. If this could not be ensured by the participant, the change in activity concentration over time must be well known. In such cases, the participant had to provide information on how to determine the mean radon activity concentration CCD from the readings of the comparison device. In general, the radon activity concentration that was established in a confined atmosphere decreased due Int. J. Environ. Res. Public Health 2021,18, 12150 6 of 15 to radioactive decay and, thus, the value for CCD at the reference time tref was obtained using CCD(tref)=1 n∑ j CCD,je−λ(tref−tj)(4) Equation (4) represents the average of the measured values corrected for the exposure time. The parameter tj represents the measurement time of CCD,j and λ represents the decay constant of radon. Equation (4) must be modified if the rate of decrease differs from that of radioactive decay. 2.5. Calculation of the Uncertainty-Weighted Average Ratio When Ri denotes the ratio R calculated for the ith of nparticipants and ui is the standard uncertainty attributed to Ri , the uncertainty-weighted average ratio Rw is determined using Rw= R1 u2 1 +· · · +Rn u2 n 1 u2 1 +· · · +1 u2 n = n ∑ i=1 wiRi(5) The parameter wirepresents the weight for ratio Ri: wi= 1 u2 i ∑n i=11 u2 i (6) The weights are calculated from the reciprocal squared standard uncertainties of Equation (2). It follows that results with lower uncertainties are weighted higher than results with high uncertainties when determining the average ratio. The variance of Rw is calculated as follows [5,6]: σ2(Rw)=u2(Rw)=1 1 u2 1 +· · · +1 u2 n =1 ∑n i=11 u2 i (7) 3. Results 3.1. Laboratory Reference Devices and the Compilation of the Results Most participants used an AlphaGUARD-type device as the laboratory reference instrument for the radon activity concentrations. Two of these participants additionally performed measurements with scintillation chambers. The ATMOS 12DPX was utilized by two participants and a Radon Scout by one participant. AlphaGUARD and ATMOS use ionization chambers (singleor multi-wire) for radiation detection. The Radon Scout deploys high-voltage enhancement and alpha pulse counting using a semiconductor detector. Unlike AlphaGUARD and Radon Scout, which operate in diffusion mode, the ATMOS-type device operates in flow-through mode. The vast majority of the participants were able to show the metrological traceability of the quantity through an unbroken chain of calibrations at recognized bodies. Two participants traced their measurements back through factory calibration. Factory calibration is a service from the manufacturer that provides the instrument with an initial calibration before delivery. Although the manufacturers also trace their measurements back to recognized bodies, compliance with quality management standards and metrological requirements need not be demonstrated. The reported results revealed that, in particular, for participants who used factory calibration, the attributed measurement uncertainties were not consistent with the deviation from the collective average. It is shown below that this has consequences for the use of these results in the assessment of the interlaboratory comparison. Figure 1shows the ratios Ri representing the radon activity concentrations as measured by the participants in relation to the corresponding readings of the comparison device Int. J. Environ. Res. Public Health 2021,18, 12150 7 of 15 according to Equation (1). The error bars represent the standard uncertainties according to Equation (2). The results from participants who traced back their measurements using factory calibration are not included in Figure 1. Int. J. Environ. Res. Public Health 2021, 18, x FOR PEER REVIEW 7 of 16 3. Results 3.1. Laboratory Reference Devices and the Compilation of the Results Most participants used an AlphaGUARD-type device as the laboratory reference instrument for the radon activity concentrations. Two of these participants additionally performed measurements with scintillation chambers. The ATMOS 12DPX was utilized by two participants and a Radon Scout by one participant. AlphaGUARD and ATMOS use ionization chambers (singleor multi-wire) for radiation detection. The Radon Scout deploys high-voltage enhancement and alpha pulse counting using a semiconductor detector. Unlike AlphaGUARD and Radon Scout, which operate in diffusion mode, the ATMOS-type device operates in flow-through mode. The vast majority of the participants were able to show the metrological traceability of the quantity through an unbroken chain of calibrations at recognized bodies. Two participants traced their measurements back through factory calibration. Factory calibration is a service from the manufacturer that provides the instrument with an initial calibration before delivery. Although the manufacturers also trace their measurements back to recognized bodies, compliance with quality management standards and metrological requirements need not be demonstrated. The reported results revealed that, in particular, for participants who used factory calibration, the attributed measurement uncertainties were not consistent with the deviation from the collective average. It is shown below that this has consequences for the use of these results in the assessment of the interlaboratory comparison. Figure 1 shows the ratios 𝑅 representing the radon activity concentrations as measured by the participants in relation to the corresponding readings of the comparison device according to Equation (1). The error bars represent the standard uncertainties according to Equation (2). The results from participants who traced back their measurements using factory calibration are not included in Figure 1. 380 400 420 440 RnC measured by participant in relation to the indication of comparison device R i 0.85 0.90 0.95 1.00 1.05 1.10 1.15 900 1000 1100 5500 6000 65002000 4000 8800 9000 Radon activity concentration as indicated by the comparison device (Bq/m 3 ) Figure 1. Ratio 𝑅 of the mean radon activity concentration (RnC) that was determined by each participant to that of the comparison device given for the different exposures; error bars indicate the standard uncertainties of the reported values, results of the same participant are indicated by the same color, blue straight lines indicate the uncertainty-weighted average ratio 𝑅 and dashed blue lines cover the range of the standard uncertainty. Figure 1. Ratio Ri of the mean radon activity concentration (RnC) that was determined by each participant to that of the comparison device given for the different exposures; error bars indicate the standard uncertainties of the reported values, results of the same participant are indicated by the same color, blue straight lines indicate the uncertainty-weighted average ratio Rwand dashed blue lines cover the range of the standard uncertainty. 3.2. Consistency Check A check of mutual consistency is required for interlaboratory comparisons using the BIPM consultative committee CCQM [ 5 ] to test the hypothesis that the participants have a collective mean value and that the deviations from this value are normally distributed. The consistency check is performed using a chi-squared test over the number of n measurements (or participants). The observed test parameter χ2 obs is calculated using χ2 obs = n ∑ i=1Ri−Rw ui2 (8) According to CCQM [ 5 ], the test parameter is compared with the quantile of the chi-squared distribution for the significance level 1 −α with α= 0.05. The following decisions have to be made: 1. If χ2 obs <n− 1, the results are mutually consistent and the uncertainties account fully for the observed dispersion of the values; 2. If n− 1 ≤χ2 obs <χ2 0.05;n−1 , the data provide no strong evidence that the reported uncertainties are inappropriate, but there remains a risk that additional factors are contributing to the dispersion; 3. If χ2 obs >χ2 0.05;n−1, the data should be considered as mutually inconsistent. The results of the consistency checks are summarized in Table 3. The tests were performed for each exposure level and for the complete data set of all levels including singular exposures. The two participants who traced their measurements back through factory calibration are not included in the results of the consistency check. Int. J. Environ. Res. Public Health 2021,18, 12150 8 of 15 Table 3. Chi-squared consistency check for the different radon levels and for all levels. Exposure Level No. of Measurements n χ2 obs (Observed) χ2 0.05;n−1 (Tabulated) 400 Bq/m310 10.45 16.92 1000 Bq/m311 5.49 18.31 6000 Bq/m310 5.16 16.92 All levels including singular exposures 36 25.17 49.80 Table 3shows that for each exposure level, the observed test parameter was below the tabulated value χ2 0.05;n−1 . Therefore, the conclusion can be drawn that the results were mutually consistent. There was no evidence of significant inconsistencies for each of the individual radon levels and the overall exposure range. The uncertainties fully accounted for the observed dispersion of the values. For the radon level of 400 Bq/m 3 , the test parameter was greater than n− 1 at the stated significance level. The higher value of the observed test parameter was caused by results that showed increased deviations from the average ratio without a corresponding uncertainty being assigned to them. In these cases, the uncertainties that were attributed by some participants might have been too small for the observed deviation from the mean value. The presented consistency of the data set failed when the results of the two participants who traced their measurements back through factory calibration were included in the data set. To ensure the consistency of the data set and to maintain the degree of representativeness of the intercomparison, the data from the two participants were not included in the derivation of the average ratio and, thus, the comparison reference value. The coordinator (from BfS) was also not considered further due to his special position as part of the supervising laboratory. 3.3. The Uncertainty-Weighted Average Ratio Table 4shows the uncertainty-weighted average ratio Rw for the different exposure levels. Rw is calculated according to Equation (5). The square root of the variance from Equation (7) is the standard uncertainty u(Rw) . The values of the average ratio obtained for the various exposure levels agreed very well, taking into account the standard uncertainties. Table 4. Uncertainty-weighted average ratio and its standard uncertainty for the different exposure levels. Exposure Level Uncertainty-Weighted Average Ratio Rw Standard Uncertainty Associated with Rw u(Rw) 400 Bq/m31.018 10.010 1000 Bq/m31.021 10.009 6000 Bq/m31.012 10.007 6000 Bq/m 3 including singular exposures 1.015 0.004 All levels including singular exposures 1.016 0.003 1Indicated by the blue straight lines in Figure 1. Assuming that the comparison device represents the weighted collective average radon activity concentration for each exposure level, the average ratio would be compensated, resulting in Rw= 1. However, the calculated values for Rw showed a bias of about 1.5% above the expected compensation value. The bias was caused by the comparison device due to the calibration of the device at the coordinator’s facility and indicated the coordinator’s deviation in the measurement of the quantity from the collective mean. The measurements of the comparison device were, on average, 1.5% lower than the weighted average radon activity concentration that was measured by the participants for the respective exposure level. It was observed that the average ratio Rw varied only slightly for the Int. J. Environ. Res. Public Health 2021,18, 12150 9 of 15 different exposure levels, confirming the performance and stability of the comparative measurements. 4. Discussion 4.1. The Key Comparison Reference Value and the Dispersion of Measurement Values The key comparison reference value (KCRV) is the value of the quantity representing the specific property of the material under consideration [ 5 ]. The specific property that was under consideration in this interlaboratory comparison was the activity concentration of radon in air. However, the single radon activity concentrations in the atmospheres that were measured at participants’ facilities differed between participants. Moreover, three different main levels of radon activity concentration were measured by each participant, covering a large range over more than one magnitude. The comparison device that was provided by the coordinator was used as a comparator to normalize the different radon activity concentrations that were established by the participants and thus allowed for comparability of the respective measurements of the quantities. As the comparison device is characterized by an indication, which is verifiably linear over the entire range, the comparison of the different radon activity concentrations found in the participant’s facilities was made possible by their ratio to the indication of the comparison device, as is given by Equation (1). The average ratio Rw , which can be deemed to be the KCRV, was calculated from the single ratios according to Equation (5). The consequences were as follows: 1. The observed Rw had a bias of about 1.5% (Table 4) compared to the expected value of Rw= 1, which would result if the comparison device were to represent the uncertainty-weighted collective mean radon activity concentration and, thus, all individual deviations were compensated. 2. The variance of Rw that was calculated using Equation (7) led to the small values for u(Rw) given in Table 4. As was also shown in other studies [ 6 – 8 ], the reciprocal square root of the sum of the weights becomes too small with an increasing number of participants such that many laboratories fall outside the uncertainty interval. It is therefore assumed that this parameter is not an appropriate measure of the degree of agreement between the participants. To overcome the disadvantages in terms of Rw and also to eliminate the impact of the comparison device, a modified ratio, namely, R∗ i, for the ith participant is formed by R∗ i=Ri Rw(9) The rationale behind this modified ratio, now considered as a new comparison value, is that the expectation value ER∗ i that is obtained from the weighted sum over each participant is equal to 1: E(R∗ i)= n ∑ i=1 wiR∗ i=1 Rw n ∑ i=1 wiRi=1 (10) The weights wi are given by Equation (6). Equation (10) implies that the values R∗ i are distributed around the common mean. Of particular importance for the results of the comparison is the mean square deviation of the participants: σ2= n ∑ i=1 wi(R∗ i−1)2= n ∑ i=1 wiR∗ i 2−2R∗ i+1= n ∑ i=1 wiR∗ i 2−1 (11)